Overview
- Group
- SmallGroup(1920,237609)
- Rank
- 3
- Schläfli Type
- {60,8}
- Vertices, edges, …
- 120, 480, 16
- Order of s0s1s2
- 15
- Order of s0s1s2s1
- 8
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Non-Orientable
Quotients maximal quotients in bold
2-fold
5-fold
8-fold
10-fold
16-fold
40-fold
80-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.
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 5, 6)( 9, 15)( 10, 16)( 11, 14)( 12, 13)( 17, 28)( 18, 27)( 19, 25)( 20, 26)( 21, 31)( 22, 32)( 23, 30)( 24, 29)( 33,129)( 34,130)( 35,132)( 36,131)( 37,134)( 38,133) ( 39,135)( 40,136)( 41,143)( 42,144)( 43,142)( 44,141)( 45,140)( 46,139)( 47,137)( 48,138)( 49,156)( 50,155)( 51,153)( 52,154)( 53,159)( 54,160)( 55,158)( 56,157)( 57,147)( 58,148)( 59,146)( 60,145)( 61,152)( 62,151)( 63,149)( 64,150)( 65, 97)( 66, 98)( 67,100)( 68, 99)( 69,102)( 70,101)( 71,103)( 72,104)( 73,111)( 74,112)( 75,110)( 76,109)( 77,108)( 78,107)( 79,105)( 80,106)( 81,124)( 82,123)( 83,121)( 84,122)( 85,127)( 86,128)( 87,126)( 88,125)( 89,115)( 90,116)( 91,114)( 92,113)( 93,120)( 94,119)( 95,117)( 96,118)(161,321)(162,322)(163,324)(164,323)(165,326)(166,325)(167,327)(168,328)(169,335)(170,336)(171,334)(172,333)(173,332)(174,331)(175,329)(176,330)(177,348)(178,347)(179,345)(180,346)(181,351)(182,352)(183,350)(184,349)(185,339)(186,340)(187,338)(188,337)(189,344)(190,343)(191,341)(192,342)(193,449)(194,450)(195,452)(196,451)(197,454)(198,453)(199,455)(200,456)(201,463)(202,464)(203,462)(204,461)(205,460)(206,459)(207,457)(208,458)(209,476)(210,475)(211,473)(212,474)(213,479)(214,480)(215,478)(216,477)(217,467)(218,468)(219,466)(220,465)(221,472)(222,471)(223,469)(224,470)(225,417)(226,418)(227,420)(228,419)(229,422)(230,421)(231,423)(232,424)(233,431)(234,432)(235,430)(236,429)(237,428)(238,427)(239,425)(240,426)(241,444)(242,443)(243,441)(244,442)(245,447)(246,448)(247,446)(248,445)(249,435)(250,436)(251,434)(252,433)(253,440)(254,439)(255,437)(256,438)(257,385)(258,386)(259,388)(260,387)(261,390)(262,389)(263,391)(264,392)(265,399)(266,400)(267,398)(268,397)(269,396)(270,395)(271,393)(272,394)(273,412)(274,411)(275,409)(276,410)(277,415)(278,416)(279,414)(280,413)(281,403)(282,404)(283,402)(284,401)(285,408)(286,407)(287,405)(288,406)(289,353)(290,354)(291,356)(292,355)(293,358)(294,357)(295,359)(296,360)(297,367)(298,368)(299,366)(300,365)(301,364)(302,363)(303,361)(304,362)(305,380)(306,379)(307,377)(308,378)(309,383)(310,384)(311,382)(312,381)(313,371)(314,372)(315,370)(316,369)(317,376)(318,375)(319,373)(320,374)(481,487)(482,488)(483,486)(484,485)(491,492)(493,494)(497,510)(498,509)(499,511)(500,512)(501,505)(502,506)(503,508)(504,507)(513,615)(514,616)(515,614)(516,613)(517,612)(518,611)(519,609)(520,610)(521,617)(522,618)(523,620)(524,619)(525,622)(526,621)(527,623)(528,624)(529,638)(530,637)(531,639)(532,640)(533,633)(534,634)(535,636)(536,635)(537,629)(538,630)(539,632)(540,631)(541,626)(542,625)(543,627)(544,628)(545,583)(546,584)(547,582)(548,581)(549,580)(550,579)(551,577)(552,578)(553,585)(554,586)(555,588)(556,587)(557,590)(558,589)(559,591)(560,592)(561,606)(562,605)(563,607)(564,608)(565,601)(566,602)(567,604)(568,603)(569,597)(570,598)(571,600)(572,599)(573,594)(574,593)(575,595)(576,596)(641,807)(642,808)(643,806)(644,805)(645,804)(646,803)(647,801)(648,802)(649,809)(650,810)(651,812)(652,811)(653,814)(654,813)(655,815)(656,816)(657,830)(658,829)(659,831)(660,832)(661,825)(662,826)(663,828)(664,827)(665,821)(666,822)(667,824)(668,823)(669,818)(670,817)(671,819)(672,820)(673,935)(674,936)(675,934)(676,933)(677,932)(678,931)(679,929)(680,930)(681,937)(682,938)(683,940)(684,939)(685,942)(686,941)(687,943)(688,944)(689,958)(690,957)(691,959)(692,960)(693,953)(694,954)(695,956)(696,955)(697,949)(698,950)(699,952)(700,951)(701,946)(702,945)(703,947)(704,948)(705,903)(706,904)(707,902)(708,901)(709,900)(710,899)(711,897)(712,898)(713,905)(714,906)(715,908)(716,907)(717,910)(718,909)(719,911)(720,912)(721,926)(722,925)(723,927)(724,928)(725,921)(726,922)(727,924)(728,923)(729,917)(730,918)(731,920)(732,919)(733,914)(734,913)(735,915)(736,916)(737,871)(738,872)(739,870)(740,869)(741,868)(742,867)(743,865)(744,866)(745,873)(746,874)(747,876)(748,875)(749,878)(750,877)(751,879)(752,880)(753,894)(754,893)(755,895)(756,896)(757,889)(758,890)(759,892)(760,891)(761,885)(762,886)(763,888)(764,887)(765,882)(766,881)(767,883)(768,884)(769,839)(770,840)(771,838)(772,837)(773,836)(774,835)(775,833)(776,834)(777,841)(778,842)(779,844)(780,843)(781,846)(782,845)(783,847)(784,848)(785,862)(786,861)(787,863)(788,864)(789,857)(790,858)(791,860)(792,859)(793,853)(794,854)(795,856)(796,855)(797,850)(798,849) (799,851)(800,852);; s1 := ( 1,673)( 2,676)( 3,675)( 4,674)( 5,677)( 6,680)( 7,679)( 8,678)( 9,698)( 10,699)( 11,700)( 12,697)( 13,702)( 14,703)( 15,704)( 16,701)( 17,695)( 18,694)( 19,693)( 20,696) ( 21,691)( 22,690)( 23,689)( 24,692)( 25,684)( 26,681)( 27,682)( 28,683)( 29,688)( 30,685)( 31,686)( 32,687)( 33,641)( 34,644)( 35,643)( 36,642)( 37,645)( 38,648)( 39,647)( 40,646)( 41,666)( 42,667)( 43,668)( 44,665)( 45,670)( 46,671)( 47,672)( 48,669)( 49,663)( 50,662)( 51,661)( 52,664)( 53,659)( 54,658)( 55,657)( 56,660)( 57,652)( 58,649)( 59,650)( 60,651)( 61,656)( 62,653)( 63,654)( 64,655)( 65,769)( 66,772)( 67,771)( 68,770)( 69,773)( 70,776)( 71,775)( 72,774)( 73,794)( 74,795)( 75,796)( 76,793)( 77,798)( 78,799)( 79,800)( 80,797)( 81,791)( 82,790)( 83,789)( 84,792)( 85,787)( 86,786)( 87,785)( 88,788)( 89,780)( 90,777)( 91,778)( 92,779)( 93,784)( 94,781)( 95,782)( 96,783)( 97,737)( 98,740)( 99,739)(100,738)(101,741)(102,744)(103,743)(104,742)(105,762)(106,763)(107,764)(108,761)(109,766)(110,767)(111,768)(112,765)(113,759)(114,758)(115,757)(116,760)(117,755)(118,754)(119,753)(120,756)(121,748)(122,745)(123,746)(124,747)(125,752)(126,749)(127,750)(128,751)(129,705)(130,708)(131,707)(132,706)(133,709)(134,712)(135,711)(136,710)(137,730)(138,731)(139,732)(140,729)(141,734)(142,735)(143,736)(144,733)(145,727)(146,726)(147,725)(148,728)(149,723)(150,722)(151,721)(152,724)(153,716)(154,713)(155,714)(156,715)(157,720)(158,717)(159,718)(160,719)(161,513)(162,516)(163,515)(164,514)(165,517)(166,520)(167,519)(168,518)(169,538)(170,539)(171,540)(172,537)(173,542)(174,543)(175,544)(176,541)(177,535)(178,534)(179,533)(180,536)(181,531)(182,530)(183,529)(184,532)(185,524)(186,521)(187,522)(188,523)(189,528)(190,525)(191,526)(192,527)(193,481)(194,484)(195,483)(196,482)(197,485)(198,488)(199,487)(200,486)(201,506)(202,507)(203,508)(204,505)(205,510)(206,511)(207,512)(208,509)(209,503)(210,502)(211,501)(212,504)(213,499)(214,498)(215,497)(216,500)(217,492)(218,489)(219,490)(220,491)(221,496)(222,493)(223,494)(224,495)(225,609)(226,612)(227,611)(228,610)(229,613)(230,616)(231,615)(232,614)(233,634)(234,635)(235,636)(236,633)(237,638)(238,639)(239,640)(240,637)(241,631)(242,630)(243,629)(244,632)(245,627)(246,626)(247,625)(248,628)(249,620)(250,617)(251,618)(252,619)(253,624)(254,621)(255,622)(256,623)(257,577)(258,580)(259,579)(260,578)(261,581)(262,584)(263,583)(264,582)(265,602)(266,603)(267,604)(268,601)(269,606)(270,607)(271,608)(272,605)(273,599)(274,598)(275,597)(276,600)(277,595)(278,594)(279,593)(280,596)(281,588)(282,585)(283,586)(284,587)(285,592)(286,589)(287,590)(288,591)(289,545)(290,548)(291,547)(292,546)(293,549)(294,552)(295,551)(296,550)(297,570)(298,571)(299,572)(300,569)(301,574)(302,575)(303,576)(304,573)(305,567)(306,566)(307,565)(308,568)(309,563)(310,562)(311,561)(312,564)(313,556)(314,553)(315,554)(316,555)(317,560)(318,557)(319,558)(320,559)(321,833)(322,836)(323,835)(324,834)(325,837)(326,840)(327,839)(328,838)(329,858)(330,859)(331,860)(332,857)(333,862)(334,863)(335,864)(336,861)(337,855)(338,854)(339,853)(340,856)(341,851)(342,850)(343,849)(344,852)(345,844)(346,841)(347,842)(348,843)(349,848)(350,845)(351,846)(352,847)(353,801)(354,804)(355,803)(356,802)(357,805)(358,808)(359,807)(360,806)(361,826)(362,827)(363,828)(364,825)(365,830)(366,831)(367,832)(368,829)(369,823)(370,822)(371,821)(372,824)(373,819)(374,818)(375,817)(376,820)(377,812)(378,809)(379,810)(380,811)(381,816)(382,813)(383,814)(384,815)(385,929)(386,932)(387,931)(388,930)(389,933)(390,936)(391,935)(392,934)(393,954)(394,955)(395,956)(396,953)(397,958)(398,959)(399,960)(400,957)(401,951)(402,950)(403,949)(404,952)(405,947)(406,946)(407,945)(408,948)(409,940)(410,937)(411,938)(412,939)(413,944)(414,941)(415,942)(416,943)(417,897)(418,900)(419,899)(420,898)(421,901)(422,904)(423,903)(424,902)(425,922)(426,923)(427,924)(428,921)(429,926)(430,927)(431,928)(432,925)(433,919)(434,918)(435,917)(436,920)(437,915)(438,914)(439,913)(440,916)(441,908)(442,905)(443,906)(444,907)(445,912)(446,909)(447,910)(448,911)(449,865)(450,868)(451,867)(452,866)(453,869)(454,872)(455,871)(456,870)(457,890)(458,891)(459,892)(460,889)(461,894)(462,895)(463,896)(464,893)(465,887)(466,886)(467,885)(468,888)(469,883)(470,882)(471,881)(472,884)(473,876)(474,873) (475,874)(476,875)(477,880)(478,877)(479,878)(480,879);; s2 := ( 1,489)( 2,490)( 3,491)( 4,492)( 5,493)( 6,494)( 7,495)( 8,496)( 9,487)( 10,488)( 11,485)( 12,486)( 13,483)( 14,484)( 15,481)( 16,482)( 17,507)( 18,508)( 19,505)( 20,506) ( 21,511)( 22,512)( 23,509)( 24,510)( 25,501)( 26,502)( 27,503)( 28,504)( 29,497)( 30,498)( 31,499)( 32,500)( 33,521)( 34,522)( 35,523)( 36,524)( 37,525)( 38,526)( 39,527)( 40,528)( 41,519)( 42,520)( 43,517)( 44,518)( 45,515)( 46,516)( 47,513)( 48,514)( 49,539)( 50,540)( 51,537)( 52,538)( 53,543)( 54,544)( 55,541)( 56,542)( 57,533)( 58,534)( 59,535)( 60,536)( 61,529)( 62,530)( 63,531)( 64,532)( 65,553)( 66,554)( 67,555)( 68,556)( 69,557)( 70,558)( 71,559)( 72,560)( 73,551)( 74,552)( 75,549)( 76,550)( 77,547)( 78,548)( 79,545)( 80,546)( 81,571)( 82,572)( 83,569)( 84,570)( 85,575)( 86,576)( 87,573)( 88,574)( 89,565)( 90,566)( 91,567)( 92,568)( 93,561)( 94,562)( 95,563)( 96,564)( 97,585)( 98,586)( 99,587)(100,588)(101,589)(102,590)(103,591)(104,592)(105,583)(106,584)(107,581)(108,582)(109,579)(110,580)(111,577)(112,578)(113,603)(114,604)(115,601)(116,602)(117,607)(118,608)(119,605)(120,606)(121,597)(122,598)(123,599)(124,600)(125,593)(126,594)(127,595)(128,596)(129,617)(130,618)(131,619)(132,620)(133,621)(134,622)(135,623)(136,624)(137,615)(138,616)(139,613)(140,614)(141,611)(142,612)(143,609)(144,610)(145,635)(146,636)(147,633)(148,634)(149,639)(150,640)(151,637)(152,638)(153,629)(154,630)(155,631)(156,632)(157,625)(158,626)(159,627)(160,628)(161,649)(162,650)(163,651)(164,652)(165,653)(166,654)(167,655)(168,656)(169,647)(170,648)(171,645)(172,646)(173,643)(174,644)(175,641)(176,642)(177,667)(178,668)(179,665)(180,666)(181,671)(182,672)(183,669)(184,670)(185,661)(186,662)(187,663)(188,664)(189,657)(190,658)(191,659)(192,660)(193,681)(194,682)(195,683)(196,684)(197,685)(198,686)(199,687)(200,688)(201,679)(202,680)(203,677)(204,678)(205,675)(206,676)(207,673)(208,674)(209,699)(210,700)(211,697)(212,698)(213,703)(214,704)(215,701)(216,702)(217,693)(218,694)(219,695)(220,696)(221,689)(222,690)(223,691)(224,692)(225,713)(226,714)(227,715)(228,716)(229,717)(230,718)(231,719)(232,720)(233,711)(234,712)(235,709)(236,710)(237,707)(238,708)(239,705)(240,706)(241,731)(242,732)(243,729)(244,730)(245,735)(246,736)(247,733)(248,734)(249,725)(250,726)(251,727)(252,728)(253,721)(254,722)(255,723)(256,724)(257,745)(258,746)(259,747)(260,748)(261,749)(262,750)(263,751)(264,752)(265,743)(266,744)(267,741)(268,742)(269,739)(270,740)(271,737)(272,738)(273,763)(274,764)(275,761)(276,762)(277,767)(278,768)(279,765)(280,766)(281,757)(282,758)(283,759)(284,760)(285,753)(286,754)(287,755)(288,756)(289,777)(290,778)(291,779)(292,780)(293,781)(294,782)(295,783)(296,784)(297,775)(298,776)(299,773)(300,774)(301,771)(302,772)(303,769)(304,770)(305,795)(306,796)(307,793)(308,794)(309,799)(310,800)(311,797)(312,798)(313,789)(314,790)(315,791)(316,792)(317,785)(318,786)(319,787)(320,788)(321,809)(322,810)(323,811)(324,812)(325,813)(326,814)(327,815)(328,816)(329,807)(330,808)(331,805)(332,806)(333,803)(334,804)(335,801)(336,802)(337,827)(338,828)(339,825)(340,826)(341,831)(342,832)(343,829)(344,830)(345,821)(346,822)(347,823)(348,824)(349,817)(350,818)(351,819)(352,820)(353,841)(354,842)(355,843)(356,844)(357,845)(358,846)(359,847)(360,848)(361,839)(362,840)(363,837)(364,838)(365,835)(366,836)(367,833)(368,834)(369,859)(370,860)(371,857)(372,858)(373,863)(374,864)(375,861)(376,862)(377,853)(378,854)(379,855)(380,856)(381,849)(382,850)(383,851)(384,852)(385,873)(386,874)(387,875)(388,876)(389,877)(390,878)(391,879)(392,880)(393,871)(394,872)(395,869)(396,870)(397,867)(398,868)(399,865)(400,866)(401,891)(402,892)(403,889)(404,890)(405,895)(406,896)(407,893)(408,894)(409,885)(410,886)(411,887)(412,888)(413,881)(414,882)(415,883)(416,884)(417,905)(418,906)(419,907)(420,908)(421,909)(422,910)(423,911)(424,912)(425,903)(426,904)(427,901)(428,902)(429,899)(430,900)(431,897)(432,898)(433,923)(434,924)(435,921)(436,922)(437,927)(438,928)(439,925)(440,926)(441,917)(442,918)(443,919)(444,920)(445,913)(446,914)(447,915)(448,916)(449,937)(450,938)(451,939)(452,940)(453,941)(454,942)(455,943)(456,944)(457,935)(458,936)(459,933)(460,934)(461,931)(462,932)(463,929)(464,930)(465,955)(466,956)(467,953)(468,954)(469,959)(470,960)(471,957)(472,958)(473,949)(474,950) (475,951)(476,952)(477,945)(478,946)(479,947)(480,948);; 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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(960)!( 3, 4)( 5, 6)( 9, 15)( 10, 16)( 11, 14)( 12, 13)( 17, 28)( 18, 27)( 19, 25)( 20, 26)( 21, 31)( 22, 32)( 23, 30)( 24, 29)( 33,129)( 34,130)( 35,132)( 36,131)( 37,134) ( 38,133)( 39,135)( 40,136)( 41,143)( 42,144)( 43,142)( 44,141)( 45,140)( 46,139)( 47,137)( 48,138)( 49,156)( 50,155)( 51,153)( 52,154)( 53,159)( 54,160)( 55,158)( 56,157)( 57,147)( 58,148)( 59,146)( 60,145)( 61,152)( 62,151)( 63,149)( 64,150)( 65, 97)( 66, 98)( 67,100)( 68, 99)( 69,102)( 70,101)( 71,103)( 72,104)( 73,111)( 74,112)( 75,110)( 76,109)( 77,108)( 78,107)( 79,105)( 80,106)( 81,124)( 82,123)( 83,121)( 84,122)( 85,127)( 86,128)( 87,126)( 88,125)( 89,115)( 90,116)( 91,114)( 92,113)( 93,120)( 94,119)( 95,117)( 96,118)(161,321)(162,322)(163,324)(164,323)(165,326)(166,325)(167,327)(168,328)(169,335)(170,336)(171,334)(172,333)(173,332)(174,331)(175,329)(176,330)(177,348)(178,347)(179,345)(180,346)(181,351)(182,352)(183,350)(184,349)(185,339)(186,340)(187,338)(188,337)(189,344)(190,343)(191,341)(192,342)(193,449)(194,450)(195,452)(196,451)(197,454)(198,453)(199,455)(200,456)(201,463)(202,464)(203,462)(204,461)(205,460)(206,459)(207,457)(208,458)(209,476)(210,475)(211,473)(212,474)(213,479)(214,480)(215,478)(216,477)(217,467)(218,468)(219,466)(220,465)(221,472)(222,471)(223,469)(224,470)(225,417)(226,418)(227,420)(228,419)(229,422)(230,421)(231,423)(232,424)(233,431)(234,432)(235,430)(236,429)(237,428)(238,427)(239,425)(240,426)(241,444)(242,443)(243,441)(244,442)(245,447)(246,448)(247,446)(248,445)(249,435)(250,436)(251,434)(252,433)(253,440)(254,439)(255,437)(256,438)(257,385)(258,386)(259,388)(260,387)(261,390)(262,389)(263,391)(264,392)(265,399)(266,400)(267,398)(268,397)(269,396)(270,395)(271,393)(272,394)(273,412)(274,411)(275,409)(276,410)(277,415)(278,416)(279,414)(280,413)(281,403)(282,404)(283,402)(284,401)(285,408)(286,407)(287,405)(288,406)(289,353)(290,354)(291,356)(292,355)(293,358)(294,357)(295,359)(296,360)(297,367)(298,368)(299,366)(300,365)(301,364)(302,363)(303,361)(304,362)(305,380)(306,379)(307,377)(308,378)(309,383)(310,384)(311,382)(312,381)(313,371)(314,372)(315,370)(316,369)(317,376)(318,375)(319,373)(320,374)(481,487)(482,488)(483,486)(484,485)(491,492)(493,494)(497,510)(498,509)(499,511)(500,512)(501,505)(502,506)(503,508)(504,507)(513,615)(514,616)(515,614)(516,613)(517,612)(518,611)(519,609)(520,610)(521,617)(522,618)(523,620)(524,619)(525,622)(526,621)(527,623)(528,624)(529,638)(530,637)(531,639)(532,640)(533,633)(534,634)(535,636)(536,635)(537,629)(538,630)(539,632)(540,631)(541,626)(542,625)(543,627)(544,628)(545,583)(546,584)(547,582)(548,581)(549,580)(550,579)(551,577)(552,578)(553,585)(554,586)(555,588)(556,587)(557,590)(558,589)(559,591)(560,592)(561,606)(562,605)(563,607)(564,608)(565,601)(566,602)(567,604)(568,603)(569,597)(570,598)(571,600)(572,599)(573,594)(574,593)(575,595)(576,596)(641,807)(642,808)(643,806)(644,805)(645,804)(646,803)(647,801)(648,802)(649,809)(650,810)(651,812)(652,811)(653,814)(654,813)(655,815)(656,816)(657,830)(658,829)(659,831)(660,832)(661,825)(662,826)(663,828)(664,827)(665,821)(666,822)(667,824)(668,823)(669,818)(670,817)(671,819)(672,820)(673,935)(674,936)(675,934)(676,933)(677,932)(678,931)(679,929)(680,930)(681,937)(682,938)(683,940)(684,939)(685,942)(686,941)(687,943)(688,944)(689,958)(690,957)(691,959)(692,960)(693,953)(694,954)(695,956)(696,955)(697,949)(698,950)(699,952)(700,951)(701,946)(702,945)(703,947)(704,948)(705,903)(706,904)(707,902)(708,901)(709,900)(710,899)(711,897)(712,898)(713,905)(714,906)(715,908)(716,907)(717,910)(718,909)(719,911)(720,912)(721,926)(722,925)(723,927)(724,928)(725,921)(726,922)(727,924)(728,923)(729,917)(730,918)(731,920)(732,919)(733,914)(734,913)(735,915)(736,916)(737,871)(738,872)(739,870)(740,869)(741,868)(742,867)(743,865)(744,866)(745,873)(746,874)(747,876)(748,875)(749,878)(750,877)(751,879)(752,880)(753,894)(754,893)(755,895)(756,896)(757,889)(758,890)(759,892)(760,891)(761,885)(762,886)(763,888)(764,887)(765,882)(766,881)(767,883)(768,884)(769,839)(770,840)(771,838)(772,837)(773,836)(774,835)(775,833)(776,834)(777,841)(778,842)(779,844)(780,843)(781,846)(782,845)(783,847)(784,848)(785,862)(786,861)(787,863)(788,864)(789,857)(790,858)(791,860)(792,859)(793,853)(794,854)(795,856)(796,855)(797,850) (798,849)(799,851)(800,852); s1 := Sym(960)!( 1,673)( 2,676)( 3,675)( 4,674)( 5,677)( 6,680)( 7,679)( 8,678)( 9,698)( 10,699)( 11,700)( 12,697)( 13,702)( 14,703)( 15,704)( 16,701)( 17,695)( 18,694)( 19,693) ( 20,696)( 21,691)( 22,690)( 23,689)( 24,692)( 25,684)( 26,681)( 27,682)( 28,683)( 29,688)( 30,685)( 31,686)( 32,687)( 33,641)( 34,644)( 35,643)( 36,642)( 37,645)( 38,648)( 39,647)( 40,646)( 41,666)( 42,667)( 43,668)( 44,665)( 45,670)( 46,671)( 47,672)( 48,669)( 49,663)( 50,662)( 51,661)( 52,664)( 53,659)( 54,658)( 55,657)( 56,660)( 57,652)( 58,649)( 59,650)( 60,651)( 61,656)( 62,653)( 63,654)( 64,655)( 65,769)( 66,772)( 67,771)( 68,770)( 69,773)( 70,776)( 71,775)( 72,774)( 73,794)( 74,795)( 75,796)( 76,793)( 77,798)( 78,799)( 79,800)( 80,797)( 81,791)( 82,790)( 83,789)( 84,792)( 85,787)( 86,786)( 87,785)( 88,788)( 89,780)( 90,777)( 91,778)( 92,779)( 93,784)( 94,781)( 95,782)( 96,783)( 97,737)( 98,740)( 99,739)(100,738)(101,741)(102,744)(103,743)(104,742)(105,762)(106,763)(107,764)(108,761)(109,766)(110,767)(111,768)(112,765)(113,759)(114,758)(115,757)(116,760)(117,755)(118,754)(119,753)(120,756)(121,748)(122,745)(123,746)(124,747)(125,752)(126,749)(127,750)(128,751)(129,705)(130,708)(131,707)(132,706)(133,709)(134,712)(135,711)(136,710)(137,730)(138,731)(139,732)(140,729)(141,734)(142,735)(143,736)(144,733)(145,727)(146,726)(147,725)(148,728)(149,723)(150,722)(151,721)(152,724)(153,716)(154,713)(155,714)(156,715)(157,720)(158,717)(159,718)(160,719)(161,513)(162,516)(163,515)(164,514)(165,517)(166,520)(167,519)(168,518)(169,538)(170,539)(171,540)(172,537)(173,542)(174,543)(175,544)(176,541)(177,535)(178,534)(179,533)(180,536)(181,531)(182,530)(183,529)(184,532)(185,524)(186,521)(187,522)(188,523)(189,528)(190,525)(191,526)(192,527)(193,481)(194,484)(195,483)(196,482)(197,485)(198,488)(199,487)(200,486)(201,506)(202,507)(203,508)(204,505)(205,510)(206,511)(207,512)(208,509)(209,503)(210,502)(211,501)(212,504)(213,499)(214,498)(215,497)(216,500)(217,492)(218,489)(219,490)(220,491)(221,496)(222,493)(223,494)(224,495)(225,609)(226,612)(227,611)(228,610)(229,613)(230,616)(231,615)(232,614)(233,634)(234,635)(235,636)(236,633)(237,638)(238,639)(239,640)(240,637)(241,631)(242,630)(243,629)(244,632)(245,627)(246,626)(247,625)(248,628)(249,620)(250,617)(251,618)(252,619)(253,624)(254,621)(255,622)(256,623)(257,577)(258,580)(259,579)(260,578)(261,581)(262,584)(263,583)(264,582)(265,602)(266,603)(267,604)(268,601)(269,606)(270,607)(271,608)(272,605)(273,599)(274,598)(275,597)(276,600)(277,595)(278,594)(279,593)(280,596)(281,588)(282,585)(283,586)(284,587)(285,592)(286,589)(287,590)(288,591)(289,545)(290,548)(291,547)(292,546)(293,549)(294,552)(295,551)(296,550)(297,570)(298,571)(299,572)(300,569)(301,574)(302,575)(303,576)(304,573)(305,567)(306,566)(307,565)(308,568)(309,563)(310,562)(311,561)(312,564)(313,556)(314,553)(315,554)(316,555)(317,560)(318,557)(319,558)(320,559)(321,833)(322,836)(323,835)(324,834)(325,837)(326,840)(327,839)(328,838)(329,858)(330,859)(331,860)(332,857)(333,862)(334,863)(335,864)(336,861)(337,855)(338,854)(339,853)(340,856)(341,851)(342,850)(343,849)(344,852)(345,844)(346,841)(347,842)(348,843)(349,848)(350,845)(351,846)(352,847)(353,801)(354,804)(355,803)(356,802)(357,805)(358,808)(359,807)(360,806)(361,826)(362,827)(363,828)(364,825)(365,830)(366,831)(367,832)(368,829)(369,823)(370,822)(371,821)(372,824)(373,819)(374,818)(375,817)(376,820)(377,812)(378,809)(379,810)(380,811)(381,816)(382,813)(383,814)(384,815)(385,929)(386,932)(387,931)(388,930)(389,933)(390,936)(391,935)(392,934)(393,954)(394,955)(395,956)(396,953)(397,958)(398,959)(399,960)(400,957)(401,951)(402,950)(403,949)(404,952)(405,947)(406,946)(407,945)(408,948)(409,940)(410,937)(411,938)(412,939)(413,944)(414,941)(415,942)(416,943)(417,897)(418,900)(419,899)(420,898)(421,901)(422,904)(423,903)(424,902)(425,922)(426,923)(427,924)(428,921)(429,926)(430,927)(431,928)(432,925)(433,919)(434,918)(435,917)(436,920)(437,915)(438,914)(439,913)(440,916)(441,908)(442,905)(443,906)(444,907)(445,912)(446,909)(447,910)(448,911)(449,865)(450,868)(451,867)(452,866)(453,869)(454,872)(455,871)(456,870)(457,890)(458,891)(459,892)(460,889)(461,894)(462,895)(463,896)(464,893)(465,887)(466,886)(467,885)(468,888)(469,883)(470,882)(471,881)(472,884)(473,876) (474,873)(475,874)(476,875)(477,880)(478,877)(479,878)(480,879); s2 := Sym(960)!( 1,489)( 2,490)( 3,491)( 4,492)( 5,493)( 6,494)( 7,495)( 8,496)( 9,487)( 10,488)( 11,485)( 12,486)( 13,483)( 14,484)( 15,481)( 16,482)( 17,507)( 18,508)( 19,505) ( 20,506)( 21,511)( 22,512)( 23,509)( 24,510)( 25,501)( 26,502)( 27,503)( 28,504)( 29,497)( 30,498)( 31,499)( 32,500)( 33,521)( 34,522)( 35,523)( 36,524)( 37,525)( 38,526)( 39,527)( 40,528)( 41,519)( 42,520)( 43,517)( 44,518)( 45,515)( 46,516)( 47,513)( 48,514)( 49,539)( 50,540)( 51,537)( 52,538)( 53,543)( 54,544)( 55,541)( 56,542)( 57,533)( 58,534)( 59,535)( 60,536)( 61,529)( 62,530)( 63,531)( 64,532)( 65,553)( 66,554)( 67,555)( 68,556)( 69,557)( 70,558)( 71,559)( 72,560)( 73,551)( 74,552)( 75,549)( 76,550)( 77,547)( 78,548)( 79,545)( 80,546)( 81,571)( 82,572)( 83,569)( 84,570)( 85,575)( 86,576)( 87,573)( 88,574)( 89,565)( 90,566)( 91,567)( 92,568)( 93,561)( 94,562)( 95,563)( 96,564)( 97,585)( 98,586)( 99,587)(100,588)(101,589)(102,590)(103,591)(104,592)(105,583)(106,584)(107,581)(108,582)(109,579)(110,580)(111,577)(112,578)(113,603)(114,604)(115,601)(116,602)(117,607)(118,608)(119,605)(120,606)(121,597)(122,598)(123,599)(124,600)(125,593)(126,594)(127,595)(128,596)(129,617)(130,618)(131,619)(132,620)(133,621)(134,622)(135,623)(136,624)(137,615)(138,616)(139,613)(140,614)(141,611)(142,612)(143,609)(144,610)(145,635)(146,636)(147,633)(148,634)(149,639)(150,640)(151,637)(152,638)(153,629)(154,630)(155,631)(156,632)(157,625)(158,626)(159,627)(160,628)(161,649)(162,650)(163,651)(164,652)(165,653)(166,654)(167,655)(168,656)(169,647)(170,648)(171,645)(172,646)(173,643)(174,644)(175,641)(176,642)(177,667)(178,668)(179,665)(180,666)(181,671)(182,672)(183,669)(184,670)(185,661)(186,662)(187,663)(188,664)(189,657)(190,658)(191,659)(192,660)(193,681)(194,682)(195,683)(196,684)(197,685)(198,686)(199,687)(200,688)(201,679)(202,680)(203,677)(204,678)(205,675)(206,676)(207,673)(208,674)(209,699)(210,700)(211,697)(212,698)(213,703)(214,704)(215,701)(216,702)(217,693)(218,694)(219,695)(220,696)(221,689)(222,690)(223,691)(224,692)(225,713)(226,714)(227,715)(228,716)(229,717)(230,718)(231,719)(232,720)(233,711)(234,712)(235,709)(236,710)(237,707)(238,708)(239,705)(240,706)(241,731)(242,732)(243,729)(244,730)(245,735)(246,736)(247,733)(248,734)(249,725)(250,726)(251,727)(252,728)(253,721)(254,722)(255,723)(256,724)(257,745)(258,746)(259,747)(260,748)(261,749)(262,750)(263,751)(264,752)(265,743)(266,744)(267,741)(268,742)(269,739)(270,740)(271,737)(272,738)(273,763)(274,764)(275,761)(276,762)(277,767)(278,768)(279,765)(280,766)(281,757)(282,758)(283,759)(284,760)(285,753)(286,754)(287,755)(288,756)(289,777)(290,778)(291,779)(292,780)(293,781)(294,782)(295,783)(296,784)(297,775)(298,776)(299,773)(300,774)(301,771)(302,772)(303,769)(304,770)(305,795)(306,796)(307,793)(308,794)(309,799)(310,800)(311,797)(312,798)(313,789)(314,790)(315,791)(316,792)(317,785)(318,786)(319,787)(320,788)(321,809)(322,810)(323,811)(324,812)(325,813)(326,814)(327,815)(328,816)(329,807)(330,808)(331,805)(332,806)(333,803)(334,804)(335,801)(336,802)(337,827)(338,828)(339,825)(340,826)(341,831)(342,832)(343,829)(344,830)(345,821)(346,822)(347,823)(348,824)(349,817)(350,818)(351,819)(352,820)(353,841)(354,842)(355,843)(356,844)(357,845)(358,846)(359,847)(360,848)(361,839)(362,840)(363,837)(364,838)(365,835)(366,836)(367,833)(368,834)(369,859)(370,860)(371,857)(372,858)(373,863)(374,864)(375,861)(376,862)(377,853)(378,854)(379,855)(380,856)(381,849)(382,850)(383,851)(384,852)(385,873)(386,874)(387,875)(388,876)(389,877)(390,878)(391,879)(392,880)(393,871)(394,872)(395,869)(396,870)(397,867)(398,868)(399,865)(400,866)(401,891)(402,892)(403,889)(404,890)(405,895)(406,896)(407,893)(408,894)(409,885)(410,886)(411,887)(412,888)(413,881)(414,882)(415,883)(416,884)(417,905)(418,906)(419,907)(420,908)(421,909)(422,910)(423,911)(424,912)(425,903)(426,904)(427,901)(428,902)(429,899)(430,900)(431,897)(432,898)(433,923)(434,924)(435,921)(436,922)(437,927)(438,928)(439,925)(440,926)(441,917)(442,918)(443,919)(444,920)(445,913)(446,914)(447,915)(448,916)(449,937)(450,938)(451,939)(452,940)(453,941)(454,942)(455,943)(456,944)(457,935)(458,936)(459,933)(460,934)(461,931)(462,932)(463,929)(464,930)(465,955)(466,956)(467,953)(468,954)(469,959)(470,960)(471,957)(472,958)(473,949) (474,950)(475,951)(476,952)(477,945)(478,946)(479,947)(480,948); poly := sub<Sym(960)|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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.