Polytope of Type {4,60}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,60}*1920i
if this polytope has a name.
Group : SmallGroup(1920,240273)
Rank : 3
Schlafli Type : {4,60}
Number of vertices, edges, etc : 16, 480, 240
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,30}*960d
   3-fold quotients : {4,20}*640d
   4-fold quotients : {4,15}*480
   6-fold quotients : {4,10}*320b
   12-fold quotients : {4,5}*160
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope