Polytope of Type {8,60}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,60}*1920f
if this polytope has a name.
Group : SmallGroup(1920,239469)
Rank : 3
Schlafli Type : {8,60}
Number of vertices, edges, etc : 16, 480, 120
Order of s₀s₁s₂ : 60
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {4,60}*960b, {8,30}*960c
   4-fold quotients : {4,60}*480b, {4,60}*480c, {4,30}*480
   5-fold quotients : {8,12}*384f
   8-fold quotients : {2,60}*240, {4,15}*240, {4,30}*240b, {4,30}*240c
   10-fold quotients : {4,12}*192b, {8,6}*192c
   16-fold quotients : {4,15}*120, {2,30}*120
   20-fold quotients : {4,12}*96b, {4,12}*96c, {4,6}*96
   24-fold quotients : {2,20}*80
   32-fold quotients : {2,15}*60
   40-fold quotients : {2,12}*48, {4,3}*48, {4,6}*48b, {4,6}*48c
   48-fold quotients : {2,10}*40
   80-fold quotients : {4,3}*24, {2,6}*24
   96-fold quotients : {2,5}*20
   120-fold quotients : {2,4}*16
   160-fold quotients : {2,3}*12
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope