Overview
- Group
- SmallGroup(1728,31623)
- Rank
- 3
- Schläfli Type
- {12,24}
- Vertices, edges, …
- 36, 432, 72
- Order of s0s1s2
- 8
- Order of s0s1s2s1
- 12
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
12-fold
24-fold
27-fold
54-fold
108-fold
216-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
P/N, where N=<(s1*s0)^3*s2*(s1*s0)^2*s1*s2> of order 2
36 facets
- 36 of {12}*24
18 vertex figures
- 18 of {24}*48
Representations
Permutation Representation (GAP)
s0 := ( 1,325)( 2,327)( 3,326)( 4,331)( 5,333)( 6,332)( 7,328)( 8,330)( 9,329)( 10,343)( 11,345)( 12,344)( 13,349)( 14,351)( 15,350)( 16,346)( 17,348)( 18,347)( 19,334)( 20,336)( 21,335)( 22,340)( 23,342)( 24,341)( 25,337)( 26,339)( 27,338)( 28,352)( 29,354)( 30,353)( 31,358)( 32,360)( 33,359)( 34,355)( 35,357)( 36,356)( 37,370)( 38,372)( 39,371)( 40,376)( 41,378)( 42,377)( 43,373)( 44,375)( 45,374)( 46,361)( 47,363)( 48,362)( 49,367)( 50,369)( 51,368)( 52,364)( 53,366)( 54,365)( 55,379)( 56,381)( 57,380)( 58,385)( 59,387)( 60,386)( 61,382)( 62,384)( 63,383)( 64,397)( 65,399)( 66,398)( 67,403)( 68,405)( 69,404)( 70,400)( 71,402)( 72,401)( 73,388)( 74,390)( 75,389)( 76,394)( 77,396)( 78,395)( 79,391)( 80,393)( 81,392)( 82,406)( 83,408)( 84,407)( 85,412)( 86,414)( 87,413)( 88,409)( 89,411)( 90,410)( 91,424)( 92,426)( 93,425)( 94,430)( 95,432)( 96,431)( 97,427)( 98,429)( 99,428)(100,415)(101,417)(102,416)(103,421)(104,423)(105,422)(106,418)(107,420)(108,419)(109,217)(110,219)(111,218)(112,223)(113,225)(114,224)(115,220)(116,222)(117,221)(118,235)(119,237)(120,236)(121,241)(122,243)(123,242)(124,238)(125,240)(126,239)(127,226)(128,228)(129,227)(130,232)(131,234)(132,233)(133,229)(134,231)(135,230)(136,244)(137,246)(138,245)(139,250)(140,252)(141,251)(142,247)(143,249)(144,248)(145,262)(146,264)(147,263)(148,268)(149,270)(150,269)(151,265)(152,267)(153,266)(154,253)(155,255)(156,254)(157,259)(158,261)(159,260)(160,256)(161,258)(162,257)(163,271)(164,273)(165,272)(166,277)(167,279)(168,278)(169,274)(170,276)(171,275)(172,289)(173,291)(174,290)(175,295)(176,297)(177,296)(178,292)(179,294)(180,293)(181,280)(182,282)(183,281)(184,286)(185,288)(186,287)(187,283)(188,285)(189,284)(190,298)(191,300)(192,299)(193,304)(194,306)(195,305)(196,301)(197,303)(198,302)(199,316)(200,318)(201,317)(202,322)(203,324)(204,323)(205,319)(206,321)(207,320)(208,307)(209,309)(210,308)(211,313)(212,315)(213,314)(214,310)(215,312)(216,311)(433,757)(434,759)(435,758)(436,763)(437,765)(438,764)(439,760)(440,762)(441,761)(442,775)(443,777)(444,776)(445,781)(446,783)(447,782)(448,778)(449,780)(450,779)(451,766)(452,768)(453,767)(454,772)(455,774)(456,773)(457,769)(458,771)(459,770)(460,784)(461,786)(462,785)(463,790)(464,792)(465,791)(466,787)(467,789)(468,788)(469,802)(470,804)(471,803)(472,808)(473,810)(474,809)(475,805)(476,807)(477,806)(478,793)(479,795)(480,794)(481,799)(482,801)(483,800)(484,796)(485,798)(486,797)(487,811)(488,813)(489,812)(490,817)(491,819)(492,818)(493,814)(494,816)(495,815)(496,829)(497,831)(498,830)(499,835)(500,837)(501,836)(502,832)(503,834)(504,833)(505,820)(506,822)(507,821)(508,826)(509,828)(510,827)(511,823)(512,825)(513,824)(514,838)(515,840)(516,839)(517,844)(518,846)(519,845)(520,841)(521,843)(522,842)(523,856)(524,858)(525,857)(526,862)(527,864)(528,863)(529,859)(530,861)(531,860)(532,847)(533,849)(534,848)(535,853)(536,855)(537,854)(538,850)(539,852)(540,851)(541,649)(542,651)(543,650)(544,655)(545,657)(546,656)(547,652)(548,654)(549,653)(550,667)(551,669)(552,668)(553,673)(554,675)(555,674)(556,670)(557,672)(558,671)(559,658)(560,660)(561,659)(562,664)(563,666)(564,665)(565,661)(566,663)(567,662)(568,676)(569,678)(570,677)(571,682)(572,684)(573,683)(574,679)(575,681)(576,680)(577,694)(578,696)(579,695)(580,700)(581,702)(582,701)(583,697)(584,699)(585,698)(586,685)(587,687)(588,686)(589,691)(590,693)(591,692)(592,688)(593,690)(594,689)(595,703)(596,705)(597,704)(598,709)(599,711)(600,710)(601,706)(602,708)(603,707)(604,721)(605,723)(606,722)(607,727)(608,729)(609,728)(610,724)(611,726)(612,725)(613,712)(614,714)(615,713)(616,718)(617,720)(618,719)(619,715)(620,717)(621,716)(622,730)(623,732)(624,731)(625,736)(626,738)(627,737)(628,733)(629,735)(630,734)(631,748)(632,750)(633,749)(634,754)(635,756)(636,755)(637,751)(638,753)(639,752)(640,739)(641,741)(642,740)(643,745)(644,747)(645,746)(646,742)(647,744)(648,743);; s1 := ( 1,767)( 2,766)( 3,768)( 4,771)( 5,770)( 6,769)( 7,772)( 8,774)( 9,773)( 10,758)( 11,757)( 12,759)( 13,762)( 14,761)( 15,760)( 16,763)( 17,765)( 18,764)( 19,776)( 20,775)( 21,777)( 22,780)( 23,779)( 24,778)( 25,781)( 26,783)( 27,782)( 28,794)( 29,793)( 30,795)( 31,798)( 32,797)( 33,796)( 34,799)( 35,801)( 36,800)( 37,785)( 38,784)( 39,786)( 40,789)( 41,788)( 42,787)( 43,790)( 44,792)( 45,791)( 46,803)( 47,802)( 48,804)( 49,807)( 50,806)( 51,805)( 52,808)( 53,810)( 54,809)( 55,821)( 56,820)( 57,822)( 58,825)( 59,824)( 60,823)( 61,826)( 62,828)( 63,827)( 64,812)( 65,811)( 66,813)( 67,816)( 68,815)( 69,814)( 70,817)( 71,819)( 72,818)( 73,830)( 74,829)( 75,831)( 76,834)( 77,833)( 78,832)( 79,835)( 80,837)( 81,836)( 82,848)( 83,847)( 84,849)( 85,852)( 86,851)( 87,850)( 88,853)( 89,855)( 90,854)( 91,839)( 92,838)( 93,840)( 94,843)( 95,842)( 96,841)( 97,844)( 98,846)( 99,845)(100,857)(101,856)(102,858)(103,861)(104,860)(105,859)(106,862)(107,864)(108,863)(109,659)(110,658)(111,660)(112,663)(113,662)(114,661)(115,664)(116,666)(117,665)(118,650)(119,649)(120,651)(121,654)(122,653)(123,652)(124,655)(125,657)(126,656)(127,668)(128,667)(129,669)(130,672)(131,671)(132,670)(133,673)(134,675)(135,674)(136,686)(137,685)(138,687)(139,690)(140,689)(141,688)(142,691)(143,693)(144,692)(145,677)(146,676)(147,678)(148,681)(149,680)(150,679)(151,682)(152,684)(153,683)(154,695)(155,694)(156,696)(157,699)(158,698)(159,697)(160,700)(161,702)(162,701)(163,713)(164,712)(165,714)(166,717)(167,716)(168,715)(169,718)(170,720)(171,719)(172,704)(173,703)(174,705)(175,708)(176,707)(177,706)(178,709)(179,711)(180,710)(181,722)(182,721)(183,723)(184,726)(185,725)(186,724)(187,727)(188,729)(189,728)(190,740)(191,739)(192,741)(193,744)(194,743)(195,742)(196,745)(197,747)(198,746)(199,731)(200,730)(201,732)(202,735)(203,734)(204,733)(205,736)(206,738)(207,737)(208,749)(209,748)(210,750)(211,753)(212,752)(213,751)(214,754)(215,756)(216,755)(217,605)(218,604)(219,606)(220,609)(221,608)(222,607)(223,610)(224,612)(225,611)(226,596)(227,595)(228,597)(229,600)(230,599)(231,598)(232,601)(233,603)(234,602)(235,614)(236,613)(237,615)(238,618)(239,617)(240,616)(241,619)(242,621)(243,620)(244,632)(245,631)(246,633)(247,636)(248,635)(249,634)(250,637)(251,639)(252,638)(253,623)(254,622)(255,624)(256,627)(257,626)(258,625)(259,628)(260,630)(261,629)(262,641)(263,640)(264,642)(265,645)(266,644)(267,643)(268,646)(269,648)(270,647)(271,551)(272,550)(273,552)(274,555)(275,554)(276,553)(277,556)(278,558)(279,557)(280,542)(281,541)(282,543)(283,546)(284,545)(285,544)(286,547)(287,549)(288,548)(289,560)(290,559)(291,561)(292,564)(293,563)(294,562)(295,565)(296,567)(297,566)(298,578)(299,577)(300,579)(301,582)(302,581)(303,580)(304,583)(305,585)(306,584)(307,569)(308,568)(309,570)(310,573)(311,572)(312,571)(313,574)(314,576)(315,575)(316,587)(317,586)(318,588)(319,591)(320,590)(321,589)(322,592)(323,594)(324,593)(325,497)(326,496)(327,498)(328,501)(329,500)(330,499)(331,502)(332,504)(333,503)(334,488)(335,487)(336,489)(337,492)(338,491)(339,490)(340,493)(341,495)(342,494)(343,506)(344,505)(345,507)(346,510)(347,509)(348,508)(349,511)(350,513)(351,512)(352,524)(353,523)(354,525)(355,528)(356,527)(357,526)(358,529)(359,531)(360,530)(361,515)(362,514)(363,516)(364,519)(365,518)(366,517)(367,520)(368,522)(369,521)(370,533)(371,532)(372,534)(373,537)(374,536)(375,535)(376,538)(377,540)(378,539)(379,443)(380,442)(381,444)(382,447)(383,446)(384,445)(385,448)(386,450)(387,449)(388,434)(389,433)(390,435)(391,438)(392,437)(393,436)(394,439)(395,441)(396,440)(397,452)(398,451)(399,453)(400,456)(401,455)(402,454)(403,457)(404,459)(405,458)(406,470)(407,469)(408,471)(409,474)(410,473)(411,472)(412,475)(413,477)(414,476)(415,461)(416,460)(417,462)(418,465)(419,464)(420,463)(421,466)(422,468)(423,467)(424,479)(425,478)(426,480)(427,483)(428,482)(429,481)(430,484)(431,486)(432,485);; s2 := ( 1,217)( 2,224)( 3,222)( 4,223)( 5,221)( 6,219)( 7,220)( 8,218)( 9,225)( 10,235)( 11,242)( 12,240)( 13,241)( 14,239)( 15,237)( 16,238)( 17,236)( 18,243)( 19,226)( 20,233)( 21,231)( 22,232)( 23,230)( 24,228)( 25,229)( 26,227)( 27,234)( 28,244)( 29,251)( 30,249)( 31,250)( 32,248)( 33,246)( 34,247)( 35,245)( 36,252)( 37,262)( 38,269)( 39,267)( 40,268)( 41,266)( 42,264)( 43,265)( 44,263)( 45,270)( 46,253)( 47,260)( 48,258)( 49,259)( 50,257)( 51,255)( 52,256)( 53,254)( 54,261)( 55,298)( 56,305)( 57,303)( 58,304)( 59,302)( 60,300)( 61,301)( 62,299)( 63,306)( 64,316)( 65,323)( 66,321)( 67,322)( 68,320)( 69,318)( 70,319)( 71,317)( 72,324)( 73,307)( 74,314)( 75,312)( 76,313)( 77,311)( 78,309)( 79,310)( 80,308)( 81,315)( 82,271)( 83,278)( 84,276)( 85,277)( 86,275)( 87,273)( 88,274)( 89,272)( 90,279)( 91,289)( 92,296)( 93,294)( 94,295)( 95,293)( 96,291)( 97,292)( 98,290)( 99,297)(100,280)(101,287)(102,285)(103,286)(104,284)(105,282)(106,283)(107,281)(108,288)(109,325)(110,332)(111,330)(112,331)(113,329)(114,327)(115,328)(116,326)(117,333)(118,343)(119,350)(120,348)(121,349)(122,347)(123,345)(124,346)(125,344)(126,351)(127,334)(128,341)(129,339)(130,340)(131,338)(132,336)(133,337)(134,335)(135,342)(136,352)(137,359)(138,357)(139,358)(140,356)(141,354)(142,355)(143,353)(144,360)(145,370)(146,377)(147,375)(148,376)(149,374)(150,372)(151,373)(152,371)(153,378)(154,361)(155,368)(156,366)(157,367)(158,365)(159,363)(160,364)(161,362)(162,369)(163,406)(164,413)(165,411)(166,412)(167,410)(168,408)(169,409)(170,407)(171,414)(172,424)(173,431)(174,429)(175,430)(176,428)(177,426)(178,427)(179,425)(180,432)(181,415)(182,422)(183,420)(184,421)(185,419)(186,417)(187,418)(188,416)(189,423)(190,379)(191,386)(192,384)(193,385)(194,383)(195,381)(196,382)(197,380)(198,387)(199,397)(200,404)(201,402)(202,403)(203,401)(204,399)(205,400)(206,398)(207,405)(208,388)(209,395)(210,393)(211,394)(212,392)(213,390)(214,391)(215,389)(216,396)(433,784)(434,791)(435,789)(436,790)(437,788)(438,786)(439,787)(440,785)(441,792)(442,802)(443,809)(444,807)(445,808)(446,806)(447,804)(448,805)(449,803)(450,810)(451,793)(452,800)(453,798)(454,799)(455,797)(456,795)(457,796)(458,794)(459,801)(460,757)(461,764)(462,762)(463,763)(464,761)(465,759)(466,760)(467,758)(468,765)(469,775)(470,782)(471,780)(472,781)(473,779)(474,777)(475,778)(476,776)(477,783)(478,766)(479,773)(480,771)(481,772)(482,770)(483,768)(484,769)(485,767)(486,774)(487,811)(488,818)(489,816)(490,817)(491,815)(492,813)(493,814)(494,812)(495,819)(496,829)(497,836)(498,834)(499,835)(500,833)(501,831)(502,832)(503,830)(504,837)(505,820)(506,827)(507,825)(508,826)(509,824)(510,822)(511,823)(512,821)(513,828)(514,838)(515,845)(516,843)(517,844)(518,842)(519,840)(520,841)(521,839)(522,846)(523,856)(524,863)(525,861)(526,862)(527,860)(528,858)(529,859)(530,857)(531,864)(532,847)(533,854)(534,852)(535,853)(536,851)(537,849)(538,850)(539,848)(540,855)(541,649)(542,656)(543,654)(544,655)(545,653)(546,651)(547,652)(548,650)(549,657)(550,667)(551,674)(552,672)(553,673)(554,671)(555,669)(556,670)(557,668)(558,675)(559,658)(560,665)(561,663)(562,664)(563,662)(564,660)(565,661)(566,659)(567,666)(568,676)(569,683)(570,681)(571,682)(572,680)(573,678)(574,679)(575,677)(576,684)(577,694)(578,701)(579,699)(580,700)(581,698)(582,696)(583,697)(584,695)(585,702)(586,685)(587,692)(588,690)(589,691)(590,689)(591,687)(592,688)(593,686)(594,693)(595,730)(596,737)(597,735)(598,736)(599,734)(600,732)(601,733)(602,731)(603,738)(604,748)(605,755)(606,753)(607,754)(608,752)(609,750)(610,751)(611,749)(612,756)(613,739)(614,746)(615,744)(616,745)(617,743)(618,741)(619,742)(620,740)(621,747)(622,703)(623,710)(624,708)(625,709)(626,707)(627,705)(628,706)(629,704)(630,711)(631,721)(632,728)(633,726)(634,727)(635,725)(636,723)(637,724)(638,722)(639,729)(640,712)(641,719)(642,717)(643,718)(644,716)(645,714)(646,715)(647,713)(648,720);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(864)!( 1,325)( 2,327)( 3,326)( 4,331)( 5,333)( 6,332)( 7,328)( 8,330)( 9,329)( 10,343)( 11,345)( 12,344)( 13,349)( 14,351)( 15,350)( 16,346)( 17,348)( 18,347)( 19,334)( 20,336)( 21,335)( 22,340)( 23,342)( 24,341)( 25,337)( 26,339)( 27,338)( 28,352)( 29,354)( 30,353)( 31,358)( 32,360)( 33,359)( 34,355)( 35,357)( 36,356)( 37,370)( 38,372)( 39,371)( 40,376)( 41,378)( 42,377)( 43,373)( 44,375)( 45,374)( 46,361)( 47,363)( 48,362)( 49,367)( 50,369)( 51,368)( 52,364)( 53,366)( 54,365)( 55,379)( 56,381)( 57,380)( 58,385)( 59,387)( 60,386)( 61,382)( 62,384)( 63,383)( 64,397)( 65,399)( 66,398)( 67,403)( 68,405)( 69,404)( 70,400)( 71,402)( 72,401)( 73,388)( 74,390)( 75,389)( 76,394)( 77,396)( 78,395)( 79,391)( 80,393)( 81,392)( 82,406)( 83,408)( 84,407)( 85,412)( 86,414)( 87,413)( 88,409)( 89,411)( 90,410)( 91,424)( 92,426)( 93,425)( 94,430)( 95,432)( 96,431)( 97,427)( 98,429)( 99,428)(100,415)(101,417)(102,416)(103,421)(104,423)(105,422)(106,418)(107,420)(108,419)(109,217)(110,219)(111,218)(112,223)(113,225)(114,224)(115,220)(116,222)(117,221)(118,235)(119,237)(120,236)(121,241)(122,243)(123,242)(124,238)(125,240)(126,239)(127,226)(128,228)(129,227)(130,232)(131,234)(132,233)(133,229)(134,231)(135,230)(136,244)(137,246)(138,245)(139,250)(140,252)(141,251)(142,247)(143,249)(144,248)(145,262)(146,264)(147,263)(148,268)(149,270)(150,269)(151,265)(152,267)(153,266)(154,253)(155,255)(156,254)(157,259)(158,261)(159,260)(160,256)(161,258)(162,257)(163,271)(164,273)(165,272)(166,277)(167,279)(168,278)(169,274)(170,276)(171,275)(172,289)(173,291)(174,290)(175,295)(176,297)(177,296)(178,292)(179,294)(180,293)(181,280)(182,282)(183,281)(184,286)(185,288)(186,287)(187,283)(188,285)(189,284)(190,298)(191,300)(192,299)(193,304)(194,306)(195,305)(196,301)(197,303)(198,302)(199,316)(200,318)(201,317)(202,322)(203,324)(204,323)(205,319)(206,321)(207,320)(208,307)(209,309)(210,308)(211,313)(212,315)(213,314)(214,310)(215,312)(216,311)(433,757)(434,759)(435,758)(436,763)(437,765)(438,764)(439,760)(440,762)(441,761)(442,775)(443,777)(444,776)(445,781)(446,783)(447,782)(448,778)(449,780)(450,779)(451,766)(452,768)(453,767)(454,772)(455,774)(456,773)(457,769)(458,771)(459,770)(460,784)(461,786)(462,785)(463,790)(464,792)(465,791)(466,787)(467,789)(468,788)(469,802)(470,804)(471,803)(472,808)(473,810)(474,809)(475,805)(476,807)(477,806)(478,793)(479,795)(480,794)(481,799)(482,801)(483,800)(484,796)(485,798)(486,797)(487,811)(488,813)(489,812)(490,817)(491,819)(492,818)(493,814)(494,816)(495,815)(496,829)(497,831)(498,830)(499,835)(500,837)(501,836)(502,832)(503,834)(504,833)(505,820)(506,822)(507,821)(508,826)(509,828)(510,827)(511,823)(512,825)(513,824)(514,838)(515,840)(516,839)(517,844)(518,846)(519,845)(520,841)(521,843)(522,842)(523,856)(524,858)(525,857)(526,862)(527,864)(528,863)(529,859)(530,861)(531,860)(532,847)(533,849)(534,848)(535,853)(536,855)(537,854)(538,850)(539,852)(540,851)(541,649)(542,651)(543,650)(544,655)(545,657)(546,656)(547,652)(548,654)(549,653)(550,667)(551,669)(552,668)(553,673)(554,675)(555,674)(556,670)(557,672)(558,671)(559,658)(560,660)(561,659)(562,664)(563,666)(564,665)(565,661)(566,663)(567,662)(568,676)(569,678)(570,677)(571,682)(572,684)(573,683)(574,679)(575,681)(576,680)(577,694)(578,696)(579,695)(580,700)(581,702)(582,701)(583,697)(584,699)(585,698)(586,685)(587,687)(588,686)(589,691)(590,693)(591,692)(592,688)(593,690)(594,689)(595,703)(596,705)(597,704)(598,709)(599,711)(600,710)(601,706)(602,708)(603,707)(604,721)(605,723)(606,722)(607,727)(608,729)(609,728)(610,724)(611,726)(612,725)(613,712)(614,714)(615,713)(616,718)(617,720)(618,719)(619,715)(620,717)(621,716)(622,730)(623,732)(624,731)(625,736)(626,738)(627,737)(628,733)(629,735)(630,734)(631,748)(632,750)(633,749)(634,754)(635,756)(636,755)(637,751)(638,753)(639,752)(640,739)(641,741)(642,740)(643,745)(644,747)(645,746)(646,742)(647,744)(648,743); s1 := Sym(864)!( 1,767)( 2,766)( 3,768)( 4,771)( 5,770)( 6,769)( 7,772)( 8,774)( 9,773)( 10,758)( 11,757)( 12,759)( 13,762)( 14,761)( 15,760)( 16,763)( 17,765)( 18,764)( 19,776)( 20,775)( 21,777)( 22,780)( 23,779)( 24,778)( 25,781)( 26,783)( 27,782)( 28,794)( 29,793)( 30,795)( 31,798)( 32,797)( 33,796)( 34,799)( 35,801)( 36,800)( 37,785)( 38,784)( 39,786)( 40,789)( 41,788)( 42,787)( 43,790)( 44,792)( 45,791)( 46,803)( 47,802)( 48,804)( 49,807)( 50,806)( 51,805)( 52,808)( 53,810)( 54,809)( 55,821)( 56,820)( 57,822)( 58,825)( 59,824)( 60,823)( 61,826)( 62,828)( 63,827)( 64,812)( 65,811)( 66,813)( 67,816)( 68,815)( 69,814)( 70,817)( 71,819)( 72,818)( 73,830)( 74,829)( 75,831)( 76,834)( 77,833)( 78,832)( 79,835)( 80,837)( 81,836)( 82,848)( 83,847)( 84,849)( 85,852)( 86,851)( 87,850)( 88,853)( 89,855)( 90,854)( 91,839)( 92,838)( 93,840)( 94,843)( 95,842)( 96,841)( 97,844)( 98,846)( 99,845)(100,857)(101,856)(102,858)(103,861)(104,860)(105,859)(106,862)(107,864)(108,863)(109,659)(110,658)(111,660)(112,663)(113,662)(114,661)(115,664)(116,666)(117,665)(118,650)(119,649)(120,651)(121,654)(122,653)(123,652)(124,655)(125,657)(126,656)(127,668)(128,667)(129,669)(130,672)(131,671)(132,670)(133,673)(134,675)(135,674)(136,686)(137,685)(138,687)(139,690)(140,689)(141,688)(142,691)(143,693)(144,692)(145,677)(146,676)(147,678)(148,681)(149,680)(150,679)(151,682)(152,684)(153,683)(154,695)(155,694)(156,696)(157,699)(158,698)(159,697)(160,700)(161,702)(162,701)(163,713)(164,712)(165,714)(166,717)(167,716)(168,715)(169,718)(170,720)(171,719)(172,704)(173,703)(174,705)(175,708)(176,707)(177,706)(178,709)(179,711)(180,710)(181,722)(182,721)(183,723)(184,726)(185,725)(186,724)(187,727)(188,729)(189,728)(190,740)(191,739)(192,741)(193,744)(194,743)(195,742)(196,745)(197,747)(198,746)(199,731)(200,730)(201,732)(202,735)(203,734)(204,733)(205,736)(206,738)(207,737)(208,749)(209,748)(210,750)(211,753)(212,752)(213,751)(214,754)(215,756)(216,755)(217,605)(218,604)(219,606)(220,609)(221,608)(222,607)(223,610)(224,612)(225,611)(226,596)(227,595)(228,597)(229,600)(230,599)(231,598)(232,601)(233,603)(234,602)(235,614)(236,613)(237,615)(238,618)(239,617)(240,616)(241,619)(242,621)(243,620)(244,632)(245,631)(246,633)(247,636)(248,635)(249,634)(250,637)(251,639)(252,638)(253,623)(254,622)(255,624)(256,627)(257,626)(258,625)(259,628)(260,630)(261,629)(262,641)(263,640)(264,642)(265,645)(266,644)(267,643)(268,646)(269,648)(270,647)(271,551)(272,550)(273,552)(274,555)(275,554)(276,553)(277,556)(278,558)(279,557)(280,542)(281,541)(282,543)(283,546)(284,545)(285,544)(286,547)(287,549)(288,548)(289,560)(290,559)(291,561)(292,564)(293,563)(294,562)(295,565)(296,567)(297,566)(298,578)(299,577)(300,579)(301,582)(302,581)(303,580)(304,583)(305,585)(306,584)(307,569)(308,568)(309,570)(310,573)(311,572)(312,571)(313,574)(314,576)(315,575)(316,587)(317,586)(318,588)(319,591)(320,590)(321,589)(322,592)(323,594)(324,593)(325,497)(326,496)(327,498)(328,501)(329,500)(330,499)(331,502)(332,504)(333,503)(334,488)(335,487)(336,489)(337,492)(338,491)(339,490)(340,493)(341,495)(342,494)(343,506)(344,505)(345,507)(346,510)(347,509)(348,508)(349,511)(350,513)(351,512)(352,524)(353,523)(354,525)(355,528)(356,527)(357,526)(358,529)(359,531)(360,530)(361,515)(362,514)(363,516)(364,519)(365,518)(366,517)(367,520)(368,522)(369,521)(370,533)(371,532)(372,534)(373,537)(374,536)(375,535)(376,538)(377,540)(378,539)(379,443)(380,442)(381,444)(382,447)(383,446)(384,445)(385,448)(386,450)(387,449)(388,434)(389,433)(390,435)(391,438)(392,437)(393,436)(394,439)(395,441)(396,440)(397,452)(398,451)(399,453)(400,456)(401,455)(402,454)(403,457)(404,459)(405,458)(406,470)(407,469)(408,471)(409,474)(410,473)(411,472)(412,475)(413,477)(414,476)(415,461)(416,460)(417,462)(418,465)(419,464)(420,463)(421,466)(422,468)(423,467)(424,479)(425,478)(426,480)(427,483)(428,482)(429,481)(430,484)(431,486)(432,485); s2 := Sym(864)!( 1,217)( 2,224)( 3,222)( 4,223)( 5,221)( 6,219)( 7,220)( 8,218)( 9,225)( 10,235)( 11,242)( 12,240)( 13,241)( 14,239)( 15,237)( 16,238)( 17,236)( 18,243)( 19,226)( 20,233)( 21,231)( 22,232)( 23,230)( 24,228)( 25,229)( 26,227)( 27,234)( 28,244)( 29,251)( 30,249)( 31,250)( 32,248)( 33,246)( 34,247)( 35,245)( 36,252)( 37,262)( 38,269)( 39,267)( 40,268)( 41,266)( 42,264)( 43,265)( 44,263)( 45,270)( 46,253)( 47,260)( 48,258)( 49,259)( 50,257)( 51,255)( 52,256)( 53,254)( 54,261)( 55,298)( 56,305)( 57,303)( 58,304)( 59,302)( 60,300)( 61,301)( 62,299)( 63,306)( 64,316)( 65,323)( 66,321)( 67,322)( 68,320)( 69,318)( 70,319)( 71,317)( 72,324)( 73,307)( 74,314)( 75,312)( 76,313)( 77,311)( 78,309)( 79,310)( 80,308)( 81,315)( 82,271)( 83,278)( 84,276)( 85,277)( 86,275)( 87,273)( 88,274)( 89,272)( 90,279)( 91,289)( 92,296)( 93,294)( 94,295)( 95,293)( 96,291)( 97,292)( 98,290)( 99,297)(100,280)(101,287)(102,285)(103,286)(104,284)(105,282)(106,283)(107,281)(108,288)(109,325)(110,332)(111,330)(112,331)(113,329)(114,327)(115,328)(116,326)(117,333)(118,343)(119,350)(120,348)(121,349)(122,347)(123,345)(124,346)(125,344)(126,351)(127,334)(128,341)(129,339)(130,340)(131,338)(132,336)(133,337)(134,335)(135,342)(136,352)(137,359)(138,357)(139,358)(140,356)(141,354)(142,355)(143,353)(144,360)(145,370)(146,377)(147,375)(148,376)(149,374)(150,372)(151,373)(152,371)(153,378)(154,361)(155,368)(156,366)(157,367)(158,365)(159,363)(160,364)(161,362)(162,369)(163,406)(164,413)(165,411)(166,412)(167,410)(168,408)(169,409)(170,407)(171,414)(172,424)(173,431)(174,429)(175,430)(176,428)(177,426)(178,427)(179,425)(180,432)(181,415)(182,422)(183,420)(184,421)(185,419)(186,417)(187,418)(188,416)(189,423)(190,379)(191,386)(192,384)(193,385)(194,383)(195,381)(196,382)(197,380)(198,387)(199,397)(200,404)(201,402)(202,403)(203,401)(204,399)(205,400)(206,398)(207,405)(208,388)(209,395)(210,393)(211,394)(212,392)(213,390)(214,391)(215,389)(216,396)(433,784)(434,791)(435,789)(436,790)(437,788)(438,786)(439,787)(440,785)(441,792)(442,802)(443,809)(444,807)(445,808)(446,806)(447,804)(448,805)(449,803)(450,810)(451,793)(452,800)(453,798)(454,799)(455,797)(456,795)(457,796)(458,794)(459,801)(460,757)(461,764)(462,762)(463,763)(464,761)(465,759)(466,760)(467,758)(468,765)(469,775)(470,782)(471,780)(472,781)(473,779)(474,777)(475,778)(476,776)(477,783)(478,766)(479,773)(480,771)(481,772)(482,770)(483,768)(484,769)(485,767)(486,774)(487,811)(488,818)(489,816)(490,817)(491,815)(492,813)(493,814)(494,812)(495,819)(496,829)(497,836)(498,834)(499,835)(500,833)(501,831)(502,832)(503,830)(504,837)(505,820)(506,827)(507,825)(508,826)(509,824)(510,822)(511,823)(512,821)(513,828)(514,838)(515,845)(516,843)(517,844)(518,842)(519,840)(520,841)(521,839)(522,846)(523,856)(524,863)(525,861)(526,862)(527,860)(528,858)(529,859)(530,857)(531,864)(532,847)(533,854)(534,852)(535,853)(536,851)(537,849)(538,850)(539,848)(540,855)(541,649)(542,656)(543,654)(544,655)(545,653)(546,651)(547,652)(548,650)(549,657)(550,667)(551,674)(552,672)(553,673)(554,671)(555,669)(556,670)(557,668)(558,675)(559,658)(560,665)(561,663)(562,664)(563,662)(564,660)(565,661)(566,659)(567,666)(568,676)(569,683)(570,681)(571,682)(572,680)(573,678)(574,679)(575,677)(576,684)(577,694)(578,701)(579,699)(580,700)(581,698)(582,696)(583,697)(584,695)(585,702)(586,685)(587,692)(588,690)(589,691)(590,689)(591,687)(592,688)(593,686)(594,693)(595,730)(596,737)(597,735)(598,736)(599,734)(600,732)(601,733)(602,731)(603,738)(604,748)(605,755)(606,753)(607,754)(608,752)(609,750)(610,751)(611,749)(612,756)(613,739)(614,746)(615,744)(616,745)(617,743)(618,741)(619,742)(620,740)(621,747)(622,703)(623,710)(624,708)(625,709)(626,707)(627,705)(628,706)(629,704)(630,711)(631,721)(632,728)(633,726)(634,727)(635,725)(636,723)(637,724)(638,722)(639,729)(640,712)(641,719)(642,717)(643,718)(644,716)(645,714)(646,715)(647,713)(648,720); poly := sub<Sym(864)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1, s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 >;
References
None.
to this polytope.