Wikipǣdia angwiki https://ang.wikipedia.org/wiki/Heafodtramet MediaWiki 1.43.0-wmf.2 first-letter Media Syndrig Mōtung Brūcend Brūcendmōtung Wikipǣdia Wikipǣdiamōtung Ymele Ymelmōtung MediaWiki MediaWikimōtung Bysen Bysenmōtung Help Helpmōtung Flocc Floccmōtung TimedText TimedText talk Module Module talk 4 2875 216081 210588 2024-04-25T16:32:06Z 81.108.220.146 wikitext text/x-wiki Stycce is niƿē and smæl geƿrit. Þæt mǣste dǣl stycca cann ēacan. {{stycce}} k08lcngu17djyna1jlcqykjnr4txqcv 4 5784 216085 215659 2024-04-25T20:20:04Z MediaWiki message delivery 57034 /* Vote now to select members of the first U4C */ new section wikitext text/x-wiki {{/Head}} {{Brūcend:MABot/config |archive = Wikipǣdia:Se Þorpes Wella/%(year)s |algo = old(30d) |counter = 1 |archiveheader = |minthreadstoarchive = 1 |minthreadsleft = 2 }} == <span lang="en" dir="ltr" class="mw-content-ltr"> Wikimedia Foundation Board of Trustees 2024 Selection</span> == <div lang="en" dir="ltr" class="mw-content-ltr"> <section begin="announcement-content" /> : ''[[m:Special:MyLanguage/Wikimedia Foundation elections/2024/Announcement/Selection announcement| You can find this message translated into additional languages on Meta-wiki.]]'' : ''<div class="plainlinks">[[m:Special:MyLanguage/Wikimedia Foundation elections/2024/Announcement/Selection announcement|{{int:interlanguage-link-mul}}]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&group=page-{{urlencode:Wikimedia Foundation elections/2024/Announcement/Selection announcement}}&language=&action=page&filter= {{int:please-translate}}]</div>'' Dear all, This year, the term of 4 (four) Community- and Affiliate-selected Trustees on the Wikimedia Foundation Board of Trustees will come to an end [1]. The Board invites the whole movement to participate in this year’s selection process and vote to fill those seats. The [[m:Special:MyLanguage/Wikimedia Foundation elections committee|Elections Committee]] will oversee this process with support from Foundation staff [2]. The Board Governance Committee created a Board Selection Working Group from Trustees who cannot be candidates in the 2024 community- and affiliate-selected trustee selection process composed of Dariusz Jemielniak, Nataliia Tymkiv, Esra'a Al Shafei, Kathy Collins, and Shani Evenstein Sigalov [3]. The group is tasked with providing Board oversight for the 2024 trustee selection process, and for keeping the Board informed. More details on the roles of the Elections Committee, Board, and staff are here [4]. Here are the key planned dates: * May 2024: Call for candidates and call for questions * June 2024: Affiliates vote to shortlist 12 candidates (no shortlisting if 15 or less candidates apply) [5] * June-August 2024: Campaign period * End of August / beginning of September 2024: Two-week community voting period * October–November 2024: Background check of selected candidates * Board's Meeting in December 2024: New trustees seated Learn more about the 2024 selection process - including the detailed timeline, the candidacy process, the campaign rules, and the voter eligibility criteria - on [[m:Special:MyLanguage/Wikimedia Foundation elections/2024|this Meta-wiki page]], and make your plan. '''Election Volunteers''' Another way to be involved with the 2024 selection process is to be an Election Volunteer. Election Volunteers are a bridge between the Elections Committee and their respective community. They help ensure their community is represented and mobilize them to vote. Learn more about the program and how to join on this [[m:Special:MyLanguage/Wikimedia Foundation elections/2024/Election Volunteers|Meta-wiki page]]. Best regards, [[m:Special:MyLanguage/User:Pundit|Dariusz Jemielniak]] (Governance Committee Chair, Board Selection Working Group) [1] https://meta.wikimedia.org/wiki/Special:MyLanguage/Wikimedia_Foundation_elections/2021/Results#Elected [2] https://foundation.wikimedia.org/wiki/Committee:Elections_Committee_Charter [3] https://foundation.wikimedia.org/wiki/Minutes:2023-08-15#Governance_Committee [4] https://meta.wikimedia.org/wiki/Wikimedia_Foundation_elections_committee/Roles [5] Even though the ideal number is 12 candidates for 4 open seats, the shortlisting process will be triggered if there are more than 15 candidates because the 1-3 candidates that are removed might feel ostracized and it would be a lot of work for affiliates to carry out the shortlisting process to only eliminate 1-3 candidates from the candidate list.<section end="announcement-content" /> </div> [[User:MPossoupe_(WMF)|MPossoupe_(WMF)]]19:56, 12 Hreðmonað 2024 (UTC) <!-- Message sent by User:MPossoupe (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&oldid=26349432 --> == <span lang="en" dir="ltr" class="mw-content-ltr">Your wiki will be in read-only soon</span> == <div lang="en" dir="ltr" class="mw-content-ltr"> <section begin="server-switch"/><div class="plainlinks"> [[:m:Special:MyLanguage/Tech/Server switch|Read this message in another language]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&group=page-Tech%2FServer+switch&language=&action=page&filter= {{int:please-translate}}] The [[foundation:|Wikimedia Foundation]] will switch the traffic between its data centers. This will make sure that Wikipedia and the other Wikimedia wikis can stay online even after a disaster. All traffic will switch on '''{{#time:j xg|2024-03-20|en}}'''. The test will start at '''[https://zonestamp.toolforge.org/{{#time:U|2024-03-20T14:00|en}} {{#time:H:i e|2024-03-20T14:00}}]'''. Unfortunately, because of some limitations in [[mw:Special:MyLanguage/Manual:What is MediaWiki?|MediaWiki]], all editing must stop while the switch is made. We apologize for this disruption, and we are working to minimize it in the future. '''You will be able to read, but not edit, all wikis for a short period of time.''' *You will not be able to edit for up to an hour on {{#time:l j xg Y|2024-03-20|en}}. *If you try to edit or save during these times, you will see an error message. We hope that no edits will be lost during these minutes, but we can't guarantee it. If you see the error message, then please wait until everything is back to normal. Then you should be able to save your edit. But, we recommend that you make a copy of your changes first, just in case. ''Other effects'': *Background jobs will be slower and some may be dropped. Red links might not be updated as quickly as normal. If you create an article that is already linked somewhere else, the link will stay red longer than usual. Some long-running scripts will have to be stopped. * We expect the code deployments to happen as any other week. However, some case-by-case code freezes could punctually happen if the operation require them afterwards. * [[mw:Special:MyLanguage/GitLab|GitLab]] will be unavailable for about 90 minutes. This project may be postponed if necessary. You can [[wikitech:Switch_Datacenter|read the schedule at wikitech.wikimedia.org]]. Any changes will be announced in the schedule. There will be more notifications about this. A banner will be displayed on all wikis 30 minutes before this operation happens. '''Please share this information with your community.'''</div><section end="server-switch"/> </div> [[user:Trizek (WMF)|Trizek (WMF)]], 00:00, 15 Hreðmonað 2024 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Non-Technical_Village_Pumps_distribution_list&oldid=25636619 --> == <span lang="en" dir="ltr" class="mw-content-ltr">Vote now to select members of the first U4C</span> == <div lang="en" dir="ltr" class="mw-content-ltr"> <section begin="announcement-content" /> :''[[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024/Announcement – vote opens|You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&group=page-{{urlencode:Universal Code of Conduct/Coordinating Committee/Election/2024/Announcement – vote opens}}&language=&action=page&filter= {{int:please-translate}}]'' Dear all, I am writing to you to let you know the voting period for the Universal Code of Conduct Coordinating Committee (U4C) is open now through May 9, 2024. Read the information on the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024|voting page on Meta-wiki]] to learn more about voting and voter eligibility. The Universal Code of Conduct Coordinating Committee (U4C) is a global group dedicated to providing an equitable and consistent implementation of the UCoC. Community members were invited to submit their applications for the U4C. For more information and the responsibilities of the U4C, please [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Charter|review the U4C Charter]]. Please share this message with members of your community so they can participate as well. On behalf of the UCoC project team,<section end="announcement-content" /> </div> [[m:User:RamzyM (WMF)|RamzyM (WMF)]] 20:20, 25 Eastermonað 2024 (UTC) <!-- Message sent by User:RamzyM (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&oldid=26390244 --> cnql8yugxwtr37cm40ccveg8lfyo9rf 216087 216085 2024-04-26T02:38:43Z MABot 82184 Bot: Archiving 1 thread (older than 30 days) to [[Wikipǣdia:Se Þorpes Wella/2024]] wikitext text/x-wiki {{/Head}} {{Brūcend:MABot/config |archive = Wikipǣdia:Se Þorpes Wella/%(year)s |algo = old(30d) |counter = 1 |archiveheader = |minthreadstoarchive = 1 |minthreadsleft = 2 }} == <span lang="en" dir="ltr" class="mw-content-ltr">Your wiki will be in read-only soon</span> == <div lang="en" dir="ltr" class="mw-content-ltr"> <section begin="server-switch"/><div class="plainlinks"> [[:m:Special:MyLanguage/Tech/Server switch|Read this message in another language]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&group=page-Tech%2FServer+switch&language=&action=page&filter= {{int:please-translate}}] The [[foundation:|Wikimedia Foundation]] will switch the traffic between its data centers. This will make sure that Wikipedia and the other Wikimedia wikis can stay online even after a disaster. All traffic will switch on '''{{#time:j xg|2024-03-20|en}}'''. The test will start at '''[https://zonestamp.toolforge.org/{{#time:U|2024-03-20T14:00|en}} {{#time:H:i e|2024-03-20T14:00}}]'''. Unfortunately, because of some limitations in [[mw:Special:MyLanguage/Manual:What is MediaWiki?|MediaWiki]], all editing must stop while the switch is made. We apologize for this disruption, and we are working to minimize it in the future. '''You will be able to read, but not edit, all wikis for a short period of time.''' *You will not be able to edit for up to an hour on {{#time:l j xg Y|2024-03-20|en}}. *If you try to edit or save during these times, you will see an error message. We hope that no edits will be lost during these minutes, but we can't guarantee it. If you see the error message, then please wait until everything is back to normal. Then you should be able to save your edit. But, we recommend that you make a copy of your changes first, just in case. ''Other effects'': *Background jobs will be slower and some may be dropped. Red links might not be updated as quickly as normal. If you create an article that is already linked somewhere else, the link will stay red longer than usual. Some long-running scripts will have to be stopped. * We expect the code deployments to happen as any other week. However, some case-by-case code freezes could punctually happen if the operation require them afterwards. * [[mw:Special:MyLanguage/GitLab|GitLab]] will be unavailable for about 90 minutes. This project may be postponed if necessary. You can [[wikitech:Switch_Datacenter|read the schedule at wikitech.wikimedia.org]]. Any changes will be announced in the schedule. There will be more notifications about this. A banner will be displayed on all wikis 30 minutes before this operation happens. '''Please share this information with your community.'''</div><section end="server-switch"/> </div> [[user:Trizek (WMF)|Trizek (WMF)]], 00:00, 15 Hreðmonað 2024 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Non-Technical_Village_Pumps_distribution_list&oldid=25636619 --> == <span lang="en" dir="ltr" class="mw-content-ltr">Vote now to select members of the first U4C</span> == <div lang="en" dir="ltr" class="mw-content-ltr"> <section begin="announcement-content" /> :''[[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024/Announcement – vote opens|You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&group=page-{{urlencode:Universal Code of Conduct/Coordinating Committee/Election/2024/Announcement – vote opens}}&language=&action=page&filter= {{int:please-translate}}]'' Dear all, I am writing to you to let you know the voting period for the Universal Code of Conduct Coordinating Committee (U4C) is open now through May 9, 2024. Read the information on the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024|voting page on Meta-wiki]] to learn more about voting and voter eligibility. The Universal Code of Conduct Coordinating Committee (U4C) is a global group dedicated to providing an equitable and consistent implementation of the UCoC. Community members were invited to submit their applications for the U4C. For more information and the responsibilities of the U4C, please [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Charter|review the U4C Charter]]. Please share this message with members of your community so they can participate as well. On behalf of the UCoC project team,<section end="announcement-content" /> </div> [[m:User:RamzyM (WMF)|RamzyM (WMF)]] 20:20, 25 Eastermonað 2024 (UTC) <!-- Message sent by User:RamzyM (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&oldid=26390244 --> luq75cfxxb3kbbrzmmsdcoxqilxnksw 0 23398 216091 215102 2024-04-26T05:05:29Z Rylesbourne 125148 Redirected page to [[Lāsfægas]] wikitext text/x-wiki #REDIRECT [[Lāsfægas]] mrh7nsajx94q3iz7c023p62dq6kv2x2 10 23532 216101 214153 2024-04-26T05:19:22Z Rylesbourne 125148 wikitext text/x-wiki {{Infobox |name = California |bodystyle = font-size:90%; width:100% |abovestyle = background:#ccccff; font-size:118%; |above = [[California]] [[File:Flag_of_California.svg|25px]] |labelstyle = background:#ddddff; width:10%; text-align:right |label1 = Hēafodstōl |data1 = [[Hālgþingstede]] |label2 = Grēatbyrig <!--Top 10 most populated cities --> |data2 = [[Lōsandgelis]] <!-- Los Angeles --> {{•w}}[[Hālgadidacus]] <!-- San Diego--> • [[Hālgafrancis]] <!-- San Francisco --> • [[Hālgaiosep, Californie|Hālgaiosep]] <!-- San Jose --> • [[Asċetrēow]] <!-- Fresno--> • [[Hālgþingstede]] <!-- Sacramento--> • [[Langstrond]] <!-- Long Beach --> • [[Ǣcland]] <!-- Oakland --> • [[Bæceresfeld]] <!-- Bakersfield --> • [[Anahām]] <!-- Anaheim --> {{div col end}} |label3 = Middlebyrig |data3 = [[Stocctūn (Californie)|Stocctūn]]<!--Stockton--> • [[Ēasċora (Californie)|Ēasċora]] • [[Sanctanne, Californie|Sanctanne]]<!--Santa Ana--> • [[Īrfine]]<!--Irvine--> • [[Ēamfullegesiht]]<!--Chula Vista--> • [[Frēonmund (Californie)|Frēonmund]]<!--Fremont--> • Santa Clarita • [[Hālgabernhard]]<!--San Bernardino--> • [[Mahdesto (Californie)|Mahdesto]]<!--Modesto--> • Moreno Valley • Fontana • [[Oxnanardu]]<!--Oxnard--> • [[Huntenabeċe]]<!--Huntington Beach--> • [[Glenndæl (Californie)|Glenndæl]]<!--Glendale--> • Santa Rosa • Elk Grove • Ontario • [[Rancocucamanga]]<!--Rancho Cucamonga--> • [[Gārsecgasīde (Californie)|Gārsecgasīde]]<!--Oceanside--> • [[Lonċeaster (Californie)|Lonċeaster]]<!--Lancaster--> • Garden Grove • [[Palmadæl (Californie)|Palmadæl]]<!--Palmdale--> • Salinas • Hayward • Corona • [[Sunniedæl (Californie)|Sunniedæl]]<!--Sunnyvale--> • Pomona • Escondido • Roseville • Torrance • [[Fullertūn (Californie)|Fullertūn]]<!--Fullerton--> • Visalia • Orange • Pasadena • [[Ficturburh (Californie)|Ficturburh]]<!--Victorville--> • Santa Clara • [[Þūsendǣċen]]<!--Thousand Oaks--> • [[Sīmidene]]<!--Simi Valley--> • [[Uælgio (Californie)|Uælgio]]<!--Vallejo--> • Concord • Berkeley • Clovis • [[Fægerfeld (Californie)|Fægerfeld]]<!--Fairfield--> • [[Rīċemund (Californie)|Rīċemund]]<!--Richmond--> • Anitoch • [[Carlsbæd (Californie)|Carlsbæd]]<!--Carlsbad--> • [[Dūneg (Californie)|Dūneg]]<!--Downey--> • Costa Mesa • Murrieta • [[Fennturra (Californie)|Fennturra]]<!--Ventura--> • [[Tæmemeculla]]<!--Temecula--> • West Covina • El Monte • Inglewood • Burbank • El Cajon • San Mateo • Jurupa Valley • Daly City • Rialto • [[Norwealcan (Californie)|Norwealcan]]<!--Norwalk--> • Menifee • [[Faccabyrg]]<!--Vacaville--> • Chico {{div col end}} <!-- |label4 = Smælbyrig |data4 = Hesperia • Vista • Compton • Carson • San Marcos • Mission Viejo • Redding • Santa Monica • Tracy • South Gate • Chino • San Leandro • Westminster • Hemet • Santa Barbara • Hawthorne • Livermore • Citrus Heights • Whittier • Merced • Lake Forest • Newport Beach • San Ramon • Redwood City • Buena Park • Manteca • Alhambra • Lakewood • Mountain View • Folsom • [[Tūstin]] • Milpitas • Pleasanton • Rancho Cordova • Napa • Bellflower • Upland • Perris • Chino Hills • Alameda • Pittsburg • Apple Valley {{div col end}} <!-- |label5 = Oþþebyrig |data5 = Yuba City • Madera • Santa Cruz • San Rafael • Woodland • Hanford • San Luis Obispo • El Centro • Hollister • Martinez • Eureka • Oroville • Susanville • Ukiah • Red Bluff • Auburn • Marysville • Placerville • Yreka • Crescent City • Colusa • Willows • Lakeport • Jackson • Sonora • Nevada City • Alturas |label6 = Scīra |data6 = [[Accomæcsċīr|Accomæc]] • AlamedaAlpineAmadorButteCalaverasColusaContra CostaDel NorteEl DoradoFresnoGlennHumboldtImperialInyoKernKingsLakeLassenLos AngelesMaderaMarinMariposaMendocinoMercedModocMonoMontereyNapaNevadaOrangePlacerPlumasRiversideSacramentoSan BenitoSan BernardinoSan DiegoSan FranciscoSan JoaquinSan Luis ObispoSan MateoSanta BarbaraSanta ClaraSanta CruzShastaSierraSiskiyouSolanoSonomaStanislausSutterTehamaTrinityTulareTuolumneVenturaYoloYuba {{div col end}} |label7 = Regyounes |data7 = Antelope Valley • Big Sur • California Coast Ranges • Cascade Range • Central California • Central Coast • Central Valley • Channel Islands • Coachella Valley • Coastal California • Conejo Valley • Cucamonga Valley • Death Valley • East Bay (SF Bay Area) • East County (SD) • Eastern California • Emerald Triangle • Gold Country • Great Basin • Greater San Bernardino • Inland Empire • Klamath Basin • Lake Tahoe • Greater Los Angeles • Los Angeles Basin • Lost Coast • Mojave Desert • Mountain Empire • North Bay (SF) • North Coast • North County (SD) • Northern California • Orange Coast • Owens Valley • Oxnard Plain • Peninsular Ranges • Pomona Valley • Sacramento–San Joaquin River Delta • Sacramento Valley • Saddleback Valley • Salinas Valley • San Fernando Valley • San Francisco Bay Area • San Francisco Peninsula • San Gabriel Valley • San Joaquin Valley • Santa Clara Valley • Santa Clara River Valley • Santa Clarita Valley • Santa Ynez Valley • Shasta Cascade • Sierra Nevada • Silicon Valley • South Bay (LA) • South Bay (SD) • South Bay (SF) • South Coast • Southern Border Region • Southern California • Transverse Ranges • Tri-Valley • Victor Valley • Wine Country {{div col end}} --> |belowstyle = }}<noinclude> {{collapsible option}} [[Flocc:California|τ]] </noinclude> <!-- Stockton - Stoccbyrig Riverside - Flōdstrēam Santa Ana - Sancta Ana Īrfine - Īrfine Chula Vista - Cēapbyrig Fremont - Frēamūnt Santa Clarita - Sancta Clarita San Bernardino - Sanctus Bernardino Modesto - Modestō Moreno Valley - Morēa Gēafol Fontana - Fontana Oxnard - Oxnard Huntington Beach - Huntungatūn Strond Glendale - Glendale Santa Rosa - Sancta Rōsa Elk Grove - Elc Grōf Ontario - Ontario Rancho Cucamonga - Ranc Cucamangum Oceanside - Sǣstrond Lancaster - Lancaestre Garden Grove - Gerdan Grōf Palmdale - Palmdalu Salinas - Sǣlīnas Hayward - Hēaward Corona - Corona Sunnyvale - Sunegfeald Pomona - Pomona Escondido - Escondido Roseville - Rōsebyrig Torrance - Torrence Fullerton - Fullertūn Visalia - Visalia Orange - Orange Pasadena - Pasadena Santa Clara - Sancta Clara Concord - Concōrd Berkeley - Bercelēah Clovis - Clōfes Fairfield - Fægrefeld Richmond - Rīcmund Antioch - Antioche Carlsbad - Carlsbæd Downey - Dūneg Costa Mesa - Costabyrig Murrieta - Murrieta Ventura - Ventura Temecula - Tēmeceola West Covina - West Cōfan El Monte - Ēl Munt Inglewood - Inglewudu Burbank - Burgabanc El Cajon - Ēl Cājon San Mateo - Sanctus Mātēus Jurupa Valley - Iurupa Strond Daly City - Dālig Ċēastre Rialto - Rīaltūn Norwalk - Norwælce Menifee - Menifee Vacaville - Wæcfeld Chico - Ċicestere --> 9smb888akvx5sscka2xk0yqo7d7sifd 10 23617 216084 215325 2024-04-25T18:07:07Z Rylesbourne 125148 wikitext text/x-wiki {{Infobox |name = USPopulusCities |bodystyle = font-size:90%; width:100% |abovestyle = background:#ccccff; font-size:118%; |labelstyle = background:#ddddff; width:10%; text-align:right |above = 100 mæstenbyrig on [[Geanedan Ricu America]] |label1 = |data1 = [[Niweoforwicburg|Niƿeoforƿicburg]] • [[Lōsandgelis]] • [[Cicēa]] • [[Hūsestūn]] • [[Fēonix (Ārrisona)|Fēonix]] • [[Broþorlufeburh]] • [[Hālgantōnius]] • [[Dællas]] • [[Hālgadidacus]] • [[Ēastūnburh]] • [[Iǣxcūnbyrg]] • [[Hālgaiosep, Californie|Hālgaiosep]] • [[Weorthwīc|Ƿeorthƿīc]]<!--Fort Worth--> • [[Columbus (Ohio)|Columbus]] • [[Ceorlette (Norþcarolīna)|Ceorlette]] • [[Indigabyrg]] • [[Hālgafrancis]] • [[Sīatl]] • [[Denaford]] • [[Oclahomaceaster]] • [[Gnashburh]] • [[Þafæþm]]<!--El Paso--> • [[Hwæsingatun, D.C.|Hƿæsingatun]] • [[Lāsuēagas]] • [[Botwulfstūn|Botƿulfstūn]] • [[Portlond (Orēgūn)|Portlond]] • [[Luisburg (Centuccīg)|Luisburg]] • [[Memfis (Tennesīeg)|Memfis]] • [[Dēotford]] • [[Bealdimōr]] • [[Mylenwic|Mylenƿic]]<!--Milwaukee--> • [[Ælbūrcerrce]] • [[Tūsōn]] • [[Asċetrēow|Asċetrēoƿ]] • [[Hālgþingstede]] • [[Tabulehyll, Ārrisona|Tabulehyll]]<!--Mesa, AZ--> • [[Cǣnsasburg (Misseōra)|Cǣnsasburg]] • [[Ætlanda]] • [[Coloradespryngs]] • [[Ōmahha]] • [[Raleah]] • [[Firginiestrond]] • [[Langstrond]] • [[Mīamig]] • [[Ǣcland]] • [[Minnegceaster]] • [[Tulse]] • [[Bæceresfeld]] • [[Tampa]] • [[Hwīcite|Hƿīcite]]<!--Wichita--> • [[Ælfrēdingtūn, Tēahsas|Ælfrēdingtūn]] • [[Eostrabyrg]] • [[Niwēorlēanas|Niƿēorlēanas]] • [[Clēafaland]] • [[Anahām]] • [[Hānolūlu]] • [[Heanricson (Gnefada)|Heanricson]] • [[Stocctūn (Californie)|Stocctūn]] • [[Ēasċora (Californie)|Ēasċora]] • [[Leaxingatūn (Centuccīg)|Leaxingatūn]] • [[Cristbodiġ]]<!--Corpus Christi--> • [[Orlando]] • [[Īrfine]] • [[Sinsignātig]] • [[Sanctanne, Californie|Sanctanne]] • [[Niweweorche (Nīwe Cēsarēa)|Niƿeƿeorche]] • [[Hālgapaulus (Minesohta)|Hālgapaulus]] • [[Pyttesburh]] • [[Grœnesburh]] • [[Lincoln (Gnebrāsca)|Lincoln]] • [[Dūnholm (Norþcarolīna)|Dūnholm]] • [[Pleyno (Tēahsas)|Pleyno]] • [[Ancoredage]] • [[Cēsarēaceaster]] • [[Hālgaluis]] • [[Candyller (Arizona)|Candyller]] • [[Norþlāsuēagas]] • [[Ēamfullegesiht]] <!--Chula Vista--> • [[Būfalō (Nīwe Eoforwīc)|Būfalō]] • [[Gīlbeorht (Arizona)|Gīlbeorht]] •<!--resume here--> [[Hrēnō (Gnefada)|Hrēnō]] • [[Mædison (Wiscōnsēn)|Mædison]] • [[Wyrhtwægnwīc|Ƿyrhtƿægnƿīc]]<!--Fort Wayne--> • [[Tolēodo (Ohio)|Tolēodo]] • [[Lubbeċ]] • [[Sanctes Petresburg (Florida)|Sanctes Petresburg]] • [[Larēodo (Tēahsas)|Larēodo]] • [[Irfig (Tēahsas)|Irfig]] • [[Ceosapēac (Firginiæ)|Ceosapēac]] • [[Glenndæl (Arizona)|Glenndæl]] • [[Winestānsǣlham|Ƿinestānsǣlham]] • [[Scottesdæl (Arizona)|Scottesdæl]] • [[Gærland (Tēahsas)|Gærland]] • [[Boise|Bōisē]] • [[Norþfolc (Firginiæ)|Norþfolc]] • [[Portsanctlucius (Florida)|Portsanctlucius]] • [[Spocāne (Hwæsingatun)|Spocāne]] • [[Rīċemund, Firginiæ|Rīċemund]] • [[Frēomund (Californie)|Frēomund]] • [[Huntanbyrig (Alabama)|Huntanbyrg]]</li> </ol> | below = Cities ranked by [[United States Census Bureau]] population estimates for July 1, 2022. }}<noinclude> {{collapsible option}} [[Category:Largest cities of the United States templates|Populous]] [[Category:United States city navigational boxes|Cities, Populous]] </noinclude> 2h58q92onshez88spo1vlq6jje5jz3r 216094 216084 2024-04-26T05:06:53Z Rylesbourne 125148 wikitext text/x-wiki {{Infobox |name = USPopulusCities |bodystyle = font-size:90%; width:100% |abovestyle = background:#ccccff; font-size:118%; |labelstyle = background:#ddddff; width:10%; text-align:right |above = 100 mæstenbyrig on [[Geanedan Ricu America]] |label1 = |data1 = [[Niweoforwicburg|Niƿeoforƿicburg]] • [[Lōsandgelis]] • [[Cicēa]] • [[Hūsestūn]] • [[Fēonix (Ārrisona)|Fēonix]] • [[Broþorlufeburh]] • [[Hālgantōnius]] • [[Dællas]] • [[Hālgadidacus]] • [[Ēastūnburh]] • [[Iǣxcūnbyrg]] • [[Hālgaiosep, Californie|Hālgaiosep]] • [[Weorthwīc|Ƿeorthƿīc]]<!--Fort Worth--> • [[Columbus (Ohio)|Columbus]] • [[Ceorlette (Norþcarolīna)|Ceorlette]] • [[Indigabyrg]] • [[Hālgafrancis]] • [[Sīatl]] • [[Denaford]] • [[Oclahomaceaster]] • [[Gnashburh]] • [[Þafæþm]]<!--El Paso--> • [[Hwæsingatun, D.C.|Hƿæsingatun]] • [[Lāsfægas]] • [[Botwulfstūn|Botƿulfstūn]] • [[Portlond (Orēgūn)|Portlond]] • [[Luisburg (Centuccīg)|Luisburg]] • [[Memfis (Tennesīeg)|Memfis]] • [[Dēotford]] • [[Bealdimōr]] • [[Mylenwic|Mylenƿic]]<!--Milwaukee--> • [[Ælbūrcerrce]] • [[Tūsōn]] • [[Asċetrēow|Asċetrēoƿ]] • [[Hālgþingstede]] • [[Tabulehyll, Ārrisona|Tabulehyll]]<!--Mesa, AZ--> • [[Cǣnsasburg (Misseōra)|Cǣnsasburg]] • [[Ætlanda]] • [[Coloradespryngs]] • [[Ōmahha]] • [[Raleah]] • [[Firginiestrond]] • [[Langstrond]] • [[Mīamig]] • [[Ǣcland]] • [[Minnegceaster]] • [[Tulse]] • [[Bæceresfeld]] • [[Tampa]] • [[Hwīcite|Hƿīcite]]<!--Wichita--> • [[Ælfrēdingtūn, Tēahsas|Ælfrēdingtūn]] • [[Eostrabyrg]] • [[Niwēorlēanas|Niƿēorlēanas]] • [[Clēafaland]] • [[Anahām]] • [[Hānolūlu]] • [[Heanricson (Gnefada)|Heanricson]] • [[Stocctūn (Californie)|Stocctūn]] • [[Ēasċora (Californie)|Ēasċora]] • [[Leaxingatūn (Centuccīg)|Leaxingatūn]] • [[Cristbodiġ]]<!--Corpus Christi--> • [[Orlando]] • [[Īrfine]] • [[Sinsignātig]] • [[Sanctanne, Californie|Sanctanne]] • [[Niweweorche (Nīwe Cēsarēa)|Niƿeƿeorche]] • [[Hālgapaulus (Minesohta)|Hālgapaulus]] • [[Pyttesburh]] • [[Grœnesburh]] • [[Lincoln (Gnebrāsca)|Lincoln]] • [[Dūnholm (Norþcarolīna)|Dūnholm]] • [[Pleyno (Tēahsas)|Pleyno]] • [[Ancoredage]] • [[Cēsarēaceaster]] • [[Hālgaluis]] • [[Candyller (Arizona)|Candyller]] • [[Norþlāsuēagas]] • [[Ēamfullegesiht]] <!--Chula Vista--> • [[Būfalō (Nīwe Eoforwīc)|Būfalō]] • [[Gīlbeorht (Arizona)|Gīlbeorht]] •<!--resume here--> [[Hrēnō (Gnefada)|Hrēnō]] • [[Mædison (Wiscōnsēn)|Mædison]] • [[Wyrhtwægnwīc|Ƿyrhtƿægnƿīc]]<!--Fort Wayne--> • [[Tolēodo (Ohio)|Tolēodo]] • [[Lubbeċ]] • [[Sanctes Petresburg (Florida)|Sanctes Petresburg]] • [[Larēodo (Tēahsas)|Larēodo]] • [[Irfig (Tēahsas)|Irfig]] • [[Ceosapēac (Firginiæ)|Ceosapēac]] • [[Glenndæl (Arizona)|Glenndæl]] • [[Winestānsǣlham|Ƿinestānsǣlham]] • [[Scottesdæl (Arizona)|Scottesdæl]] • [[Gærland (Tēahsas)|Gærland]] • [[Boise|Bōisē]] • [[Norþfolc (Firginiæ)|Norþfolc]] • [[Portsanctlucius (Florida)|Portsanctlucius]] • [[Spocāne (Hwæsingatun)|Spocāne]] • [[Rīċemund, Firginiæ|Rīċemund]] • [[Frēomund (Californie)|Frēomund]] • [[Huntanbyrig (Alabama)|Huntanbyrg]]</li> </ol> | below = Cities ranked by [[United States Census Bureau]] population estimates for July 1, 2022. }}<noinclude> {{collapsible option}} [[Category:Largest cities of the United States templates|Populous]] [[Category:United States city navigational boxes|Cities, Populous]] </noinclude> 1w3zrpbfu3ye8yctpwmqfzickq5m2yb 216095 216094 2024-04-26T05:08:15Z Rylesbourne 125148 wikitext text/x-wiki {{Infobox |name = USPopulusCities |bodystyle = font-size:90%; width:100% |abovestyle = background:#ccccff; font-size:118%; |labelstyle = background:#ddddff; width:10%; text-align:right |above = 100 mæstenbyrig on [[Geanedan Ricu America]] |label1 = |data1 = [[Niweoforwicburg|Niƿeoforƿicburg]] • [[Lōsandgelis]] • [[Cicēa]] • [[Hūsestūn]] • [[Fēonix (Ārrisona)|Fēonix]] • [[Broþorlufeburh]] • [[Hālgantōnius]] • [[Dællas]] • [[Hālgadidacus]] • [[Ēastūnburh]] • [[Iǣxcūnbyrg]] • [[Hālgaiosep, Californie|Hālgaiosep]] • [[Weorthwīc|Ƿeorthƿīc]]<!--Fort Worth--> • [[Columbus (Ohio)|Columbus]] • [[Ceorlette (Norþcarolīna)|Ceorlette]] • [[Indigabyrg]] • [[Hālgafrancis]] • [[Sīatl]] • [[Denaford]] • [[Oclahomaceaster]] • [[Gnashburh]] • [[Þafæþm]]<!--El Paso--> • [[Hwæsingatun, D.C.|Hƿæsingatun]] • [[Lāsfægas]] • [[Botwulfstūn|Botƿulfstūn]] • [[Portlond (Orēgūn)|Portlond]] • [[Luisburg (Centuccīg)|Luisburg]] • [[Memfis (Tennesīeg)|Memfis]] • [[Dēotford]] • [[Bealdimōr]] • [[Mylenwic|Mylenƿic]]<!--Milwaukee--> • [[Ælbūrcerrce]] • [[Tūsōn]] • [[Asċetrēow|Asċetrēoƿ]] • [[Hālgþingstede]] • [[Tabulehyll, Ārrisona|Tabulehyll]]<!--Mesa, AZ--> • [[Cǣnsasburg (Misseōra)|Cǣnsasburg]] • [[Ætlanda]] • [[Coloradespryngs]] • [[Ōmahha]] • [[Raleah]] • [[Firginiestrond]] • [[Langstrond]] • [[Mīamig]] • [[Ǣcland]] • [[Minnegceaster]] • [[Tulse]] • [[Bæceresfeld]] • [[Tampa]] • [[Hwīcite|Hƿīcite]]<!--Wichita--> • [[Ælfrēdingtūn, Tēahsas|Ælfrēdingtūn]] • [[Eostrabyrg]] • [[Niwēorlēanas|Niƿēorlēanas]] • [[Clēafaland]] • [[Anahām]] • [[Hānolūlu]] • [[Heanricson (Gnefada)|Heanricson]] • [[Stocctūn (Californie)|Stocctūn]] • [[Ēasċora (Californie)|Ēasċora]] • [[Leaxingatūn (Centuccīg)|Leaxingatūn]] • [[Cristbodiġ]]<!--Corpus Christi--> • [[Orlando]] • [[Īrfine]] • [[Sinsignātig]] • [[Sanctanne, Californie|Sanctanne]] • [[Niweweorche (Nīwe Cēsarēa)|Niƿeƿeorche]] • [[Hālgapaulus (Minesohta)|Hālgapaulus]] • [[Pyttesburh]] • [[Grœnesburh]] • [[Lincoln (Gnebrāsca)|Lincoln]] • [[Dūnholm (Norþcarolīna)|Dūnholm]] • [[Pleyno (Tēahsas)|Pleyno]] • [[Ancoredage]] • [[Cēsarēaceaster]] • [[Hālgaluis]] • [[Candyller (Arizona)|Candyller]] • [[Norþlāsfægas]] • [[Ēamfullegesiht]] <!--Chula Vista--> • [[Būfalō (Nīwe Eoforwīc)|Būfalō]] • [[Gīlbeorht (Arizona)|Gīlbeorht]] •<!--resume here--> [[Hrēnō (Gnefada)|Hrēnō]] • [[Mædison (Wiscōnsēn)|Mædison]] • [[Wyrhtwægnwīc|Ƿyrhtƿægnƿīc]]<!--Fort Wayne--> • [[Tolēodo (Ohio)|Tolēodo]] • [[Lubbeċ]] • [[Sanctes Petresburg (Florida)|Sanctes Petresburg]] • [[Larēodo (Tēahsas)|Larēodo]] • [[Irfig (Tēahsas)|Irfig]] • [[Ceosapēac (Firginiæ)|Ceosapēac]] • [[Glenndæl (Arizona)|Glenndæl]] • [[Winestānsǣlham|Ƿinestānsǣlham]] • [[Scottesdæl (Arizona)|Scottesdæl]] • [[Gærland (Tēahsas)|Gærland]] • [[Boise|Bōisē]] • [[Norþfolc (Firginiæ)|Norþfolc]] • [[Portsanctlucius (Florida)|Portsanctlucius]] • [[Spocāne (Hwæsingatun)|Spocāne]] • [[Rīċemund, Firginiæ|Rīċemund]] • [[Frēomund (Californie)|Frēomund]] • [[Huntanbyrig (Alabama)|Huntanbyrg]]</li> </ol> | below = Cities ranked by [[United States Census Bureau]] population estimates for July 1, 2022. }}<noinclude> {{collapsible option}} [[Category:Largest cities of the United States templates|Populous]] [[Category:United States city navigational boxes|Cities, Populous]] </noinclude> 0e4n4quxwr023pl9oges5edelt2b1dw 4 23874 216086 215658 2024-04-26T02:38:33Z MABot 82184 Bot: Archiving 1 thread from [[Wikipǣdia:Se Þorpes Wella]] wikitext text/x-wiki == Do you use Wikidata in Wikimedia sibling projects? Tell us about your experiences == <div lang="en" dir="ltr" class="mw-content-ltr"> ''Note: Apologies for cross-posting and sending in English.'' Hello, the '''[[m:WD4WMP|Wikidata for Wikimedia Projects]]''' team at Wikimedia Deutschland would like to hear about your experiences using Wikidata in the sibling projects. If you are interested in sharing your opinion and insights, please consider signing up for an interview with us in this '''[https://wikimedia.sslsurvey.de/Wikidata-for-Wikimedia-Interviews Registration form]'''.<br> ''Currently, we are only able to conduct interviews in English.'' The front page of the form has more details about what the conversation will be like, including how we would '''compensate''' you for your time. For more information, visit our ''[[m:WD4WMP/AddIssue|project issue page]]'' where you can also share your experiences in written form, without an interview.<br>We look forward to speaking with you, [[m:User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[m:User talk:Danny Benjafield (WMDE)|talk]]) 08:53, 5 January 2024 (UTC) </div> <!-- Message sent by User:Danny Benjafield (WMDE)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/WD4WMP/ScreenerInvite&oldid=26027495 --> == Reusing references: Can we look over your shoulder? == ''Apologies for writing in English.'' The Technical Wishes team at Wikimedia Deutschland is planning to [[m:WMDE Technical Wishes/Reusing references|make reusing references easier]]. For our research, we are looking for wiki contributors willing to show us how they are interacting with references. * The format will be a 1-hour video call, where you would share your screen. [https://wikimedia.sslsurvey.de/User-research-into-Reusing-References-Sign-up-Form-2024/en/ More information here]. * Interviews can be conducted in English, German or Dutch. * [[mw:WMDE_Engineering/Participate_in_UX_Activities#Compensation|Compensation is available]]. * Sessions will be held in January and February. * [https://wikimedia.sslsurvey.de/User-research-into-Reusing-References-Sign-up-Form-2024/en/ Sign up here if you are interested.] * Please note that we probably won’t be able to have sessions with everyone who is interested. Our UX researcher will try to create a good balance of wiki contributors, e.g. in terms of wiki experience, tech experience, editing preferences, gender, disability and more. If you’re a fit, she will reach out to you to schedule an appointment. We’re looking forward to seeing you, [[m:User:Thereza Mengs (WMDE)| Thereza Mengs (WMDE)]] <!-- Message sent by User:Thereza Mengs (WMDE)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=WMDE_Technical_Wishes/Technical_Wishes_News_list_all_village_pumps&oldid=25956752 --> == Feminism and Folklore 2024 == <div style="border:8px maroon ridge;padding:6px;> [[File:Feminism and Folklore 2024 logo.svg|centre|550px|frameless]] ::<div lang="en" dir="ltr" class="mw-content-ltr"> <center>''{{int:please-translate}}''</center> Dear Wiki Community, You are humbly invited to organize the '''[[:m:Feminism and Folklore 2024|Feminism and Folklore 2024]]''' writing competition from February 1, 2024, to March 31, 2024 on your local Wikipedia. This year, Feminism and Folklore will focus on feminism, women's issues, and gender-focused topics for the project, with a [[:c:Commons:Wiki Loves Folklore 2024|Wiki Loves Folklore]] gender gap focus and a folk culture theme on Wikipedia. You can help Wikipedia's coverage of folklore from your area by writing or improving articles about things like folk festivals, folk dances, folk music, women and queer folklore figures, folk game athletes, women in mythology, women warriors in folklore, witches and witch hunting, fairy tales, and more. Users can help create new articles, expand or translate from a generated list of suggested articles. Organisers are requested to work on the following action items to sign up their communities for the project: # Create a page for the contest on the local wiki. # Set up a campaign on '''CampWiz''' tool. # Create the local list and mention the timeline and local and international prizes. # Request local admins for site notice. # Link the local page and the CampWiz link on the [[:m:Feminism and Folklore 2024/Project Page|meta project page]]. This year, the Wiki Loves Folklore Tech Team has introduced two new tools to enhance support for the campaign. These tools include the '''Article List Generator by Topic''' and '''CampWiz'''. The Article List Generator by Topic enables users to identify articles on the English Wikipedia that are not present in their native language Wikipedia. Users can customize their selection criteria, and the tool will present a table showcasing the missing articles along with suggested titles. Additionally, users have the option to download the list in both CSV and wikitable formats. Notably, the CampWiz tool will be employed for the project for the first time, empowering users to effectively host the project with a jury. Both tools are now available for use in the campaign. [https://tools.wikilovesfolklore.org/ '''Click here to access these tools'''] Learn more about the contest and prizes on our [[:m:Feminism and Folklore 2024|project page]]. Feel free to contact us on our [[:m:Talk:Feminism and Folklore 2024/Project Page|meta talk page]] or by email us if you need any assistance. We look forward to your immense coordination. Thank you and Best wishes, '''[[:m:Feminism and Folklore 2024|Feminism and Folklore 2024 International Team]]''' ::::Stay connected [[File:B&W Facebook icon.png|link=https://www.facebook.com/feminismandfolklore/|30x30px]]&nbsp; [[File:B&W Twitter icon.png|link=https://twitter.com/wikifolklore|30x30px]] </div></div> --[[Brūcend:MediaWiki message delivery|MediaWiki message delivery]] ([[Brūcendmōtung:MediaWiki message delivery|motung]]) 07:26, 18 Se Æfterra Gēola 2024 (UTC) == Wiki Loves Folklore is back! == <div lang="en" dir="ltr" class="mw-content-ltr"> {{int:please-translate}} [[File:Wiki Loves Folklore Logo.svg|right|150px|frameless]] Dear Wiki Community, You are humbly invited to participate in the '''[[:c:Commons:Wiki Loves Folklore 2024|Wiki Loves Folklore 2024]]''' an international photography contest organized on Wikimedia Commons to document folklore and intangible cultural heritage from different regions, including, folk creative activities and many more. It is held every year from the '''1st till the 31st''' of March. You can help in enriching the folklore documentation on Commons from your region by taking photos, audios, videos, and [https://commons.wikimedia.org/w/index.php?title=Special:UploadWizard&campaign=wlf_2024 submitting] them in this commons contest. You can also [[:c:Commons:Wiki Loves Folklore 2024/Organize|organize a local contest]] in your country and support us in translating the [[:c:Commons:Wiki Loves Folklore 2024/Translations|project pages]] to help us spread the word in your native language. Feel free to contact us on our [[:c:Commons talk:Wiki Loves Folklore 2024|project Talk page]] if you need any assistance. '''Kind regards,''' '''Wiki loves Folklore International Team''' -- [[Brūcend:MediaWiki message delivery|MediaWiki message delivery]] ([[Brūcendmōtung:MediaWiki message delivery|motung]]) 07:26, 18 Se Æfterra Gēola 2024 (UTC) </div></div> <!-- Message sent by User:Tiven2240@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery/Wikipedia&oldid=23942484 --> == <span lang="en" dir="ltr" class="mw-content-ltr">Vote on the Charter for the Universal Code of Conduct Coordinating Committee</span> == <div lang="en" dir="ltr" class="mw-content-ltr"> <section begin="announcement-content" /> :''[[m:Special:MyLanguage/wiki/Universal Code of Conduct/Coordinating Committee/Charter/Announcement - voting opens|You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&group=page-{{urlencode:wiki/Universal Code of Conduct/Coordinating Committee/Charter/Announcement - voting opens}}&language=&action=page&filter= {{int:please-translate}}]'' Hello all, I am reaching out to you today to announce that the voting period for the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee|Universal Code of Conduct Coordinating Committee]] (U4C) Charter is now open. Community members may [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee/Charter/Voter_information|cast their vote and provide comments about the charter via SecurePoll]] now through '''2 February 2024'''. Those of you who voiced your opinions during the development of the [[foundation:Special:MyLanguage/Policy:Universal_Code_of_Conduct/Enforcement_guidelines|UCoC Enforcement Guidelines]] will find this process familiar. The [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Charter|current version of the U4C Charter]] is on Meta-wiki with translations available. Read the charter, go vote and share this note with others in your community. I can confidently say the U4C Building Committee looks forward to your participation. On behalf of the UCoC Project team,<section end="announcement-content" /> </div> [[m:User:RamzyM (WMF)|RamzyM (WMF)]] 18:08, 19 Se Æfterra Gēola 2024 (UTC) <!-- Message sent by User:RamzyM (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&oldid=25853527 --> == <span lang="en" dir="ltr" class="mw-content-ltr">Last days to vote on the Charter for the Universal Code of Conduct Coordinating Committee</span> == <div lang="en" dir="ltr" class="mw-content-ltr"> <section begin="announcement-content" /> :''[[m:Special:MyLanguage/wiki/Universal Code of Conduct/Coordinating Committee/Charter/Announcement - voting reminder|You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&group=page-{{urlencode:wiki/Universal Code of Conduct/Coordinating Committee/Charter/Announcement - voting reminder}}&language=&action=page&filter= {{int:please-translate}}]'' Hello all, I am reaching out to you today to remind you that the voting period for the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee|Universal Code of Conduct Coordinating Committee]] (U4C) charter will close on '''2 February 2024'''. Community members may [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee/Charter/Voter_information|cast their vote and provide comments about the charter via SecurePoll]]. Those of you who voiced your opinions during the development of the [[foundation:Special:MyLanguage/Policy:Universal_Code_of_Conduct/Enforcement_guidelines|UCoC Enforcement Guidelines]] will find this process familiar. The [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Charter|current version of the U4C charter]] is on Meta-wiki with translations available. Read the charter, go vote and share this note with others in your community. I can confidently say the U4C Building Committee looks forward to your participation. On behalf of the UCoC Project team,<section end="announcement-content" /> </div> [[m:User:RamzyM (WMF)|RamzyM (WMF)]] 17:00, 31 Se Æfterra Gēola 2024 (UTC) <!-- Message sent by User:RamzyM (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&oldid=25853527 --> == IMPORTANT: Admin activity review == Hello. A policy regarding the removal of "advanced rights" (administrator, bureaucrat, interface administrator, etc.) was adopted by [[:m:Requests for comment/Activity levels of advanced administrative rights holders|global community consensus]] in 2013. According to this policy, the [[:m:stewards|stewards]] are reviewing administrators' activity on all Wikimedia Foundation wikis with no inactivity policy. To the best of our knowledge, your wiki does not have a formal process for removing "advanced rights" from inactive accounts. This means that the stewards will take care of this according to the [[:m:Admin activity review|admin activity review]]. We have determined that the following users meet the inactivity criteria (no edits and no logged actions for more than 2 years): # [[Special:Contributions/Gottistgut|Gottistgut]] (administrator) This users will receive a notification soon, asking them to start a community discussion if they want to retain some or all of their rights. If the users do not respond, then their advanced rights will be removed by the stewards. However, if you as a community would like to create your own activity review process superseding the global one, want to make another decision about these inactive rights holders, or already have a policy that we missed, then please notify the [[:m:Stewards' noticeboard|stewards on Meta-Wiki]] so that we know not to proceed with the rights review on your wiki. Thanks, [[Brūcend:Superpes15|Superpes15]] ([[Brūcendmōtung:Superpes15|motung]]) 14:23, 7 Solmonaþ 2024 (UTC) == <span lang="en" dir="ltr" class="mw-content-ltr">Announcing the results of the UCoC Coordinating Committee Charter ratification vote</span> == <div lang="en" dir="ltr" class="mw-content-ltr"> <section begin="announcement-content" /> :''[[m:Special:MyLanguage/wiki/Universal Code of Conduct/Coordinating Committee/Charter/Announcement - results|You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&group=page-{{urlencode:wiki/Universal Code of Conduct/Coordinating Committee/Charter/Announcement - results}}&language=&action=page&filter= {{int:please-translate}}]'' Dear all, Thank you everyone for following the progress of the Universal Code of Conduct. I am writing to you today to announce the outcome of the [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee/Charter/Voter_information|ratification vote]] on the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Charter|Universal Code of Conduct Coordinating Committee Charter]]. 1746 contributors voted in this ratification vote with 1249 voters supporting the Charter and 420 voters not. The ratification vote process allowed for voters to provide comments about the Charter. A report of voting statistics and a summary of voter comments will be published on Meta-wiki in the coming weeks. Please look forward to hearing about the next steps soon. On behalf of the UCoC Project team,<section end="announcement-content" /> </div> [[m:User:RamzyM (WMF)|RamzyM (WMF)]] 18:23, 12 Solmonaþ 2024 (UTC) <!-- Message sent by User:RamzyM (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&oldid=26160150 --> == Enabling machine translation support, Section and Content translation tools in your Wikipedia == {{Int:hello}} Old English Wikipedians! Apologies as this message is not in your language, {{int:Please-translate}}. The WMF Language team plans to enable the Section and Content translation tools to Old English Wikipedia by default. Also, the team is considering adding [[mw:Help:Content_translation/Translating/Initial_machine_translation|machine translation]] (MT) support with [[mw:MinT|MinT]] to the tools. MinT may be providing limited support for your language, so we want to make sure it is useful for the community. For this, my team would like members of your community to: * Test the machine translation support [https://translate.wmcloud.org/ in a test instance]. You can paste multiple pieces of content from different Wikipedia articles and check whether the provided result is a useful starting point for a translation. * Give us feedback if the machine translation quality is okay to be on your Wikipedia by default, as an optional service or if it is not useful at all. * Let us know if you have any objections to having the Section and Content translation enabled by default in this Wikipedia. Below is background information about the tools and how you can test them. '''Background information''' [[mw:Content_translation|Content Translation]] has been a successful tool for editors to create content in their language. Since its release in 2015, the tool has aided the translation of more than one million articles across all languages. However, the tool is in beta in Old English Wikipedia, limiting its discoverability and use. Being in beta also blocks enabling the Section translation in your Wikipedia. [[mw:Content_translation/Section_translation|Section Translation]] extends the capabilities of Content Translation to support mobile devices. On mobile, the tool will: * Guide you to translate one section at a time to expand existing articles or create new ones * Make it easy to transfer knowledge across languages anytime from your mobile device MinT (Machine in Translation) is a machine translation service hosted in the Wikimedia Infrastructure. It is designed to provide translations from many MT models. The model available for your Wikipedia is the [https://github.com/google-research/google-research/tree/master/madlad_400 MADLAD-400 open-source translation model]. '''Our request''' The MADLAD-400 MT is available for your Wiki in our test instance. We want you to test it (translate sentences and paragraphs from articles) in our test instance:[https://translate.wmcloud.org/ https://translate.wmcloud.org]. Let us know in this thread if the quality of the automatic translation generated is okay to enable it in Old English Wikipedia along with the Section and Content translation tool. '''Our plans to enable the tools and the machine translation support''' We plan to deploy the tools with the MT support by the 4th of March. If there are no objections from your community, we will deploy them. We want to provide the tools in the way they best serve the community, so we are open to make further adjustments after the deployment based on the experience of the community. We look forward to getting your feedback in this thread. Thank you! On behalf of the WMF Language team. [[Brūcend:UOzurumba (WMF)|UOzurumba (WMF)]] ([[Brūcendmōtung:UOzurumba (WMF)|motung]]) 05:11, 15 Solmonaþ 2024 (UTC) == Ukraine's Cultural Diplomacy Month 2024: We are back! == <div lang="en" dir="ltr" class="mw-content-ltr"> [[File:UCDM 2024 general.jpg|180px|right]] {{int:please-translate}} Hello, dear Wikipedians!<br/> [[:m:Special:MyLanguage/Wikimedia Ukraine|Wikimedia Ukraine]], in cooperation with the [[:en:Ministry of Foreign Affairs of Ukraine|MFA of Ukraine]] and [[:en:Ukrainian Institute|Ukrainian Institute]], has launched the forth edition of writing challenge "'''[[:m:Special:MyLanguage/Ukraine's Cultural Diplomacy Month 2024|Ukraine's Cultural Diplomacy Month]]'''", which lasts from 1st until 31st March 2024. The campaign is dedicated to famous Ukrainian artists of cinema, music, literature, architecture, design and cultural phenomena of Ukraine that are now part of world heritage. We accept contribution in every language! The most active contesters will receive prizes.<br/> We invite you to take part and help us improve the coverage of Ukrainian culture on Wikipedia in your language! Also, we plan to set up a [[:m:CentralNotice/Request/UCDM 2024|banner]] to notify users of the possibility to participate in such a challenge! [[:m:User:ValentynNefedov (WMUA)|ValentynNefedov (WMUA)]] ([[:m:User talk:ValentynNefedov (WMUA)|talk]]) </div> <!-- Message sent by User:ValentynNefedov (WMUA)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery/Wikipedia&oldid=26166467 --> == <span lang="en" dir="ltr" class="mw-content-ltr"> Report of the U4C Charter ratification and U4C Call for Candidates now available</span> == <div lang="en" dir="ltr" class="mw-content-ltr"> <section begin="announcement-content" /> :''[[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024/Announcement – call for candidates| You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&group=page-{{urlencode:Universal Code of Conduct/Coordinating Committee/Election/2024/Announcement – call for candidates}}&language=&action=page&filter= {{int:please-translate}}]'' Hello all, I am writing to you today with two important pieces of information. First, the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Charter/Vote results|report of the comments from the Universal Code of Conduct Coordinating Committee (U4C) Charter ratification]] is now available. Secondly, the call for candidates for the U4C is open now through April 1, 2024. The [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee|Universal Code of Conduct Coordinating Committee]] (U4C) is a global group dedicated to providing an equitable and consistent implementation of the UCoC. Community members are invited to submit their applications for the U4C. For more information and the responsibilities of the U4C, please [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Charter|review the U4C Charter]]. Per the charter, there are 16 seats on the U4C: eight community-at-large seats and eight regional seats to ensure the U4C represents the diversity of the movement. Read more and submit your application on [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024|Meta-wiki]]. On behalf of the UCoC project team,<section end="announcement-content" /> </div> [[m:User:RamzyM (WMF)|RamzyM (WMF)]] 16:25, 5 Hreðmonað 2024 (UTC) <!-- Message sent by User:RamzyM (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&oldid=26276337 --> == <span lang="en" dir="ltr" class="mw-content-ltr"> Wikimedia Foundation Board of Trustees 2024 Selection</span> == <div lang="en" dir="ltr" class="mw-content-ltr"> <section begin="announcement-content" /> : ''[[m:Special:MyLanguage/Wikimedia Foundation elections/2024/Announcement/Selection announcement| You can find this message translated into additional languages on Meta-wiki.]]'' : ''<div class="plainlinks">[[m:Special:MyLanguage/Wikimedia Foundation elections/2024/Announcement/Selection announcement|{{int:interlanguage-link-mul}}]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&group=page-{{urlencode:Wikimedia Foundation elections/2024/Announcement/Selection announcement}}&language=&action=page&filter= {{int:please-translate}}]</div>'' Dear all, This year, the term of 4 (four) Community- and Affiliate-selected Trustees on the Wikimedia Foundation Board of Trustees will come to an end [1]. The Board invites the whole movement to participate in this year’s selection process and vote to fill those seats. The [[m:Special:MyLanguage/Wikimedia Foundation elections committee|Elections Committee]] will oversee this process with support from Foundation staff [2]. The Board Governance Committee created a Board Selection Working Group from Trustees who cannot be candidates in the 2024 community- and affiliate-selected trustee selection process composed of Dariusz Jemielniak, Nataliia Tymkiv, Esra'a Al Shafei, Kathy Collins, and Shani Evenstein Sigalov [3]. The group is tasked with providing Board oversight for the 2024 trustee selection process, and for keeping the Board informed. More details on the roles of the Elections Committee, Board, and staff are here [4]. Here are the key planned dates: * May 2024: Call for candidates and call for questions * June 2024: Affiliates vote to shortlist 12 candidates (no shortlisting if 15 or less candidates apply) [5] * June-August 2024: Campaign period * End of August / beginning of September 2024: Two-week community voting period * October–November 2024: Background check of selected candidates * Board's Meeting in December 2024: New trustees seated Learn more about the 2024 selection process - including the detailed timeline, the candidacy process, the campaign rules, and the voter eligibility criteria - on [[m:Special:MyLanguage/Wikimedia Foundation elections/2024|this Meta-wiki page]], and make your plan. '''Election Volunteers''' Another way to be involved with the 2024 selection process is to be an Election Volunteer. Election Volunteers are a bridge between the Elections Committee and their respective community. They help ensure their community is represented and mobilize them to vote. Learn more about the program and how to join on this [[m:Special:MyLanguage/Wikimedia Foundation elections/2024/Election Volunteers|Meta-wiki page]]. Best regards, [[m:Special:MyLanguage/User:Pundit|Dariusz Jemielniak]] (Governance Committee Chair, Board Selection Working Group) [1] https://meta.wikimedia.org/wiki/Special:MyLanguage/Wikimedia_Foundation_elections/2021/Results#Elected [2] https://foundation.wikimedia.org/wiki/Committee:Elections_Committee_Charter [3] https://foundation.wikimedia.org/wiki/Minutes:2023-08-15#Governance_Committee [4] https://meta.wikimedia.org/wiki/Wikimedia_Foundation_elections_committee/Roles [5] Even though the ideal number is 12 candidates for 4 open seats, the shortlisting process will be triggered if there are more than 15 candidates because the 1-3 candidates that are removed might feel ostracized and it would be a lot of work for affiliates to carry out the shortlisting process to only eliminate 1-3 candidates from the candidate list.<section end="announcement-content" /> </div> [[User:MPossoupe_(WMF)|MPossoupe_(WMF)]]19:56, 12 Hreðmonað 2024 (UTC) <!-- Message sent by User:MPossoupe (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Distribution_list/Global_message_delivery&oldid=26349432 --> 3au69z5bo6drif5w1s9bf2mir1nlr52 0 24114 216088 215588 2024-04-26T04:46:02Z Rylesbourne 125148 /* Samaflanc seoxhyrne */ wikitext text/x-wiki {{Rimcraeftniwenglish}} {{Infobox gesceapu | nama = Seoxhyrne | ymele = Regular polygon 6 annotated.svg | gewrit = Ǣn samaflanc seoxhyrne | rind = 6 | sclæfligruna = {6} | oferside = Manigfult | tweoflaedig = 120° }} Sēo '''seoxhyrne''' ({{lang-en|hexagon}}) oþþe '''seoxhyrne ġesceap''' is sēo ġesċeap ƿiþ [[seox]] hyrneġen. In [[geometry]], a '''hexagon''' (from [[Ancient Greek|Greek]] {{lang|grc|ἕξ}}, {{lang|grc-Latn|hex}}, mēnung "seox", and {{lang|grc|γωνία}}, {{lang|grc-Latn|gonía}}, meaning "corner, angle") is a seoxflanc [[polygon]].<ref>[https://deimel.org/images/plain_cube.gif Cube picture]</ref> Þē total æf þē internal angles æf any [[simple polygon|simple]] (non-self-intersecting) hexagon is 720°. ==Samaflanc seoxhyrne == A ''[[samaflanc gesceap|samaflanc]] seoxhyrne'' hæfde sēo [[sclæfligruna]] æf {6} ond [[innyrdigfeald]]s <!--interior angle--> æf 120°.<ref>{{citation|title=Polyhedron Models|first=Magnus J.|last=Wenninger|publisher=Cambridge University Press|year=1974|page=9|isbn=9780521098595|url=https://books.google.com/books?id=N8lX2T-4njIC&pg=PA9|access-date=2015-11-06|archiveurl=https://web.archive.org/web/20160102075753/https://books.google.com/books?id=N8lX2T-4njIC&pg=PA9|archive-date=2016-01-02|url-status=live}}.</ref> Aht cunnen eallswā bēon ācweccaned eallswā a [[sċeortode (gemetrig)|sċeortode]] [[samaflanc þrīhyrne]], t{3}, hwic oðerwiss twā ēgðus æf rindenes. A samaflanc seoxhyrne is tealde eallswā a seoxhyrne þæt is bā [[samaflanc gesceap|samaflanc]] and [[efnangul gesceap|efnangul]]<!--equiangular-->. Hit is [[twofold gesceap|twofold]], mǣnaneg þæt hit is bā [[hweorfanlic gesceap|hweorfanlic]]<!--cyclic--> (hafs a ymbehringed hring) and [[tangwise gesceap|tangƿise]] (hafs an inwriten hring). Þē ġecynde wǣg æf þē flacenes īsgelīcs þē hrēodanfex æf þē [[ymbehringed hring]]<!--circumscribed circle--> or [[ymbehringhring]], hwic yamounted<math>\tfrac{2}{\sqrt{3}}</math> tīman þē [[æpþem]] (hrēodanfex æf þē [[inwriten gesceap|inwriten hring]]). Ēall innyrdig [[feald (rīmcræft)|feald]]s earon 120 [[rīminnyrdig]]. A samaflanc seoxhyrne hafs seox [[ymbhrǣdlic gemetgemostras]] (''ymbhrǣdlic gemetgemostras ǣf ordre seox'') and seox [[reflection symmetries]] (''seox lines æf symmetry''), crǣftung upp þē [[twēoflaedig flocc]] D₆. Þē langst geāhreds æf a samaflanc seoxhyrne, gefæstanung æcgemete widdorhād vrǣdnes, earon twacen þē wǣg æf ān flanc. Fram þīs hit cunnen wesan sēon þæt a [[þrīhyrne]] ƿīþ a hwyrftstān at þē centrum æf þē samaflanc seoxhyrne and sharung ān flanc ƿīþ þē seoxhyrne is [[samaflanc þrīhyrne|samaflanc]], and þæt þē samaflanc seoxhyrne cunnen wesan dǣlfæst intō seox samaflanc þrīhyrnes. Lician [[fēowerecge (gemetrig)|fēowerecge]]s and [[samaflanc]] [[þrīhyrne]]s, samaflanc seoxhyrnes fhit tōgædere þiþout ǣniġ ġeaps tō ''tile þē plane'' (þrī seoxhyrnes meetung aht eall hwyrftstān), and so earon nyttfull fore ācweccaneg [[tessellation]]s. Þē cēlan æf a [[bēohȳf (bēocēpanung)|bēohȳf]] [[huniġcamb]] earon seoxhyrnelican fore þīs reason and bēacen þæs þē ġesceap crǣften eficient fricu æf ūtstræcan and boldung andweorces. Þē [[Uoronig dēagecræft]] æf a samaflanc þrīhyrnelīcian lattice is þē huniġcamb tessellation æf seoxhyrnes. Hit is nāht gestalteg considered a [[samaflanc gesceap|þrīhyrnetorr]], þēah hit is samaflanc. {| class="wikitable" width=40% |+ Forebȳsn |- | [[Ymele:Regular Hexagon Inscribed in a Circle.gif|240px]] || [[Ymele:01-Sechseck-Seite-vorgegeben-wiki.svg|263px]] |- | Ǣn stepebīstepe ymelestyring æf þē getimbrung æf a samaflanc seoxhyrne usung [[færanfæþm ond streċċaneċġ]], ġiefen bī [[Ewcleod]]'s ''[[Ewcleoden Ādalen|Ādalen]]'', Bōc IU, Trahtnysse 15: þīs is mæglic eallswā 6 <math>=</math> 2 × 3, a afraet æf a anweald æf twā and clæne [[Færmet formesta]]s. || Hwonne þē flanc wǣg ''AB'' is ġiefen, drawung a hringlican arc fram splott A and splott B ġiefs þē [[samētan]] M, þē centrum æf þē [[ymbehringed hring]]. Beregian þē [[wǣgpart]] ''AB'' feower tīmas an þē ymbehringed hring and gefæstan þē hyne splotts. |} == Parameters == [[Image:Regular hexagon 1.svg|thumb|''R'' = [[Circumradius]]; ''r'' = [[Inradius]]; ''t'' = side length]] The maximal [[diameter#Polygons|diameter]] (which corresponds to þē long [[diagonal]] æf þē hexagon), ''D'', is twice þē maximal radius or [[circumradius]], ''R'', which equals þē side length, ''t''. Þē minimal diameter or þē diameter æf þē [[inscribed]] circle (separation æf parallel sides, flat-to-flat distance, short diagonal or height when resting on a flat base), ''d'', is twice þē minimal radius or [[inradius]], ''r''. Þē maxima and minima are related by þē same factor: :<math>\frac{1}{2}d = r = \cos(30^\circ) R = \frac{\sqrt{3}}{2} R = \frac{\sqrt{3}}{2} t</math> &nbsp; and, similarly, <math>d = \frac{\sqrt{3}}{2} D.</math> The area æf a regular hexagon :<math>\begin{align} A &= \frac{3\sqrt{3}}{2}R^2 = 3Rr = 2\sqrt{3} r^2 \\[3pt] &= \frac{3\sqrt{3}}{8}D^2 = \frac{3}{4}Dd = \frac{\sqrt{3}}{2} d^2 \\[3pt] &\approx 2.598 R^2 \approx 3.464 r^2\\ &\approx 0.6495 D^2 \approx 0.866 d^2. \end{align}</math> For any regular [[polygon]], þē area can also be expressed in terms æf þē [[apothem]] ''a'' and þē perimeter ''p''. For þē regular hexagon these are given by ''a'' = ''r'', and ''p''<math>{} = 6R = 4r\sqrt{3}</math>, so :<math>\begin{align} A &= \frac{ap}{2} \\ &= \frac{r \cdot 4r\sqrt{3}}{2} = 2r^2\sqrt{3} \\ &\approx 3.464 r^2. \end{align}</math> The regular hexagon fills þē fraction <math>\tfrac{3\sqrt{3}}{2\pi} \approx 0.8270</math> æf its [[circumscribed circle]]. If a regular hexagon has successive vertices A, B, C, D, E, F and if P is any point on þē circumcircle between B and C, then {{nowrap|PE + PF {{=}} PA + PB + PC + PD}}. It follows from þē ratio æf [[circumradius]] to [[inradius]] that þē height-to-width ratio æf a regular hexagon is 1:1.1547005; that is, a hexagon with a long [[diagonal]] æf 1.0000000 will have a distance æf 0.8660254 between parallel sides. == Point in plane == For an arbitrary point in þē plane æf a regular hexagon with circumradius <math>R</math>, whose distances to þē centroid æf þē regular hexagon and its seox vertices are <math>L</math> and <math>d_i</math> respectively, we have<ref name=Mamuka >{{cite journal| last1= Meskhishvili |first1= Mamuka| date=2020|title=Cyclic Averages æf Regular Polygons and Platonic Solids |journal= Communications in Mathematics and Applications|volume=11|pages=335–355|doi= 10.26713/cma.v11i3.1420|doi-broken-date= 31 January 2024|arxiv= 2010.12340|url= https://www.rgnpublications.com/journals/index.php/cma/article/view/1420/1065}}</ref> :<math> d_1^2 + d_4^2 = d_2^2 + d_5^2 = d_3^2+ d_6^2= 2\left(R^2 + L^2\right), </math> :<math> d_1^2 + d_3^2+ d_5^2 = d_2^2 + d_4^2+ d_6^2 = 3\left(R^2 + L^2\right), </math> :<math> d_1^4 + d_3^4+ d_5^4 = d_2^4 + d_4^4+ d_6^4 = 3\left(\left(R^2 + L^2\right)^2 + 2 R^2 L^2\right). </math> If <math>d_i</math> are þē distances from þē vertices æf a regular hexagon to any point on its circumcircle, then <ref name= Mamuka /> :<math>\left(\sum_{i=1}^6 d_i^2\right)^2 = 4 \sum_{i=1}^6 d_i^4 .</math> == Symmetry== {| class="collapsible collapsed" align=right ! Example hexagons by symmetry |- | {| class=wikitable |- valign=top ! ! [[File:Hexagon_r12_symmetry.png|60px]]<BR>r12<BR>regular ! |rowspan=3| ! ! [[File:Hexagon_i4_symmetry.png|60px]]<BR>i4 ! |- valign=top ! [[File:Hexagon_d6_symmetry.png|60px]]<BR>d6<BR>[[isotoxal figure|isotoxal]] ! [[File:Hexagon_g6_symmetry.png|60px]]<BR>g6<BR>directed ! [[File:Hexagon_p6_symmetry.png|60px]]<BR>p6<BR>[[isogonal figure|isogonal]] ! [[File:Hexagon_d3_symmetry.png|60px]]<BR>d2 ! [[File:Hexagon_g2_symmetry.png|60px]]<BR>g2<BR>general<BR>[[parallelogon]] ! [[File:Hexagon_p2_symmetry.png|60px]]<BR>p2 |- valign=top ! ! [[File:Hexagon_g3_symmetry.png|60px]]<BR>g3 ! ! ! [[File:Hexagon_a1_symmetry.png|60px]]<BR>a1 ! |} |} [[File:Hexagon reflections.svg|thumb|160px|left|The seox lines æf [[reflection symmetry|reflection]] æf a regular hexagon, with Dih₆ or '''r12''' symmetry, order 12.]] [[File:Regular hexagon symmetries.svg|thumb|400px|The dihedral symmetries are divided depending on whether they pass through vertices ('''d''' for diagonal) or edges ('''p''' for perpendiculars) Cyclic symmetries in þē middle column are labeled as '''g''' for their central gyration orders. Full symmetry æf þē regular form is '''r12''' and no symmetry is labeled '''a1'''.]] The ''regular hexagon'' has D₆ symmetry. There are 16 subgroups. There are 8 up to isomorphism: itself (D₆), 2 dihedral: (D_3, D₂), 4 [[cyclic group|cyclic]]: (Z₆, Z₃, Z₂, Z₁) and þē trivial (e) These symmetries express nine distinct symmetries æf a regular hexagon. [[John Horton Conway|John Conway]] labels these by a letter and group order.<ref>John H. Conway, Heidi Burgiel, [[Chaim Goodman-Strauss]], (2008) The Symmetries of Things, {{ISBN|978-1-56881-220-5}} (Chapter 20, Generalized Schaefli symbols, Types of symmetry of a polygon pp. 275-278)</ref> '''r12''' is full symmetry, and '''a1''' is no symmetry. '''p6''', an [[isogonal figure|isogonal]] hexagon constructed by three mirrors can alternate long and short edges, and '''d6''', an [[isotoxal figure|isotoxal]] hexagon constructed with equal edge lengths, but vertices alternating two different internal angles. These two forms are [[dual polygon|duals]] æf each other and have half þē symmetry order æf þē regular hexagon. Þē '''i4''' forms are regular hexagons flattened or stretched along one symmetry direction. It can be seen as an [[Elongation (geometry)|elongated]] [[rhombus]], while '''d2''' and '''p2''' can be seen as horizontally and vertically elongated [[Kite (geometry)|kites]]. '''g2''' hexagons, with opposite sides parallel are also called hexagonal [[parallelogon]]s. Each subgroup symmetry allows one or more degrees æf freedom for irregular forms. Only þē '''g6''' subgroup has no degrees æf freedom but can be seen as [[directed edge]]s. Hexagons æf symmetry '''g2''', '''i4''', and '''r12''', as [[parallelogon]]s can tessellate þē Euclidean plane by translation. Other [[Hexagonal tiling#Topologically equivalent tilings|hexagon shapes can tile þē plane]] with different orientations. {| class=wikitable !''p''6''m'' (*632) !''cmm'' (2*22) !''p''2 (2222) !''p''31''m'' (3*3) !colspan=2|''pmg'' (22*) !''pg'' (××) |- ![[File:Isohedral_tiling_p6-13.png|120px]]<BR>[[hexagonal tiling|r12]] ![[File:Isohedral_tiling_p6-12.png|120px]]<BR>i4 ![[File:Isohedral_tiling_p6-7.png|120px]]<BR>g2 ![[File:Isohedral tiling p6-11.png|120px]]<BR>d2 ![[File:Isohedral tiling p6-10.png|120px]]<BR>d2 ![[File:Isohedral tiling p6-9.png|120px]]<BR>p2 ![[File:Isohedral tiling p6-1.png|120px]]<BR>a1 |- valign=top al !Dih₆ !Dih₂ !Z₂ !colspan=3|Dih₁ !Z₁ |} {{-}} === A2 and G2 groups === {| class=wikitable align=right style="text-align:center;" |- | [[File:Root system A2.svg|120px]]<BR>A2 group roots<BR>{{Dynkin|node_n1|3|node_n2}} | [[File:Root system G2.svg|120px]]<BR>G2 group roots<BR>{{Dynkin2|nodeg_n1|6a|node_n2}} |} The 6 roots æf þē [[simple Lie group]] [[Dynkin diagram#Example: A2|A2]], represented by a [[Dynkin diagram]] {{Dynkin|node_n1|3|node_n2}}, are in a regular hexagonal pattern. Þē two simple roots have a 120° angle between them. The 12 roots æf þē [[Exceptional Lie group#Exceptional cases|Exceptional Lie group]] [[G2 (mathematics)|G2]], represented by a [[Dynkin diagram]] {{Dynkin2|nodeg_n1|6a|node_n2}} are also in a hexagonal pattern. Þē two simple roots æf two lengths have a 150° angle between them. {{-}} == Dissection== {| class=wikitable align=right style="text-align:center;" ! [[6-cubī]] projection !colspan=2| 12 rhomb dissection |- | [[File:6-cube t0 A5.svg|120px]] | [[File:6-gon rhombic dissection-size2.svg|140px]] | [[File:6-gon rhombic dissection2-size2.svg|140px]] |} [[Coxeter]] states that every [[zonogon]] (a 2''m''-gon whose opposite sides are parallel and æf equal length) can be dissected into {{nowrap|{{frac|1|2}}''m''(''m'' − 1)}} parallelograms.<ref>[[Coxeter]], Mathematical recreations and Essays, Thirteenth edition, p.141</ref> In particular this is true for [[regular polygon]]s with evenly many sides, in which case þē parallelograms are all rhombi. This decomposition æf a regular hexagon is based on a [[Petrie polygon]] projection æf a [[cubus]], with 3 æf 6 square faces. Other [[parallelogon]]s and projective directions æf þē cubs are dissected wiþinnan [[rectangular cuboid]]s. {| class="wikitable collapsible" style="text-align:center;" !colspan=12| Dissection æf hexagons into three rhombs and parallelograms |- !rowspan=3| 2D ! Rhombs !colspan=3| Parallelograms |- valign=top |[[File:Hexagon_dissection.svg|80px]] |[[File:Cube-skew-orthogonal-skew-solid.png|95px]] |[[File:Cuboid_diagonal-orthogonal-solid.png|120px]] |[[File:Cuboid_skew-orthogonal-solid.png|120px]] |- valign=top | Regular {6} |colspan=3| Hexagonal [[parallelogon]]s |- !rowspan=3| 3D !colspan=2| Square faces !colspan=2| Rectangular faces |- valign=top | [[File:3-cube_graph.svg|95px]] | [[File:Cube-skew-orthogonal-skew-frame.png|95px]] | [[File:Cuboid_diagonal-orthogonal-frame.png|120px]] | [[File:Cuboid_skew-orthogonal-frame.png|120px]] |- valign=top |colspan=2| [[Cube]] |colspan=2| [[Rectangular cuboid]] |} == Related polygons and tilings == A regular hexagon has [[Schläfli symbol]] {6}. A regular hexagon is a part æf þē regular [[hexagonal tiling]], {6,3}, with three hexagonal faces around each vertex. A regular hexagon can also be created as a [[Truncation (geometry)|truncated]] [[equilateral triangle]], with Schläfli symbol t{3}. Seen with two types (colors) æf edges, this form only has D₃ symmetry. A [[truncation (geometry)|truncated]] hexagon, t{6}, is a [[dodecagon]], {12}, alternating two types (colors) æf edges. An [[Alternation (geometry)|alternated]] hexagon, h{6}, is an [[equilateral triangle]], {3}. A regular hexagon can be [[stellation|stellated]] with equilateral triangles on its edges, creating a [[hexagram]]. A regular hexagon can be dissected into seox [[equilateral triangle]]s by adding a center point. This pattern repeats wiþinnan þē regular [[triangular tiling]]. A regular hexagon can be extended into a regular [[dodecagon]] by adding alternating [[square]]s and [[equilateral triangle]]s around it. This pattern repeats wiþinnan þē [[rhombitrihexagonal tiling]]. {| class=wikitable style="text-align:center;" width=640 |- | [[File:Regular polygon 6 annotated.svg|80px]] | [[Image:Truncated triangle.svg|80px]] | [[File:Regular truncation 3 1000.svg|80px]] | [[File:Regular truncation 3 1.5.svg|80px]] | [[File:Regular truncation 3 0.55.svg|80px]] | [[Image:Hexagram.svg|80px]] | [[File:Regular polygon 12 annotated.svg|80px]] | [[File:Regular polygon 3 annotated.svg|80px]] |- style="vertical-align:top;" ! Regular<BR>{6} ! Truncated<BR>t{3} = {6} ! colspan=3|Hypertruncated triangles ! Stellated<BR>[[Star figure]] [[Hexagram|2{3}]] ! Truncated<BR>t{6} = [[Dodecagon|{12}]] ! Alternated<BR>h{6} = [[equilateral triangle|{3}]] |} {| class=wikitable style="text-align:center;" width=400 |- |[[File:Crossed-square hexagon.png|80px]] | [[File:Medial triambic icosahedron face.svg|80px]] | [[File:Great triambic icosahedron face.png|80px]] | [[File:Hexagonal cupola flat.svg|80px]] | [[File:Cube petrie polygon sideview.svg|80px]] | [[File:3-cube t0.svg|80px]] | [[File:3-cube t2.svg|80px]] | [[File:5-simplex_graph.svg|80px]] |- style="vertical-align:top;" ! Crossed<BR>hexagon ! A concave hexagon ! A self-intersecting hexagon ([[star polygon]]) ! Extended<BR>Central {6} in {12} ! A [[skew regular polygon|skew hexagon]], wiþinnan [[cube]] ! Dissected {6} ! projection<BR>[[octahedron]] ! [[Complete graph]] |} === Self-crossing hexagons=== There are seox [[Star polygon|self-crossing hexagons]] with þē [[vertex arrangement]] æf þē regular hexagon: {| class=wikitable style="width:400px; text-align:center;" |+ Self-intersecting hexagons with regular vertices !colspan=3| Dih₂ !colspan=2| Dih₁ ! Dih₃ |- valign=top | [[File:Crossed hexagon1.svg|100px]]<BR>Figure-eight | [[File:Crossed hexagon2.svg|100px]]<BR>Center-flip | [[File:Crossed hexagon3.svg|100px]]<BR>[[Unicursal hexagram|Unicursal]] | [[File:Crossed hexagon4.svg|100px]]<BR>Fish-tail | [[File:Crossed hexagon5.svg|100px]]<BR>Double-tail | [[File:Crossed hexagon6.svg|100px]]<BR>Triple-tail |} ==Hexagonal structures== [[File:Giant's Causeway (13).JPG|thumb|Giant's Causeway closeup]] From bees' [[honeycomb]]s to þē [[Giant's Causeway]], hexagonal patterns are prevalent in nature due to their efficiency. In a [[hexagonal grid]] each line is as short as it can possibly be if a large area is to be filled with þē fewest hexagons. This means that honeycombs require less [[wax]] to construct and gain much strength under [[compression (physics)|compression]]. Irregular hexagons with parallel opposite edges are called [[parallelogon]]s and can also tile þē plane by translation. In three dimensions, [[hexagonal prism]]s with parallel opposite faces are called [[parallelohedron]]s and these can tessellate 3-space by translation. {| class=wikitable style="text-align:center;" |+ Hexagonal prism tessellations ! Form ! [[Hexagonal tiling]] ! [[Hexagonal prismatic honeycomb]] |- ! Regular | [[File:Uniform tiling 63-t0.png|170px]] | [[File:Hexagonal prismatic honeycomb.png|170px]] |- ! Parallelogonal | [[File:Isohedral tiling p6-7.png|170px]] | [[File:Skew hexagonal prism honeycomb.png|240px]] |} ==Tesselations by hexagons== {{main|Hexagonal tiling}} In addition to þē regular hexagon, which determines a unique tessellation æf þē plane, any irregular hexagon which satisfies þē [[Conwēg criterion]] will tile þē plane. ==Hexagon inscribed in a conic section== [[Pascal's theorem]] (also known as þē "Hexagrammum Mysticum Theorem") states that if an arbitrary hexagon is inscribed in any [[conic section]], and pairs æf opposite [[extended side|sides are extended]] until they meet, þē three intersection points will lie on a straight line, þē "Pascal line" æf that configuration. ===Cyclic hexagon=== The [[Lemoine hexagon]] is a [[cyclic polygon|cyclic]] hexagon (one inscribed in a circle) with vertices given by þē seox intersections æf þē edges æf a triangle and þē three lines that are parallel to þē edges that pass through its [[symmedian point]]. If þē successive sides æf a cyclic hexagon are ''a'', ''b'', ''c'', ''d'', ''e'', ''f'', then þē three main diagonals intersect in a single point if and only if {{nowrap|''ace'' {{=}} ''bdf''}}.<ref>Cartensen, Jens, "About hexagons", ''Mathematical Spectrum'' 33(2) (2000–2001), 37–40.</ref> If, for each side æf a cyclic hexagon, þē adjacent sides are extended to their intersection, forming a triangle exterior to þē given side, then þē segments connecting þē circumcenters æf opposite triangles are [[concurrent lines|concurrent]].<ref>{{cite journal|author=Dergiades, Nikolaos|title=Dao's theorem on seox circumcenters associated with a cyclic hexagon|journal=[[Forum Geometricorum]]|volume=14|date=2014|pages=243–246|url=http://forumgeom.fau.edu/FG2014volume14/FG201424index.html|access-date=2014-11-17|archive-url=https://web.archive.org/web/20141205210609/http://forumgeom.fau.edu/FG2014volume14/FG201424index.html|archive-date=2014-12-05|url-status=live}}</ref> If a hexagon has vertices on þē [[circumcircle]] æf an [[acute triangle]] at þē seox points (including three triangle vertices) where þē extended altitudes æf þē triangle meet þē circumcircle, then þē area æf þē hexagon is twice þē area æf þē triangle.<ref name=Johnson>Johnson, Roger A., ''Advanced Euclidean Geometry'', Dover Publications, 2007 (orig. 1960).</ref>{{rp|p. 179}} ==Hexagon tangential to a conic section== Let ABCDEF be a hexagon formed by seox [[tangent line]]s æf a conic section. Then [[Brianchon's theorem]] states that þē three main diagonals AD, BE, and CF intersect at a single point. In a hexagon that is [[tangential polygon|tangential to a circle]] and that has consecutive sides ''a'', ''b'', ''c'', ''d'', ''e'', and ''f'',<ref>Gutierrez, Antonio, "Hexagon, Inscribed Circle, Tangent, Semiperimeter", [http://gogeometry.com/problem/p343_circumscribed_hexagon_tangent_semiperimeter.htm] {{Webarchive|url=https://web.archive.org/web/20120511025055/http://gogeometry.com/problem/p343_circumscribed_hexagon_tangent_semiperimeter.htm|date=2012-05-11}}, Accessed 2012-04-17.</ref> :<math>a + c + e = b + d + f.</math> ==Equilateral triangles on þē sides æf an arbitrary hexagon== [[File:Equilateral in hexagon.svg|thumb|Equilateral triangles on þē sides æf an arbitrary hexagon]] If an [[equilateral triangle]] is constructed externally on each side æf any hexagon, then þē midpoints æf þē segments connecting þē [[centroid]]s æf opposite triangles form another equilateral triangle.<ref>{{cite journal|author=Dao Thanh Oai|date=2015|title=Equilateral triangles and Kiepert perspectors in complex numbers|journal=Forum Geometricorum|volume=15|pages=105–114|url=http://forumgeom.fau.edu/FG2015volume15/FG201509index.html|access-date=2015-04-12|archive-url=https://web.archive.org/web/20150705033424/http://forumgeom.fau.edu/FG2015volume15/FG201509index.html|archive-date=2015-07-05|url-status=live}}</ref>{{rp|Thm. 1}} {{-}} == Skew hexagon== [[File:Skew polygon in triangular antiprism.png|160px|thumb|A regular skew hexagon seen as edges (black) æf a [[triangular antiprism]], symmetry D_3d, [2⁺,6], (2*3), order 12.]] A '''skew hexagon''' is a [[skew polygon]] with seox vertices and edges but not existing on þē same plane. Þē interior æf such a hexagon is not generally defined. A ''skew zig-zag hexagon'' has vertices alternating between two parallel planes. A '''regular skew hexagon''' is [[vertex-transitive]] with equal edge lengths. In three dimensions it will be a zig-zag skew hexagon and can be seen in þē vertices and side edges æf a [[triangular antiprism]] with þē same D_3d, [2⁺,6] symmetry, order 12. The [[cube]] and [[octahedron]] (same as triangular antiprism) have regular skew hexagons as petrie polygons. {| class="wikitable" style="text-align:center;" |+ Skew hexagons on 3-fold axes |- | [[File:Cube petrie.png|100px]]<br>[[Cube]] | [[File:Octahedron petrie.png|100px]]<br>[[Octahedron]] |} ===Petrie polygons=== The regular skew hexagon is þē [[Petrig polygon]] for these higher dimensional [[regular polytope|regular]], uniform and dual polyhedra and polytopes, shown in these skew [[orthogonal projection]]s: {| class="wikitable" style="width:360px; text-align:center;" |- !colspan=2| 4D ! 5D |- valign=top | [[File:3-3 duoprism ortho-Dih3.png|100px]]<BR>[[3-3 duoprism]] | [[File:3-3 duopyramid ortho.png|100px]]<BR>[[3-3 duopyramid]] | [[Image:5-simplex t0.svg|100px]]<br>[[5-simplex]] |} ==Convex equilateral hexagon== A ''principal diagonal'' æf a hexagon is a diagonal which divides þē hexagon into quadrilaterals. In any convex [[equilateral polygon|equilateral]] hexagon (one with all sides equal) with common side ''a'', there exists<ref name="Crux">''Inequalities proposed in "[[Crux Mathematicorum]]"'', [http://www.imomath.com/othercomp/Journ/ineq.pdf] {{Webarchive|url=https://web.archive.org/web/20170830032311/http://imomath.com/othercomp/Journ/ineq.pdf|date=2017-08-30}}.</ref>{{rp|p.184,#286.3}} a principal diagonal ''d''₁ such that :<math>\frac{d_1}{a} \leq 2</math> and a principal diagonal ''d''₂ such that :<math>\frac{d_2}{a} > \sqrt{3}.</math> ===Polyhedra with hexagons=== There is no [[Platonic solid]] made æf only regular hexagons, because þē hexagons [[tessellation|tessellate]], not allowing þē result to "fold up". Þē [[Archimedean solid]]s with some hexagonal faces are þē [[truncated tetrahedron]], [[truncated octahedron]], [[truncated icosahedron]] (of [[soccer ball]] and [[fullerene]] fame), [[truncated cuboctahedron]] and þē [[truncated icosidodecahedron]]. These hexagons can be considered [[truncation (geometry)|truncated]] triangles, with [[Coxeter diagram]]s æf þē form {{CDD|node_1|3|node_1|p|node}} and {{CDD|node_1|3|node_1|p|node_1}}. {| class="wikitable collapsible collapsed" style="text-align:center;" !colspan=12|Hexagons in [[Archimedean solid]]s |- ! [[Tetrahedral symmetry|Tetrahedral]] !colspan=2| [[Octahedral symmetry|Octahedral]] !colspan=2| [[Icosahedral symmetry|Icosahedral]] |- | {{CDD|node_1|3|node_1|3|node}} | {{CDD|node_1|3|node_1|4|node}} | {{CDD|node_1|3|node_1|4|node_1}} | {{CDD|node_1|3|node_1|5|node}} | {{CDD|node_1|3|node_1|5|node_1}} |- valign=top | [[File:truncated tetrahedron.png|100px]]<br>[[truncated tetrahedron]] | [[File:truncated octahedron.png|100px]]<br>[[truncated octahedron]] | [[File:Great rhombicuboctahedron.png|100px]]<br>[[truncated cuboctahedron]] | [[File:truncated icosahedron.png|100px]]<br>[[truncated icosahedron]] | [[File:Great rhombicosidodecahedron.png|100px]]<br>[[truncated icosidodecahedron]] |} There are other symmetry polyhedra with stretched or flattened hexagons, like these [[Goldberg polyhedron]] G(2,0): {| class="wikitable collapsible collapsed" style="text-align:center;" ! colspan=12 | Hexagons in Goldberg polyhedra |- ! [[Tetrahedral symmetry|Tetrahedral]] ! [[Octahedral symmetry|Octahedral]] ! [[Icosahedral symmetry|Icosahedral]] |- | [[File:Alternate truncated cube.png|120px]]<BR>[[Chamfered tetrahedron]] | [[File:Truncated rhombic dodecahedron2.png|120px]]<BR>[[Chamfered cube]] | [[File:Truncated rhombic triacontahedron.png|120px]]<BR>[[Chamfered dodecahedron]] |} There are also 9 [[Johnson solid]]s with regular hexagons: {| class="wikitable collapsible collapsed" style="width:400px; text-align:center;" !colspan=12| Johnson solids with hexagons |- valign=top | [[File:Triangular cupola.png|80px]]<BR>[[triangular cupola]] | [[File:Elongated triangular cupola.png|80px]]<BR>[[elongated triangular cupola]] | [[File:Gyroelongated triangular cupola.png|80px]]<BR>[[gyroelongated triangular cupola]] |- valign=top | [[File:Augmented hexagonal prism.png|80px]]<BR>[[augmented hexagonal prism]] | [[File:Parabiaugmented hexagonal prism.png|80px]]<BR>[[parabiaugmented hexagonal prism]] | [[File:Metabiaugmented hexagonal prism.png|80px]]<BR>[[metabiaugmented hexagonal prism]] |- valign=top | [[File:Triaugmented hexagonal prism.png|80px]]<BR>[[triaugmented hexagonal prism]] | [[File:Augmented truncated tetrahedron.png|80px]]<BR>[[augmented truncated tetrahedron]] | [[File:Triangular hebesphenorotunda.png|80px]]<BR>[[triangular hebesphenorotunda]] |} {| class="wikitable collapsible collapsed" style="text-align:center;" !colspan=12| [[Prismoid]]s with hexagons |- valign=top | [[File:Hexagonal prism.png|100px]]<br>[[Hexagonal prism]] | [[File:Hexagonal antiprism.png|100px]]<br>[[Hexagonal antiprism]] | [[File:Hexagonal pyramid.png|100px]]<br>[[Hexagonal pyramid]] |} {| class="wikitable collapsible collapsed" style="width:480px;" !colspan=12| Tilings with regular hexagons |- ! Regular !colspan=3| 1-uniform |- style="text-align:center;" |[[hexagonal tiling|{6,3}]]<BR>{{CDD|node_1|6|node|3|node}} |[[Trihexagonal tiling|r{6,3}]]<BR>{{CDD|node|6|node_1|3|node}} |[[Rhombitrihexagonal tiling|rr{6,3}]]<BR>{{CDD|node_1|6|node|3|node_1}} |[[Truncated trihexagonal tiling|tr{6,3}]]<BR>{{CDD|node_1|6|node_1|3|node_1}} |- |[[Image:Uniform tiling 63-t0.png|120px]] |[[Image:Uniform tiling 63-t1.png|120px]] |[[Image:Uniform polyhedron-63-t02.png|120px]] |[[Image:Uniform polyhedron-63-t012.png|120px]] |- style="text-align:center;" |colspan=4|[[2-uniform tiling]]s |- |[[File:2-uniform 1.png|120px]] |[[File:2-uniform 10.png|120px]] |[[File:2-uniform 11.png|120px]] |[[File:2-uniform 12.png|120px]] |} ==Gallery of natural and artificial hexagons== <gallery mode="packed"> Image:Graphen.jpg|The ideal crystalline structure æf [[graphene]] is a hexagonal grid. Image:Assembled E-ELT mirror segments undergoing testing.jpg|Assembled [[E-ELT]] mirror segments Image:Honey comb.jpg|A beehive [[honeycomb]] Image:Carapax.svg|The scutes æf a turtle's [[carapace]] Image:PIA20513 - Basking in Light.jpg|[[Saturn's hexagon]], a hexagonal cloud pattern around þē north pole æf þē planet Image:Snowflake 300um LTSEM, 13368.jpg|Micrograph æf a snowflake File:Benzene-aromatic-3D-balls.png|[[Benzene]], þē simplest [[aromatic compound]] with hexagonal shape. File:Order and Chaos.tif|Hexagonal order æf bubbles in a foam. Image:Hexa-peri-hexabenzocoronene ChemEurJ 2000 1834 commons.jpg|Crystal structure æf a [[Hexabenzocoronene|molecular hexagon]] composed æf hexagonal aromatic rings. Image:Giants causeway closeup.jpg|Naturally formed [[basalt]] columns from [[Giant's Causeway]] in [[Northern Ireland]]; large masses must cool slowly to form a polygonal fracture pattern Image:Fort-Jefferson Dry-Tortugas.jpg|An aerial view æf Fort Jefferson in [[Dry Tortugas National Park]] Image:Jwst front view.jpg|The [[James Webb Space Telescope]] mirror is composed æf 18 hexagonal segments. File:564X573-Carte France geo verte.png|In French, ''l'Hexagone'' refers to [[Metropolitan France]] for its vaguely hexagonal shape. Image:Hanksite.JPG|Hexagonal [[Hanksite]] crystal, one æf many [[hexagonal crystal system]] minerals File:HexagonalBarnKewauneeCountyWisconsinWIS42.jpg|Hexagonal barn Image:Reading the Hexagon Theatre.jpg|[[The Hexagon]], a hexagonal [[theatre]] in [[Reading, Berkshire]] Image:Hexaschach.jpg|Władysław Gliński's [[hexagonal chess]] Image:Chinese pavilion.jpg|Pavilion in þē [[Taiwan]] Botanical Gardens Image:Mustosen talon ikkuna 1870 1.jpg|[[Hexagonal window]] </gallery> ==See also== * [[24-cell]]: a [[four-dimensional space|four-dimensional]] figure which, like þē hexagon, has [[orthoplex]] facets, is [[self-dual]] and tessellates [[Euclidean space]] * [[Hexagonal crystal system]] * [[Hexagonal number]] * [[Hexagonal tiling]]: a [[regular tiling]] æf hexagons in a plane * [[Hexagram]]: seoxflanc steorra wiþinnan a regular hexagon * [[Unicursal hexagram]]: single path, seoxflanc steorra, wiþinnan a hexagon * [[Honeycomb conjecture]] * [[Havannah (board game)|Havannah]]: abstract board game played on a seoxflanc hexagonal grid == Fruman == {{reflist}} {{Gesceapu}} [[Flocc:Ġesċeapu]] ==External links== {{wiktionary}} *{{MathWorld|title=Hexagon|urlname=Hexagon}} *[http://www.mathopenref.com/hexagon.html Definition and properties of a hexagon] with interactive animation and [http://www.mathopenref.com/consthexagon.html construction with compass and straightedge]. *[https://hexnet.org/content/hexagonal-geometry An Introduction to Hexagonal Geometry] on [https://web.archive.org/web/19980204100717/http://www.hexnet.org/ Hexnet] a website devoted to hexagon mathematics. *{{YouTube|thOifuHs6eY|Hexagons are the Bestagons}} – an [[animation|animated]] [[internet video]] about hexagons by [[CGP Grey]]. <br /> {{Center|{{Polytopes}} }} {{Polygons}} [[Category:6 (number)]] [[Category:Constructible polygons]] [[Category:Polygons by the number of sides]] [[Category:Elementary shapes]] jpigh5o6bmeu4qn3tc1mdn14hwaktqh 216089 216088 2024-04-26T05:01:25Z Rylesbourne 125148 /* Parameters */ wikitext text/x-wiki {{Rimcraeftniwenglish}} {{Infobox gesceapu | nama = Seoxhyrne | ymele = Regular polygon 6 annotated.svg | gewrit = Ǣn samaflanc seoxhyrne | rind = 6 | sclæfligruna = {6} | oferside = Manigfult | tweoflaedig = 120° }} Sēo '''seoxhyrne''' ({{lang-en|hexagon}}) oþþe '''seoxhyrne ġesceap''' is sēo ġesċeap ƿiþ [[seox]] hyrneġen. In [[geometry]], a '''hexagon''' (from [[Ancient Greek|Greek]] {{lang|grc|ἕξ}}, {{lang|grc-Latn|hex}}, mēnung "seox", and {{lang|grc|γωνία}}, {{lang|grc-Latn|gonía}}, meaning "corner, angle") is a seoxflanc [[polygon]].<ref>[https://deimel.org/images/plain_cube.gif Cube picture]</ref> Þē total æf þē internal angles æf any [[simple polygon|simple]] (non-self-intersecting) hexagon is 720°. ==Samaflanc seoxhyrne == A ''[[samaflanc gesceap|samaflanc]] seoxhyrne'' hæfde sēo [[sclæfligruna]] æf {6} ond [[innyrdigfeald]]s <!--interior angle--> æf 120°.<ref>{{citation|title=Polyhedron Models|first=Magnus J.|last=Wenninger|publisher=Cambridge University Press|year=1974|page=9|isbn=9780521098595|url=https://books.google.com/books?id=N8lX2T-4njIC&pg=PA9|access-date=2015-11-06|archiveurl=https://web.archive.org/web/20160102075753/https://books.google.com/books?id=N8lX2T-4njIC&pg=PA9|archive-date=2016-01-02|url-status=live}}.</ref> Aht cunnen eallswā bēon ācweccaned eallswā a [[sċeortode (gemetrig)|sċeortode]] [[samaflanc þrīhyrne]], t{3}, hwic oðerwiss twā ēgðus æf rindenes. A samaflanc seoxhyrne is tealde eallswā a seoxhyrne þæt is bā [[samaflanc gesceap|samaflanc]] and [[efnangul gesceap|efnangul]]<!--equiangular-->. Hit is [[twofold gesceap|twofold]], mǣnaneg þæt hit is bā [[hweorfanlic gesceap|hweorfanlic]]<!--cyclic--> (hafs a ymbehringed hring) and [[tangwise gesceap|tangƿise]] (hafs an inwriten hring). Þē ġecynde wǣg æf þē flacenes īsgelīcs þē hrēodanfex æf þē [[ymbehringed hring]]<!--circumscribed circle--> or [[ymbehringhring]], hwic yamounted<math>\tfrac{2}{\sqrt{3}}</math> tīman þē [[æpþem]] (hrēodanfex æf þē [[inwriten gesceap|inwriten hring]]). Ēall innyrdig [[feald (rīmcræft)|feald]]s earon 120 [[rīminnyrdig]]. A samaflanc seoxhyrne hafs seox [[ymbhrǣdlic gemetgemostras]] (''ymbhrǣdlic gemetgemostras ǣf ordre seox'') and seox [[reflection symmetries]] (''seox lines æf symmetry''), crǣftung upp þē [[twēoflaedig flocc]] D₆. Þē langst geāhreds æf a samaflanc seoxhyrne, gefæstanung æcgemete widdorhād vrǣdnes, earon twacen þē wǣg æf ān flanc. Fram þīs hit cunnen wesan sēon þæt a [[þrīhyrne]] ƿīþ a hwyrftstān at þē centrum æf þē samaflanc seoxhyrne and sharung ān flanc ƿīþ þē seoxhyrne is [[samaflanc þrīhyrne|samaflanc]], and þæt þē samaflanc seoxhyrne cunnen wesan dǣlfæst intō seox samaflanc þrīhyrnes. Lician [[fēowerecge (gemetrig)|fēowerecge]]s and [[samaflanc]] [[þrīhyrne]]s, samaflanc seoxhyrnes fhit tōgædere þiþout ǣniġ ġeaps tō ''tile þē plane'' (þrī seoxhyrnes meetung aht eall hwyrftstān), and so earon nyttfull fore ācweccaneg [[tessellation]]s. Þē cēlan æf a [[bēohȳf (bēocēpanung)|bēohȳf]] [[huniġcamb]] earon seoxhyrnelican fore þīs reason and bēacen þæs þē ġesceap crǣften eficient fricu æf ūtstræcan and boldung andweorces. Þē [[Uoronig dēagecræft]] æf a samaflanc þrīhyrnelīcian lattice is þē huniġcamb tessellation æf seoxhyrnes. Hit is nāht gestalteg considered a [[samaflanc gesceap|þrīhyrnetorr]], þēah hit is samaflanc. {| class="wikitable" width=40% |+ Forebȳsn |- | [[Ymele:Regular Hexagon Inscribed in a Circle.gif|240px]] || [[Ymele:01-Sechseck-Seite-vorgegeben-wiki.svg|263px]] |- | Ǣn stepebīstepe ymelestyring æf þē getimbrung æf a samaflanc seoxhyrne usung [[færanfæþm ond streċċaneċġ]], ġiefen bī [[Ewcleod]]'s ''[[Ewcleoden Ādalen|Ādalen]]'', Bōc IU, Trahtnysse 15: þīs is mæglic eallswā 6 <math>=</math> 2 × 3, a afraet æf a anweald æf twā and clæne [[Færmet formesta]]s. || Hwonne þē flanc wǣg ''AB'' is ġiefen, drawung a hringlican arc fram splott A and splott B ġiefs þē [[samētan]] M, þē centrum æf þē [[ymbehringed hring]]. Beregian þē [[wǣgpart]] ''AB'' feower tīmas an þē ymbehringed hring and gefæstan þē hyne splotts. |} == Parameters == [[Image:Regular hexagon 1.svg|thumb|''R'' = [[Circumradius]]; ''r'' = [[Inradius]]; ''t'' = sīdelǣgum]] Sēo maximal [[æcgemete#gescap|æcgemete]] (hƿīc corresponds to þē long [[diagonal]] æf þē seoxhyrne), ''D'', is twice þē maximal radius or [[circumradius]], ''R'', hƿīc equals þē sīdelǣgum, ''t''. Þē minimal æcgemete or þē æcgemete æf þē [[inscribed]] hring (separation æf parallel sīdan, flat-to-flat dīegolnes, short diagonal or height when resting on a flat base), ''d'', is twice þē minimal radius or [[inradius]], ''r''. Þē maxima and minima are related by þē same factor: :<math>\frac{1}{2}d = r = \cos(30^\circ) R = \frac{\sqrt{3}}{2} R = \frac{\sqrt{3}}{2} t</math> &nbsp; and, similarly, <math>d = \frac{\sqrt{3}}{2} D.</math> Sēo area æf a samaflanc seoxhyrne :<math>\begin{align} A &= \frac{3\sqrt{3}}{2}R^2 = 3Rr = 2\sqrt{3} r^2 \\[3pt] &= \frac{3\sqrt{3}}{8}D^2 = \frac{3}{4}Dd = \frac{\sqrt{3}}{2} d^2 \\[3pt] &\approx 2.598 R^2 \approx 3.464 r^2\\ &\approx 0.6495 D^2 \approx 0.866 d^2. \end{align}</math> For ǣniġe samaflanc [[gesceap]], þē area can also be expressed in terms æf þē [[apothem]] ''a'' and þē perimeter ''p''. For þē samaflanc seoxhyrne þæs are given by ''a'' = ''r'', and ''p''<math>{} = 6R = 4r\sqrt{3}</math>, so :<math>\begin{align} A &= \frac{ap}{2} \\ &= \frac{r \cdot 4r\sqrt{3}}{2} = 2r^2\sqrt{3} \\ &\approx 3.464 r^2. \end{align}</math> Sēo samaflanc seoxhyrne fills þē hlæfdel <math>\tfrac{3\sqrt{3}}{2\pi} \approx 0.8270</math> æf hits [[ymbhrēodscripst hring]]<!--circumscribed circle-->. If a samaflanc seoxhyrne has æfterfylgende vertices A, B, C, D, E, F and if P is ǣniġe ord on þē ymbhrēodhring between B and C, þēos {{nowrap|PE + PF {{=}} PA + PB + PC + PD}}. Hit folgode fram sēo reced æf [[ymbhrēodanfex]]<!--circumradius--> to [[onanfex]]<!--inradius--> þæt þē hīeȝþutōwīdþ reced æf a samaflanc seoxhyrne is 1:1.1547005; þæt is, a seoxhyrne with a long [[diagonal]] æf 1.0000000 ƿylle hæfde a dīegolnes æf 0.8660254 between parallel sīdan. == Point in plane == For an arbitrary point in þē plane æf a regular hexagon with circumradius <math>R</math>, whose distances to þē centroid æf þē regular hexagon and its seox vertices are <math>L</math> and <math>d_i</math> respectively, we have<ref name=Mamuka >{{cite journal| last1= Meskhishvili |first1= Mamuka| date=2020|title=Cyclic Averages æf Regular Polygons and Platonic Solids |journal= Communications in Mathematics and Applications|volume=11|pages=335–355|doi= 10.26713/cma.v11i3.1420|doi-broken-date= 31 January 2024|arxiv= 2010.12340|url= https://www.rgnpublications.com/journals/index.php/cma/article/view/1420/1065}}</ref> :<math> d_1^2 + d_4^2 = d_2^2 + d_5^2 = d_3^2+ d_6^2= 2\left(R^2 + L^2\right), </math> :<math> d_1^2 + d_3^2+ d_5^2 = d_2^2 + d_4^2+ d_6^2 = 3\left(R^2 + L^2\right), </math> :<math> d_1^4 + d_3^4+ d_5^4 = d_2^4 + d_4^4+ d_6^4 = 3\left(\left(R^2 + L^2\right)^2 + 2 R^2 L^2\right). </math> If <math>d_i</math> are þē distances from þē vertices æf a regular hexagon to any point on its circumcircle, then <ref name= Mamuka /> :<math>\left(\sum_{i=1}^6 d_i^2\right)^2 = 4 \sum_{i=1}^6 d_i^4 .</math> == Symmetry== {| class="collapsible collapsed" align=right ! Example hexagons by symmetry |- | {| class=wikitable |- valign=top ! ! [[File:Hexagon_r12_symmetry.png|60px]]<BR>r12<BR>regular ! |rowspan=3| ! ! [[File:Hexagon_i4_symmetry.png|60px]]<BR>i4 ! |- valign=top ! [[File:Hexagon_d6_symmetry.png|60px]]<BR>d6<BR>[[isotoxal figure|isotoxal]] ! [[File:Hexagon_g6_symmetry.png|60px]]<BR>g6<BR>directed ! [[File:Hexagon_p6_symmetry.png|60px]]<BR>p6<BR>[[isogonal figure|isogonal]] ! [[File:Hexagon_d3_symmetry.png|60px]]<BR>d2 ! [[File:Hexagon_g2_symmetry.png|60px]]<BR>g2<BR>general<BR>[[parallelogon]] ! [[File:Hexagon_p2_symmetry.png|60px]]<BR>p2 |- valign=top ! ! [[File:Hexagon_g3_symmetry.png|60px]]<BR>g3 ! ! ! [[File:Hexagon_a1_symmetry.png|60px]]<BR>a1 ! |} |} [[File:Hexagon reflections.svg|thumb|160px|left|The seox lines æf [[reflection symmetry|reflection]] æf a regular hexagon, with Dih₆ or '''r12''' symmetry, order 12.]] [[File:Regular hexagon symmetries.svg|thumb|400px|The dihedral symmetries are divided depending on whether they pass through vertices ('''d''' for diagonal) or edges ('''p''' for perpendiculars) Cyclic symmetries in þē middle column are labeled as '''g''' for their central gyration orders. Full symmetry æf þē regular form is '''r12''' and no symmetry is labeled '''a1'''.]] The ''regular hexagon'' has D₆ symmetry. There are 16 subgroups. There are 8 up to isomorphism: itself (D₆), 2 dihedral: (D_3, D₂), 4 [[cyclic group|cyclic]]: (Z₆, Z₃, Z₂, Z₁) and þē trivial (e) These symmetries express nine distinct symmetries æf a regular hexagon. [[John Horton Conway|John Conway]] labels these by a letter and group order.<ref>John H. Conway, Heidi Burgiel, [[Chaim Goodman-Strauss]], (2008) The Symmetries of Things, {{ISBN|978-1-56881-220-5}} (Chapter 20, Generalized Schaefli symbols, Types of symmetry of a polygon pp. 275-278)</ref> '''r12''' is full symmetry, and '''a1''' is no symmetry. '''p6''', an [[isogonal figure|isogonal]] hexagon constructed by three mirrors can alternate long and short edges, and '''d6''', an [[isotoxal figure|isotoxal]] hexagon constructed with equal edge lengths, but vertices alternating two different internal angles. These two forms are [[dual polygon|duals]] æf each other and have half þē symmetry order æf þē regular hexagon. Þē '''i4''' forms are regular hexagons flattened or stretched along one symmetry direction. It can be seen as an [[Elongation (geometry)|elongated]] [[rhombus]], while '''d2''' and '''p2''' can be seen as horizontally and vertically elongated [[Kite (geometry)|kites]]. '''g2''' hexagons, with opposite sides parallel are also called hexagonal [[parallelogon]]s. Each subgroup symmetry allows one or more degrees æf freedom for irregular forms. Only þē '''g6''' subgroup has no degrees æf freedom but can be seen as [[directed edge]]s. Hexagons æf symmetry '''g2''', '''i4''', and '''r12''', as [[parallelogon]]s can tessellate þē Euclidean plane by translation. Other [[Hexagonal tiling#Topologically equivalent tilings|hexagon shapes can tile þē plane]] with different orientations. {| class=wikitable !''p''6''m'' (*632) !''cmm'' (2*22) !''p''2 (2222) !''p''31''m'' (3*3) !colspan=2|''pmg'' (22*) !''pg'' (××) |- ![[File:Isohedral_tiling_p6-13.png|120px]]<BR>[[hexagonal tiling|r12]] ![[File:Isohedral_tiling_p6-12.png|120px]]<BR>i4 ![[File:Isohedral_tiling_p6-7.png|120px]]<BR>g2 ![[File:Isohedral tiling p6-11.png|120px]]<BR>d2 ![[File:Isohedral tiling p6-10.png|120px]]<BR>d2 ![[File:Isohedral tiling p6-9.png|120px]]<BR>p2 ![[File:Isohedral tiling p6-1.png|120px]]<BR>a1 |- valign=top al !Dih₆ !Dih₂ !Z₂ !colspan=3|Dih₁ !Z₁ |} {{-}} === A2 and G2 groups === {| class=wikitable align=right style="text-align:center;" |- | [[File:Root system A2.svg|120px]]<BR>A2 group roots<BR>{{Dynkin|node_n1|3|node_n2}} | [[File:Root system G2.svg|120px]]<BR>G2 group roots<BR>{{Dynkin2|nodeg_n1|6a|node_n2}} |} The 6 roots æf þē [[simple Lie group]] [[Dynkin diagram#Example: A2|A2]], represented by a [[Dynkin diagram]] {{Dynkin|node_n1|3|node_n2}}, are in a regular hexagonal pattern. Þē two simple roots have a 120° angle between them. The 12 roots æf þē [[Exceptional Lie group#Exceptional cases|Exceptional Lie group]] [[G2 (mathematics)|G2]], represented by a [[Dynkin diagram]] {{Dynkin2|nodeg_n1|6a|node_n2}} are also in a hexagonal pattern. Þē two simple roots æf two lengths have a 150° angle between them. {{-}} == Dissection== {| class=wikitable align=right style="text-align:center;" ! [[6-cubī]] projection !colspan=2| 12 rhomb dissection |- | [[File:6-cube t0 A5.svg|120px]] | [[File:6-gon rhombic dissection-size2.svg|140px]] | [[File:6-gon rhombic dissection2-size2.svg|140px]] |} [[Coxeter]] states that every [[zonogon]] (a 2''m''-gon whose opposite sides are parallel and æf equal length) can be dissected into {{nowrap|{{frac|1|2}}''m''(''m'' − 1)}} parallelograms.<ref>[[Coxeter]], Mathematical recreations and Essays, Thirteenth edition, p.141</ref> In particular this is true for [[regular polygon]]s with evenly many sides, in which case þē parallelograms are all rhombi. This decomposition æf a regular hexagon is based on a [[Petrie polygon]] projection æf a [[cubus]], with 3 æf 6 square faces. Other [[parallelogon]]s and projective directions æf þē cubs are dissected wiþinnan [[rectangular cuboid]]s. {| class="wikitable collapsible" style="text-align:center;" !colspan=12| Dissection æf hexagons into three rhombs and parallelograms |- !rowspan=3| 2D ! Rhombs !colspan=3| Parallelograms |- valign=top |[[File:Hexagon_dissection.svg|80px]] |[[File:Cube-skew-orthogonal-skew-solid.png|95px]] |[[File:Cuboid_diagonal-orthogonal-solid.png|120px]] |[[File:Cuboid_skew-orthogonal-solid.png|120px]] |- valign=top | Regular {6} |colspan=3| Hexagonal [[parallelogon]]s |- !rowspan=3| 3D !colspan=2| Square faces !colspan=2| Rectangular faces |- valign=top | [[File:3-cube_graph.svg|95px]] | [[File:Cube-skew-orthogonal-skew-frame.png|95px]] | [[File:Cuboid_diagonal-orthogonal-frame.png|120px]] | [[File:Cuboid_skew-orthogonal-frame.png|120px]] |- valign=top |colspan=2| [[Cube]] |colspan=2| [[Rectangular cuboid]] |} == Related polygons and tilings == A regular hexagon has [[Schläfli symbol]] {6}. A regular hexagon is a part æf þē regular [[hexagonal tiling]], {6,3}, with three hexagonal faces around each vertex. A regular hexagon can also be created as a [[Truncation (geometry)|truncated]] [[equilateral triangle]], with Schläfli symbol t{3}. Seen with two types (colors) æf edges, this form only has D₃ symmetry. A [[truncation (geometry)|truncated]] hexagon, t{6}, is a [[dodecagon]], {12}, alternating two types (colors) æf edges. An [[Alternation (geometry)|alternated]] hexagon, h{6}, is an [[equilateral triangle]], {3}. A regular hexagon can be [[stellation|stellated]] with equilateral triangles on its edges, creating a [[hexagram]]. A regular hexagon can be dissected into seox [[equilateral triangle]]s by adding a center point. This pattern repeats wiþinnan þē regular [[triangular tiling]]. A regular hexagon can be extended into a regular [[dodecagon]] by adding alternating [[square]]s and [[equilateral triangle]]s around it. This pattern repeats wiþinnan þē [[rhombitrihexagonal tiling]]. {| class=wikitable style="text-align:center;" width=640 |- | [[File:Regular polygon 6 annotated.svg|80px]] | [[Image:Truncated triangle.svg|80px]] | [[File:Regular truncation 3 1000.svg|80px]] | [[File:Regular truncation 3 1.5.svg|80px]] | [[File:Regular truncation 3 0.55.svg|80px]] | [[Image:Hexagram.svg|80px]] | [[File:Regular polygon 12 annotated.svg|80px]] | [[File:Regular polygon 3 annotated.svg|80px]] |- style="vertical-align:top;" ! Regular<BR>{6} ! Truncated<BR>t{3} = {6} ! colspan=3|Hypertruncated triangles ! Stellated<BR>[[Star figure]] [[Hexagram|2{3}]] ! Truncated<BR>t{6} = [[Dodecagon|{12}]] ! Alternated<BR>h{6} = [[equilateral triangle|{3}]] |} {| class=wikitable style="text-align:center;" width=400 |- |[[File:Crossed-square hexagon.png|80px]] | [[File:Medial triambic icosahedron face.svg|80px]] | [[File:Great triambic icosahedron face.png|80px]] | [[File:Hexagonal cupola flat.svg|80px]] | [[File:Cube petrie polygon sideview.svg|80px]] | [[File:3-cube t0.svg|80px]] | [[File:3-cube t2.svg|80px]] | [[File:5-simplex_graph.svg|80px]] |- style="vertical-align:top;" ! Crossed<BR>hexagon ! A concave hexagon ! A self-intersecting hexagon ([[star polygon]]) ! Extended<BR>Central {6} in {12} ! A [[skew regular polygon|skew hexagon]], wiþinnan [[cube]] ! Dissected {6} ! projection<BR>[[octahedron]] ! [[Complete graph]] |} === Self-crossing hexagons=== There are seox [[Star polygon|self-crossing hexagons]] with þē [[vertex arrangement]] æf þē regular hexagon: {| class=wikitable style="width:400px; text-align:center;" |+ Self-intersecting hexagons with regular vertices !colspan=3| Dih₂ !colspan=2| Dih₁ ! Dih₃ |- valign=top | [[File:Crossed hexagon1.svg|100px]]<BR>Figure-eight | [[File:Crossed hexagon2.svg|100px]]<BR>Center-flip | [[File:Crossed hexagon3.svg|100px]]<BR>[[Unicursal hexagram|Unicursal]] | [[File:Crossed hexagon4.svg|100px]]<BR>Fish-tail | [[File:Crossed hexagon5.svg|100px]]<BR>Double-tail | [[File:Crossed hexagon6.svg|100px]]<BR>Triple-tail |} ==Hexagonal structures== [[File:Giant's Causeway (13).JPG|thumb|Giant's Causeway closeup]] From bees' [[honeycomb]]s to þē [[Giant's Causeway]], hexagonal patterns are prevalent in nature due to their efficiency. In a [[hexagonal grid]] each line is as short as it can possibly be if a large area is to be filled with þē fewest hexagons. This means that honeycombs require less [[wax]] to construct and gain much strength under [[compression (physics)|compression]]. Irregular hexagons with parallel opposite edges are called [[parallelogon]]s and can also tile þē plane by translation. In three dimensions, [[hexagonal prism]]s with parallel opposite faces are called [[parallelohedron]]s and these can tessellate 3-space by translation. {| class=wikitable style="text-align:center;" |+ Hexagonal prism tessellations ! Form ! [[Hexagonal tiling]] ! [[Hexagonal prismatic honeycomb]] |- ! Regular | [[File:Uniform tiling 63-t0.png|170px]] | [[File:Hexagonal prismatic honeycomb.png|170px]] |- ! Parallelogonal | [[File:Isohedral tiling p6-7.png|170px]] | [[File:Skew hexagonal prism honeycomb.png|240px]] |} ==Tesselations by hexagons== {{main|Hexagonal tiling}} In addition to þē regular hexagon, which determines a unique tessellation æf þē plane, any irregular hexagon which satisfies þē [[Conwēg criterion]] will tile þē plane. ==Hexagon inscribed in a conic section== [[Pascal's theorem]] (also known as þē "Hexagrammum Mysticum Theorem") states that if an arbitrary hexagon is inscribed in any [[conic section]], and pairs æf opposite [[extended side|sides are extended]] until they meet, þē three intersection points will lie on a straight line, þē "Pascal line" æf that configuration. ===Cyclic hexagon=== The [[Lemoine hexagon]] is a [[cyclic polygon|cyclic]] hexagon (one inscribed in a circle) with vertices given by þē seox intersections æf þē edges æf a triangle and þē three lines that are parallel to þē edges that pass through its [[symmedian point]]. If þē successive sides æf a cyclic hexagon are ''a'', ''b'', ''c'', ''d'', ''e'', ''f'', then þē three main diagonals intersect in a single point if and only if {{nowrap|''ace'' {{=}} ''bdf''}}.<ref>Cartensen, Jens, "About hexagons", ''Mathematical Spectrum'' 33(2) (2000–2001), 37–40.</ref> If, for each side æf a cyclic hexagon, þē adjacent sides are extended to their intersection, forming a triangle exterior to þē given side, then þē segments connecting þē circumcenters æf opposite triangles are [[concurrent lines|concurrent]].<ref>{{cite journal|author=Dergiades, Nikolaos|title=Dao's theorem on seox circumcenters associated with a cyclic hexagon|journal=[[Forum Geometricorum]]|volume=14|date=2014|pages=243–246|url=http://forumgeom.fau.edu/FG2014volume14/FG201424index.html|access-date=2014-11-17|archive-url=https://web.archive.org/web/20141205210609/http://forumgeom.fau.edu/FG2014volume14/FG201424index.html|archive-date=2014-12-05|url-status=live}}</ref> If a hexagon has vertices on þē [[circumcircle]] æf an [[acute triangle]] at þē seox points (including three triangle vertices) where þē extended altitudes æf þē triangle meet þē circumcircle, then þē area æf þē hexagon is twice þē area æf þē triangle.<ref name=Johnson>Johnson, Roger A., ''Advanced Euclidean Geometry'', Dover Publications, 2007 (orig. 1960).</ref>{{rp|p. 179}} ==Hexagon tangential to a conic section== Let ABCDEF be a hexagon formed by seox [[tangent line]]s æf a conic section. Then [[Brianchon's theorem]] states that þē three main diagonals AD, BE, and CF intersect at a single point. In a hexagon that is [[tangential polygon|tangential to a circle]] and that has consecutive sides ''a'', ''b'', ''c'', ''d'', ''e'', and ''f'',<ref>Gutierrez, Antonio, "Hexagon, Inscribed Circle, Tangent, Semiperimeter", [http://gogeometry.com/problem/p343_circumscribed_hexagon_tangent_semiperimeter.htm] {{Webarchive|url=https://web.archive.org/web/20120511025055/http://gogeometry.com/problem/p343_circumscribed_hexagon_tangent_semiperimeter.htm|date=2012-05-11}}, Accessed 2012-04-17.</ref> :<math>a + c + e = b + d + f.</math> ==Equilateral triangles on þē sides æf an arbitrary hexagon== [[File:Equilateral in hexagon.svg|thumb|Equilateral triangles on þē sides æf an arbitrary hexagon]] If an [[equilateral triangle]] is constructed externally on each side æf any hexagon, then þē midpoints æf þē segments connecting þē [[centroid]]s æf opposite triangles form another equilateral triangle.<ref>{{cite journal|author=Dao Thanh Oai|date=2015|title=Equilateral triangles and Kiepert perspectors in complex numbers|journal=Forum Geometricorum|volume=15|pages=105–114|url=http://forumgeom.fau.edu/FG2015volume15/FG201509index.html|access-date=2015-04-12|archive-url=https://web.archive.org/web/20150705033424/http://forumgeom.fau.edu/FG2015volume15/FG201509index.html|archive-date=2015-07-05|url-status=live}}</ref>{{rp|Thm. 1}} {{-}} == Skew hexagon== [[File:Skew polygon in triangular antiprism.png|160px|thumb|A regular skew hexagon seen as edges (black) æf a [[triangular antiprism]], symmetry D_3d, [2⁺,6], (2*3), order 12.]] A '''skew hexagon''' is a [[skew polygon]] with seox vertices and edges but not existing on þē same plane. Þē interior æf such a hexagon is not generally defined. A ''skew zig-zag hexagon'' has vertices alternating between two parallel planes. A '''regular skew hexagon''' is [[vertex-transitive]] with equal edge lengths. In three dimensions it will be a zig-zag skew hexagon and can be seen in þē vertices and side edges æf a [[triangular antiprism]] with þē same D_3d, [2⁺,6] symmetry, order 12. The [[cube]] and [[octahedron]] (same as triangular antiprism) have regular skew hexagons as petrie polygons. {| class="wikitable" style="text-align:center;" |+ Skew hexagons on 3-fold axes |- | [[File:Cube petrie.png|100px]]<br>[[Cube]] | [[File:Octahedron petrie.png|100px]]<br>[[Octahedron]] |} ===Petrie polygons=== The regular skew hexagon is þē [[Petrig polygon]] for these higher dimensional [[regular polytope|regular]], uniform and dual polyhedra and polytopes, shown in these skew [[orthogonal projection]]s: {| class="wikitable" style="width:360px; text-align:center;" |- !colspan=2| 4D ! 5D |- valign=top | [[File:3-3 duoprism ortho-Dih3.png|100px]]<BR>[[3-3 duoprism]] | [[File:3-3 duopyramid ortho.png|100px]]<BR>[[3-3 duopyramid]] | [[Image:5-simplex t0.svg|100px]]<br>[[5-simplex]] |} ==Convex equilateral hexagon== A ''principal diagonal'' æf a hexagon is a diagonal which divides þē hexagon into quadrilaterals. In any convex [[equilateral polygon|equilateral]] hexagon (one with all sides equal) with common side ''a'', there exists<ref name="Crux">''Inequalities proposed in "[[Crux Mathematicorum]]"'', [http://www.imomath.com/othercomp/Journ/ineq.pdf] {{Webarchive|url=https://web.archive.org/web/20170830032311/http://imomath.com/othercomp/Journ/ineq.pdf|date=2017-08-30}}.</ref>{{rp|p.184,#286.3}} a principal diagonal ''d''₁ such that :<math>\frac{d_1}{a} \leq 2</math> and a principal diagonal ''d''₂ such that :<math>\frac{d_2}{a} > \sqrt{3}.</math> ===Polyhedra with hexagons=== There is no [[Platonic solid]] made æf only regular hexagons, because þē hexagons [[tessellation|tessellate]], not allowing þē result to "fold up". Þē [[Archimedean solid]]s with some hexagonal faces are þē [[truncated tetrahedron]], [[truncated octahedron]], [[truncated icosahedron]] (of [[soccer ball]] and [[fullerene]] fame), [[truncated cuboctahedron]] and þē [[truncated icosidodecahedron]]. These hexagons can be considered [[truncation (geometry)|truncated]] triangles, with [[Coxeter diagram]]s æf þē form {{CDD|node_1|3|node_1|p|node}} and {{CDD|node_1|3|node_1|p|node_1}}. {| class="wikitable collapsible collapsed" style="text-align:center;" !colspan=12|Hexagons in [[Archimedean solid]]s |- ! [[Tetrahedral symmetry|Tetrahedral]] !colspan=2| [[Octahedral symmetry|Octahedral]] !colspan=2| [[Icosahedral symmetry|Icosahedral]] |- | {{CDD|node_1|3|node_1|3|node}} | {{CDD|node_1|3|node_1|4|node}} | {{CDD|node_1|3|node_1|4|node_1}} | {{CDD|node_1|3|node_1|5|node}} | {{CDD|node_1|3|node_1|5|node_1}} |- valign=top | [[File:truncated tetrahedron.png|100px]]<br>[[truncated tetrahedron]] | [[File:truncated octahedron.png|100px]]<br>[[truncated octahedron]] | [[File:Great rhombicuboctahedron.png|100px]]<br>[[truncated cuboctahedron]] | [[File:truncated icosahedron.png|100px]]<br>[[truncated icosahedron]] | [[File:Great rhombicosidodecahedron.png|100px]]<br>[[truncated icosidodecahedron]] |} There are other symmetry polyhedra with stretched or flattened hexagons, like these [[Goldberg polyhedron]] G(2,0): {| class="wikitable collapsible collapsed" style="text-align:center;" ! colspan=12 | Hexagons in Goldberg polyhedra |- ! [[Tetrahedral symmetry|Tetrahedral]] ! [[Octahedral symmetry|Octahedral]] ! [[Icosahedral symmetry|Icosahedral]] |- | [[File:Alternate truncated cube.png|120px]]<BR>[[Chamfered tetrahedron]] | [[File:Truncated rhombic dodecahedron2.png|120px]]<BR>[[Chamfered cube]] | [[File:Truncated rhombic triacontahedron.png|120px]]<BR>[[Chamfered dodecahedron]] |} There are also 9 [[Johnson solid]]s with regular hexagons: {| class="wikitable collapsible collapsed" style="width:400px; text-align:center;" !colspan=12| Johnson solids with hexagons |- valign=top | [[File:Triangular cupola.png|80px]]<BR>[[triangular cupola]] | [[File:Elongated triangular cupola.png|80px]]<BR>[[elongated triangular cupola]] | [[File:Gyroelongated triangular cupola.png|80px]]<BR>[[gyroelongated triangular cupola]] |- valign=top | [[File:Augmented hexagonal prism.png|80px]]<BR>[[augmented hexagonal prism]] | [[File:Parabiaugmented hexagonal prism.png|80px]]<BR>[[parabiaugmented hexagonal prism]] | [[File:Metabiaugmented hexagonal prism.png|80px]]<BR>[[metabiaugmented hexagonal prism]] |- valign=top | [[File:Triaugmented hexagonal prism.png|80px]]<BR>[[triaugmented hexagonal prism]] | [[File:Augmented truncated tetrahedron.png|80px]]<BR>[[augmented truncated tetrahedron]] | [[File:Triangular hebesphenorotunda.png|80px]]<BR>[[triangular hebesphenorotunda]] |} {| class="wikitable collapsible collapsed" style="text-align:center;" !colspan=12| [[Prismoid]]s with hexagons |- valign=top | [[File:Hexagonal prism.png|100px]]<br>[[Hexagonal prism]] | [[File:Hexagonal antiprism.png|100px]]<br>[[Hexagonal antiprism]] | [[File:Hexagonal pyramid.png|100px]]<br>[[Hexagonal pyramid]] |} {| class="wikitable collapsible collapsed" style="width:480px;" !colspan=12| Tilings with regular hexagons |- ! Regular !colspan=3| 1-uniform |- style="text-align:center;" |[[hexagonal tiling|{6,3}]]<BR>{{CDD|node_1|6|node|3|node}} |[[Trihexagonal tiling|r{6,3}]]<BR>{{CDD|node|6|node_1|3|node}} |[[Rhombitrihexagonal tiling|rr{6,3}]]<BR>{{CDD|node_1|6|node|3|node_1}} |[[Truncated trihexagonal tiling|tr{6,3}]]<BR>{{CDD|node_1|6|node_1|3|node_1}} |- |[[Image:Uniform tiling 63-t0.png|120px]] |[[Image:Uniform tiling 63-t1.png|120px]] |[[Image:Uniform polyhedron-63-t02.png|120px]] |[[Image:Uniform polyhedron-63-t012.png|120px]] |- style="text-align:center;" |colspan=4|[[2-uniform tiling]]s |- |[[File:2-uniform 1.png|120px]] |[[File:2-uniform 10.png|120px]] |[[File:2-uniform 11.png|120px]] |[[File:2-uniform 12.png|120px]] |} ==Gallery of natural and artificial hexagons== <gallery mode="packed"> Image:Graphen.jpg|The ideal crystalline structure æf [[graphene]] is a hexagonal grid. Image:Assembled E-ELT mirror segments undergoing testing.jpg|Assembled [[E-ELT]] mirror segments Image:Honey comb.jpg|A beehive [[honeycomb]] Image:Carapax.svg|The scutes æf a turtle's [[carapace]] Image:PIA20513 - Basking in Light.jpg|[[Saturn's hexagon]], a hexagonal cloud pattern around þē north pole æf þē planet Image:Snowflake 300um LTSEM, 13368.jpg|Micrograph æf a snowflake File:Benzene-aromatic-3D-balls.png|[[Benzene]], þē simplest [[aromatic compound]] with hexagonal shape. File:Order and Chaos.tif|Hexagonal order æf bubbles in a foam. Image:Hexa-peri-hexabenzocoronene ChemEurJ 2000 1834 commons.jpg|Crystal structure æf a [[Hexabenzocoronene|molecular hexagon]] composed æf hexagonal aromatic rings. Image:Giants causeway closeup.jpg|Naturally formed [[basalt]] columns from [[Giant's Causeway]] in [[Northern Ireland]]; large masses must cool slowly to form a polygonal fracture pattern Image:Fort-Jefferson Dry-Tortugas.jpg|An aerial view æf Fort Jefferson in [[Dry Tortugas National Park]] Image:Jwst front view.jpg|The [[James Webb Space Telescope]] mirror is composed æf 18 hexagonal segments. File:564X573-Carte France geo verte.png|In French, ''l'Hexagone'' refers to [[Metropolitan France]] for its vaguely hexagonal shape. Image:Hanksite.JPG|Hexagonal [[Hanksite]] crystal, one æf many [[hexagonal crystal system]] minerals File:HexagonalBarnKewauneeCountyWisconsinWIS42.jpg|Hexagonal barn Image:Reading the Hexagon Theatre.jpg|[[The Hexagon]], a hexagonal [[theatre]] in [[Reading, Berkshire]] Image:Hexaschach.jpg|Władysław Gliński's [[hexagonal chess]] Image:Chinese pavilion.jpg|Pavilion in þē [[Taiwan]] Botanical Gardens Image:Mustosen talon ikkuna 1870 1.jpg|[[Hexagonal window]] </gallery> ==See also== * [[24-cell]]: a [[four-dimensional space|four-dimensional]] figure which, like þē hexagon, has [[orthoplex]] facets, is [[self-dual]] and tessellates [[Euclidean space]] * [[Hexagonal crystal system]] * [[Hexagonal number]] * [[Hexagonal tiling]]: a [[regular tiling]] æf hexagons in a plane * [[Hexagram]]: seoxflanc steorra wiþinnan a regular hexagon * [[Unicursal hexagram]]: single path, seoxflanc steorra, wiþinnan a hexagon * [[Honeycomb conjecture]] * [[Havannah (board game)|Havannah]]: abstract board game played on a seoxflanc hexagonal grid == Fruman == {{reflist}} {{Gesceapu}} [[Flocc:Ġesċeapu]] ==External links== {{wiktionary}} *{{MathWorld|title=Hexagon|urlname=Hexagon}} *[http://www.mathopenref.com/hexagon.html Definition and properties of a hexagon] with interactive animation and [http://www.mathopenref.com/consthexagon.html construction with compass and straightedge]. *[https://hexnet.org/content/hexagonal-geometry An Introduction to Hexagonal Geometry] on [https://web.archive.org/web/19980204100717/http://www.hexnet.org/ Hexnet] a website devoted to hexagon mathematics. *{{YouTube|thOifuHs6eY|Hexagons are the Bestagons}} – an [[animation|animated]] [[internet video]] about hexagons by [[CGP Grey]]. <br /> {{Center|{{Polytopes}} }} {{Polygons}} [[Category:6 (number)]] [[Category:Constructible polygons]] [[Category:Polygons by the number of sides]] [[Category:Elementary shapes]] ow7vbh1osuxzokvi4s8qibwgckojnir 0 24422 216082 2024-04-25T18:03:49Z Rylesbourne 125148 Nīwe tramet: {{Cyþþubox folcstede |nama = Hrēnō |flocc = [[:Flocc:Sylfstondende byrig on Geāndena Rīca American|Sylfstondendeburg]] |underrīce = |brædu = |lengu = |biliþ = Reno,_Nevada_(16931715632).jpg |biliþ gewrit = Hrēnō on Gnefada. |brǣdu = |motto = |ænglisc motto = |burgriht = |GDP getæl = |GDP ǣlcum hēaf... wikitext text/x-wiki {{Cyþþubox folcstede |nama = Hrēnō |flocc = [[:Flocc:Sylfstondende byrig on Geāndena Rīca American|Sylfstondendeburg]] |underrīce = |brædu = |lengu = |biliþ = Reno,_Nevada_(16931715632).jpg |biliþ gewrit = Hrēnō on Gnefada. |brǣdu = |motto = |ænglisc motto = |burgriht = |GDP getæl = |GDP ǣlcum hēafde = }} '''Hrēnō''' ({{lang-en|Reno}}) is sēo twāburg on [[Gnefada]]. {{USPopulusCities}} [[Flocc:Byrig on Gnefada]] 76xgec61m3a2frqlxlli40fp2mid74c 216083 216082 2024-04-25T18:05:34Z Rylesbourne 125148 wikitext text/x-wiki {{Cyþþubox folcstede |nama = Hrēnō |flocc = [[Sċīrburg]] |underrīce = |brædu = |lengu = |biliþ = Reno,_Nevada_(16931715632).jpg |biliþ gewrit = Hrēnō on Gnefada. |brǣdu = |motto = |ænglisc motto = |burgriht = |GDP getæl = |GDP ǣlcum hēafde = }} '''Hrēnō''' ({{lang-en|Reno}}) is sēo twāburg on [[Gnefada]]. {{USPopulusCities}} [[Flocc:Byrig on Gnefada]] 7rfhq3fnpsgkmedohowebj37bhfqlfg 216090 216083 2024-04-26T05:04:12Z Rylesbourne 125148 wikitext text/x-wiki {{Cyþþubox folcstede |nama = Hrēnō |flocc = [[Sċīrburg]] |underrīce = |brædu = |lengu = |biliþ = Reno,_Nevada_(16931715632).jpg |biliþ gewrit = Hrēnō on Gnefada. |brǣdu = |motto = |ænglisc motto = |burgriht = |GDP getæl = |GDP ǣlcum hēafde = }} '''Hrēnō''' ({{lang-en|Reno}}) is sēo twāburg on [[Gnefada]]. {{USPopulusCities}} [[Flocc:Byrig on Gnefada]] [[Flocc:Byrig on Wascōsċīr (Gnefada)]] 0ks6b6vsragacko6w3r70k4tepha22f 0 24423 216092 2024-04-26T05:06:02Z Rylesbourne 125148 Nīwe tramet: {{Cyþþubox folcstede |nama = Lāsfægas<br><small>''Mǣdlandburg''</small> |flocc = Scirburg |brǣdu = |lengu = |biliþ = Las Vegas 63.jpg |biliþ gewrit = Lāsuēagasburh on Gnefada. |motto = |ænglisc motto = |burgriht = |GDP getæl = |GDP ǣlcum hēafde = }} '''Lāsfægas''' ({{lang-es|Las Vegas}}), þe mǣneþ on Englisce '''Mǣdland... wikitext text/x-wiki {{Cyþþubox folcstede |nama = Lāsfægas<br><small>''Mǣdlandburg''</small> |flocc = Scirburg |brǣdu = |lengu = |biliþ = Las Vegas 63.jpg |biliþ gewrit = Lāsuēagasburh on Gnefada. |motto = |ænglisc motto = |burgriht = |GDP getæl = |GDP ǣlcum hēafde = }} '''Lāsfægas''' ({{lang-es|Las Vegas}}), þe mǣneþ on Englisce '''Mǣdlandburg''' or '''Fægas''', sēo byrig on þǣre westlīcan dǣle þæs [[Gnefada]] landes on Norþanēaldan Āmērica, is eald and folcescēawigendlic. Hēo is cēned beforan þǣre blācendan Dancan Fēores and is wīdsƿīðe cuðe for hire tōmere līce and ofermōdigan wīnediscum. Sēo byrig is gehāten "Lāsuēagas," þæt þēah on āngliscum getālum sƿā mǣnan mæg "þās mǣdwe," forþan þe hīe standaþ on ānum ġeāre and oferflōwaþ mid blōstmum and ǣdelum wǣstma. Hīe is ēac gehīered for hire wīdgilpum hwǣr hīe sīe ǣfre wakian and scēawian. Lāsfægas is cūþe for hire mǣran ġlēawan, gūþmǣnan, and fǣringa lēodan. Hīe hafaþ mǣran heofonlīcan strengþ and is līðe mid āsīþfæðmum, sēo cumaþ tō sēo byrig beforan þǣm stǣnan on sēo Mārocscearpnesse. Þā sceat þāra spīlhusa and gedēofan āhębbaþ sēo gemynd and cræftigcundnes þǣre byrig. Sēo wīne byð þǣre eorðan gefrǣtwod mid bleo and lēohtfætum, and sƿā þā lēode cƿissiaþ and fēraþ sƿā sǣbyrnan on sēo Sǣ. {{USPopulusCities}} [[Flocc:Byrig on Gnefada]] [[Flocc:Sċīrbyrig on Gnefada]] [[Flocc:Byrig on Clarcsċīr (Gnefada)]] j6a4j77cfo3zkiff770qgk8yeia4l2t 216093 216092 2024-04-26T05:06:08Z Rylesbourne 125148 wikitext text/x-wiki {{Cyþþubox folcstede |nama = Lāsfægas<br><small>''Mǣdlandburg''</small> |flocc = Scirburg |brǣdu = |lengu = |biliþ = Las Vegas 63.jpg |biliþ gewrit = Lāsuēagasburh on Gnefada. |motto = |ænglisc motto = |burgriht = |GDP getæl = |GDP ǣlcum hēafde = }} '''Lāsfægas''' ({{lang-es|Las Vegas}}), þe mǣneþ on Englisce '''Mǣdlandburg''' or '''Fægas''', sēo byrig on þǣre westlīcan dǣle þæs [[Gnefada]] landes on Norþanēaldan Āmērica, is eald and folcescēawigendlic. Hēo is cēned beforan þǣre blācendan Dancan Fēores and is wīdsƿīðe cuðe for hire tōmere līce and ofermōdigan wīnediscum. Sēo byrig is gehāten "Lāsfægas," þæt þēah on āngliscum getālum sƿā mǣnan mæg "þās mǣdwe," forþan þe hīe standaþ on ānum ġeāre and oferflōwaþ mid blōstmum and ǣdelum wǣstma. Hīe is ēac gehīered for hire wīdgilpum hwǣr hīe sīe ǣfre wakian and scēawian. Lāsfægas is cūþe for hire mǣran ġlēawan, gūþmǣnan, and fǣringa lēodan. Hīe hafaþ mǣran heofonlīcan strengþ and is līðe mid āsīþfæðmum, sēo cumaþ tō sēo byrig beforan þǣm stǣnan on sēo Mārocscearpnesse. Þā sceat þāra spīlhusa and gedēofan āhębbaþ sēo gemynd and cræftigcundnes þǣre byrig. Sēo wīne byð þǣre eorðan gefrǣtwod mid bleo and lēohtfætum, and sƿā þā lēode cƿissiaþ and fēraþ sƿā sǣbyrnan on sēo Sǣ. {{USPopulusCities}} [[Flocc:Byrig on Gnefada]] [[Flocc:Sċīrbyrig on Gnefada]] [[Flocc:Byrig on Clarcsċīr (Gnefada)]] m3hk6q7id42zk6vog0b10rho1r5scqc 0 24424 216096 2024-04-26T05:11:26Z Rylesbourne 125148 Nīwe tramet: {{Cyþþubox folcstede |nama = Norþlāsfægas<br><small>''Norþ Mǣdlandburg''</small> |flocc = Scirburg |brǣdu = |lengu = |biliþ = EM_HOME_(2640651367).jpg |biliþ gewrit = Norþlāsfægas on Gnefada. |motto = |ænglisc motto = |burgriht = |GDP getæl = |GDP ǣlcum hēafde = }} '''Norþlāsfægas''' ({{lang-es|Norte de Las Vegas}}), þ... wikitext text/x-wiki {{Cyþþubox folcstede |nama = Norþlāsfægas<br><small>''Norþ Mǣdlandburg''</small> |flocc = Scirburg |brǣdu = |lengu = |biliþ = EM_HOME_(2640651367).jpg |biliþ gewrit = Norþlāsfægas on Gnefada. |motto = |ænglisc motto = |burgriht = |GDP getæl = |GDP ǣlcum hēafde = }} '''Norþlāsfægas''' ({{lang-es|Norte de Las Vegas}}), þe mǣneþ on Englisce '''Norþ Mǣdlandburg''' or '''Norþfægas''', is a byrg on [[Gnefada]]. {{USPopulusCities}} [[Flocc:Byrig on Gnefada]] [[Flocc:Byrig on Clarcsċīr (Gnefada)]] 54ad3cz3d7jb4bkdevaoq01oyprga9e 216097 216096 2024-04-26T05:15:17Z Rylesbourne 125148 wikitext text/x-wiki {{Cyþþubox folcstede |nama = Norþlāsfægas<br><small>''Norþ Mǣdlandburg''</small> |flocc = Burg |brǣdu = |lengu = |biliþ = EM_HOME_(2640651367).jpg |biliþ gewrit = Norþlāsfægas on Gnefada. |motto = |ænglisc motto = |burgriht = |GDP getæl = |GDP ǣlcum hēafde = }} '''Norþlāsfægas''' ({{lang-es|Norte de Las Vegas}}), þe mǣneþ on Englisce '''Norþ Mǣdlandburg''' or '''Norþfægas''', is a byrg on [[Gnefada]]. {{USPopulusCities}} [[Flocc:Byrig on Gnefada]] [[Flocc:Byrig on Clarcsċīr (Gnefada)]] eg7oxkg6euhpf8nrrntprarqkrbf919 0 24425 216098 2024-04-26T05:16:17Z Rylesbourne 125148 Nīwe tramet: {{Cyþþubox folcstede |nama = Ēamfullegesiht |flocc = Burg |brǣdu = |lengu = |biliþ = EM_HOME_(2640651367).jpg |biliþ gewrit = Norþlāsfægas on Gnefada. |motto = |ænglisc motto = |burgriht = |GDP getæl = |GDP ǣlcum hēafde = }} '''Ēamfullegesiht''' ({{lang-es|Chula Vista}}), is a byrg on [[California|Californie]]. {{USPopulusCi... wikitext text/x-wiki {{Cyþþubox folcstede |nama = Ēamfullegesiht |flocc = Burg |brǣdu = |lengu = |biliþ = EM_HOME_(2640651367).jpg |biliþ gewrit = Norþlāsfægas on Gnefada. |motto = |ænglisc motto = |burgriht = |GDP getæl = |GDP ǣlcum hēafde = }} '''Ēamfullegesiht''' ({{lang-es|Chula Vista}}), is a byrg on [[California|Californie]]. {{USPopulusCities}} {{DEFAULTSORT:Ēamfullegesiht}} {{California}} {{USPopulusCities}} [[Flocc:Byrig on Californie]] [[Flocc:Byrig on Hālgadidacussċīr]] [[Flocc:Beċebyrig on Californie]] 3fv5ubeowdf3ofwk70vyre2njay6ujw 216099 216098 2024-04-26T05:17:10Z Rylesbourne 125148 wikitext text/x-wiki {{Cyþþubox folcstede |nama = Ēamfullegesiht |flocc = Burg |brǣdu = |lengu = |biliþ = Gateway Buildings, Chula Vista.jpg |biliþ gewrit = Ēamfullegesiht on Californie. |motto = |ænglisc motto = |burgriht = |GDP getæl = |GDP ǣlcum hēafde = }} '''Ēamfullegesiht''' ({{lang-es|Chula Vista}}), is a byrg on [[California|Californie]]. {{USPopulusCities}} {{DEFAULTSORT:Ēamfullegesiht}} {{California}} {{USPopulusCities}} [[Flocc:Byrig on Californie]] [[Flocc:Byrig on Hālgadidacussċīr]] [[Flocc:Beċebyrig on Californie]] t0szgov0lk4at99c0k9dt6ulk6tg02g 216100 216099 2024-04-26T05:17:50Z Rylesbourne 125148 wikitext text/x-wiki {{Cyþþubox folcstede |nama = Ēamfullegesiht |flocc = Burg |brǣdu = |lengu = |biliþ = Gateway Buildings, Chula Vista.jpg |biliþ gewrit = Ēamfullegesiht on Californie. |motto = |ænglisc motto = |burgriht = |GDP getæl = |GDP ǣlcum hēafde = }} '''Ēamfullegesiht''' ({{lang-es|Chula Vista}}), is a byrg on [[California|Californie]]. {{USPopulusCities}} {{DEFAULTSORT:Eamfullegesiht}} {{California}} {{USPopulusCities}} [[Flocc:Byrig on Californie]] [[Flocc:Byrig on Hālgadidacussċīr]] [[Flocc:Beċebyrig on Californie]] py9czxa5nzdp9n9ssa5ziv0eetqjiqy