Polytope of Type {4,120}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,120}*1920c
if this polytope has a name.
Group : SmallGroup(1920,239539)
Rank : 3
Schlafli Type : {4,120}
Number of vertices, edges, etc : 8, 480, 240
Order of s₀s₁s₂ : 120
Order of s₀s₁s₂s₁ : 4
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 : {4,120}*960c, {4,120}*960d, {4,60}*960b
   4-fold quotients : {2,120}*480, {4,60}*480b, {4,60}*480c, {4,30}*480
   5-fold quotients : {4,24}*384c
   8-fold quotients : {2,60}*240, {4,15}*240, {4,30}*240b, {4,30}*240c
   10-fold quotients : {4,24}*192c, {4,24}*192d, {4,12}*192b
   12-fold quotients : {2,40}*160
   16-fold quotients : {4,15}*120, {2,30}*120
   20-fold quotients : {2,24}*96, {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
   60-fold quotients : {2,8}*32
   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 := (  1,483)(  2,484)(  3,481)(  4,482)(  5,487)(  6,488)(  7,485)(  8,486)
(  9,491)( 10,492)( 11,489)( 12,490)( 13,495)( 14,496)( 15,493)( 16,494)
( 17,499)( 18,500)( 19,497)( 20,498)( 21,503)( 22,504)( 23,501)( 24,502)
( 25,507)( 26,508)( 27,505)( 28,506)( 29,511)( 30,512)( 31,509)( 32,510)
( 33,515)( 34,516)( 35,513)( 36,514)( 37,519)( 38,520)( 39,517)( 40,518)
( 41,523)( 42,524)( 43,521)( 44,522)( 45,527)( 46,528)( 47,525)( 48,526)
( 49,531)( 50,532)( 51,529)( 52,530)( 53,535)( 54,536)( 55,533)( 56,534)
( 57,539)( 58,540)( 59,537)( 60,538)( 61,543)( 62,544)( 63,541)( 64,542)
( 65,547)( 66,548)( 67,545)( 68,546)( 69,551)( 70,552)( 71,549)( 72,550)
( 73,555)( 74,556)( 75,553)( 76,554)( 77,559)( 78,560)( 79,557)( 80,558)
( 81,563)( 82,564)( 83,561)( 84,562)( 85,567)( 86,568)( 87,565)( 88,566)
( 89,571)( 90,572)( 91,569)( 92,570)( 93,575)( 94,576)( 95,573)( 96,574)
( 97,579)( 98,580)( 99,577)(100,578)(101,583)(102,584)(103,581)(104,582)
(105,587)(106,588)(107,585)(108,586)(109,591)(110,592)(111,589)(112,590)
(113,595)(114,596)(115,593)(116,594)(117,599)(118,600)(119,597)(120,598)
(121,603)(122,604)(123,601)(124,602)(125,607)(126,608)(127,605)(128,606)
(129,611)(130,612)(131,609)(132,610)(133,615)(134,616)(135,613)(136,614)
(137,619)(138,620)(139,617)(140,618)(141,623)(142,624)(143,621)(144,622)
(145,627)(146,628)(147,625)(148,626)(149,631)(150,632)(151,629)(152,630)
(153,635)(154,636)(155,633)(156,634)(157,639)(158,640)(159,637)(160,638)
(161,643)(162,644)(163,641)(164,642)(165,647)(166,648)(167,645)(168,646)
(169,651)(170,652)(171,649)(172,650)(173,655)(174,656)(175,653)(176,654)
(177,659)(178,660)(179,657)(180,658)(181,663)(182,664)(183,661)(184,662)
(185,667)(186,668)(187,665)(188,666)(189,671)(190,672)(191,669)(192,670)
(193,675)(194,676)(195,673)(196,674)(197,679)(198,680)(199,677)(200,678)
(201,683)(202,684)(203,681)(204,682)(205,687)(206,688)(207,685)(208,686)
(209,691)(210,692)(211,689)(212,690)(213,695)(214,696)(215,693)(216,694)
(217,699)(218,700)(219,697)(220,698)(221,703)(222,704)(223,701)(224,702)
(225,707)(226,708)(227,705)(228,706)(229,711)(230,712)(231,709)(232,710)
(233,715)(234,716)(235,713)(236,714)(237,719)(238,720)(239,717)(240,718)
(241,723)(242,724)(243,721)(244,722)(245,727)(246,728)(247,725)(248,726)
(249,731)(250,732)(251,729)(252,730)(253,735)(254,736)(255,733)(256,734)
(257,739)(258,740)(259,737)(260,738)(261,743)(262,744)(263,741)(264,742)
(265,747)(266,748)(267,745)(268,746)(269,751)(270,752)(271,749)(272,750)
(273,755)(274,756)(275,753)(276,754)(277,759)(278,760)(279,757)(280,758)
(281,763)(282,764)(283,761)(284,762)(285,767)(286,768)(287,765)(288,766)
(289,771)(290,772)(291,769)(292,770)(293,775)(294,776)(295,773)(296,774)
(297,779)(298,780)(299,777)(300,778)(301,783)(302,784)(303,781)(304,782)
(305,787)(306,788)(307,785)(308,786)(309,791)(310,792)(311,789)(312,790)
(313,795)(314,796)(315,793)(316,794)(317,799)(318,800)(319,797)(320,798)
(321,803)(322,804)(323,801)(324,802)(325,807)(326,808)(327,805)(328,806)
(329,811)(330,812)(331,809)(332,810)(333,815)(334,816)(335,813)(336,814)
(337,819)(338,820)(339,817)(340,818)(341,823)(342,824)(343,821)(344,822)
(345,827)(346,828)(347,825)(348,826)(349,831)(350,832)(351,829)(352,830)
(353,835)(354,836)(355,833)(356,834)(357,839)(358,840)(359,837)(360,838)
(361,843)(362,844)(363,841)(364,842)(365,847)(366,848)(367,845)(368,846)
(369,851)(370,852)(371,849)(372,850)(373,855)(374,856)(375,853)(376,854)
(377,859)(378,860)(379,857)(380,858)(381,863)(382,864)(383,861)(384,862)
(385,867)(386,868)(387,865)(388,866)(389,871)(390,872)(391,869)(392,870)
(393,875)(394,876)(395,873)(396,874)(397,879)(398,880)(399,877)(400,878)
(401,883)(402,884)(403,881)(404,882)(405,887)(406,888)(407,885)(408,886)
(409,891)(410,892)(411,889)(412,890)(413,895)(414,896)(415,893)(416,894)
(417,899)(418,900)(419,897)(420,898)(421,903)(422,904)(423,901)(424,902)
(425,907)(426,908)(427,905)(428,906)(429,911)(430,912)(431,909)(432,910)
(433,915)(434,916)(435,913)(436,914)(437,919)(438,920)(439,917)(440,918)
(441,923)(442,924)(443,921)(444,922)(445,927)(446,928)(447,925)(448,926)
(449,931)(450,932)(451,929)(452,930)(453,935)(454,936)(455,933)(456,934)
(457,939)(458,940)(459,937)(460,938)(461,943)(462,944)(463,941)(464,942)
(465,947)(466,948)(467,945)(468,946)(469,951)(470,952)(471,949)(472,950)
(473,955)(474,956)(475,953)(476,954)(477,959)(478,960)(479,957)(480,958);;
s1 := (  3,  4)(  5, 17)(  6, 18)(  7, 20)(  8, 19)(  9, 13)( 10, 14)( 11, 16)
( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)( 27, 60)
( 28, 59)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)( 35, 52)
( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 63, 64)( 65, 77)( 66, 78)
( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)( 81,101)( 82,102)
( 83,104)( 84,103)( 85,117)( 86,118)( 87,120)( 88,119)( 89,113)( 90,114)
( 91,116)( 92,115)( 93,109)( 94,110)( 95,112)( 96,111)( 97,105)( 98,106)
( 99,108)(100,107)(121,181)(122,182)(123,184)(124,183)(125,197)(126,198)
(127,200)(128,199)(129,193)(130,194)(131,196)(132,195)(133,189)(134,190)
(135,192)(136,191)(137,185)(138,186)(139,188)(140,187)(141,221)(142,222)
(143,224)(144,223)(145,237)(146,238)(147,240)(148,239)(149,233)(150,234)
(151,236)(152,235)(153,229)(154,230)(155,232)(156,231)(157,225)(158,226)
(159,228)(160,227)(161,201)(162,202)(163,204)(164,203)(165,217)(166,218)
(167,220)(168,219)(169,213)(170,214)(171,216)(172,215)(173,209)(174,210)
(175,212)(176,211)(177,205)(178,206)(179,208)(180,207)(241,361)(242,362)
(243,364)(244,363)(245,377)(246,378)(247,380)(248,379)(249,373)(250,374)
(251,376)(252,375)(253,369)(254,370)(255,372)(256,371)(257,365)(258,366)
(259,368)(260,367)(261,401)(262,402)(263,404)(264,403)(265,417)(266,418)
(267,420)(268,419)(269,413)(270,414)(271,416)(272,415)(273,409)(274,410)
(275,412)(276,411)(277,405)(278,406)(279,408)(280,407)(281,381)(282,382)
(283,384)(284,383)(285,397)(286,398)(287,400)(288,399)(289,393)(290,394)
(291,396)(292,395)(293,389)(294,390)(295,392)(296,391)(297,385)(298,386)
(299,388)(300,387)(301,421)(302,422)(303,424)(304,423)(305,437)(306,438)
(307,440)(308,439)(309,433)(310,434)(311,436)(312,435)(313,429)(314,430)
(315,432)(316,431)(317,425)(318,426)(319,428)(320,427)(321,461)(322,462)
(323,464)(324,463)(325,477)(326,478)(327,480)(328,479)(329,473)(330,474)
(331,476)(332,475)(333,469)(334,470)(335,472)(336,471)(337,465)(338,466)
(339,468)(340,467)(341,441)(342,442)(343,444)(344,443)(345,457)(346,458)
(347,460)(348,459)(349,453)(350,454)(351,456)(352,455)(353,449)(354,450)
(355,452)(356,451)(357,445)(358,446)(359,448)(360,447)(483,484)(485,497)
(486,498)(487,500)(488,499)(489,493)(490,494)(491,496)(492,495)(501,521)
(502,522)(503,524)(504,523)(505,537)(506,538)(507,540)(508,539)(509,533)
(510,534)(511,536)(512,535)(513,529)(514,530)(515,532)(516,531)(517,525)
(518,526)(519,528)(520,527)(543,544)(545,557)(546,558)(547,560)(548,559)
(549,553)(550,554)(551,556)(552,555)(561,581)(562,582)(563,584)(564,583)
(565,597)(566,598)(567,600)(568,599)(569,593)(570,594)(571,596)(572,595)
(573,589)(574,590)(575,592)(576,591)(577,585)(578,586)(579,588)(580,587)
(601,661)(602,662)(603,664)(604,663)(605,677)(606,678)(607,680)(608,679)
(609,673)(610,674)(611,676)(612,675)(613,669)(614,670)(615,672)(616,671)
(617,665)(618,666)(619,668)(620,667)(621,701)(622,702)(623,704)(624,703)
(625,717)(626,718)(627,720)(628,719)(629,713)(630,714)(631,716)(632,715)
(633,709)(634,710)(635,712)(636,711)(637,705)(638,706)(639,708)(640,707)
(641,681)(642,682)(643,684)(644,683)(645,697)(646,698)(647,700)(648,699)
(649,693)(650,694)(651,696)(652,695)(653,689)(654,690)(655,692)(656,691)
(657,685)(658,686)(659,688)(660,687)(721,841)(722,842)(723,844)(724,843)
(725,857)(726,858)(727,860)(728,859)(729,853)(730,854)(731,856)(732,855)
(733,849)(734,850)(735,852)(736,851)(737,845)(738,846)(739,848)(740,847)
(741,881)(742,882)(743,884)(744,883)(745,897)(746,898)(747,900)(748,899)
(749,893)(750,894)(751,896)(752,895)(753,889)(754,890)(755,892)(756,891)
(757,885)(758,886)(759,888)(760,887)(761,861)(762,862)(763,864)(764,863)
(765,877)(766,878)(767,880)(768,879)(769,873)(770,874)(771,876)(772,875)
(773,869)(774,870)(775,872)(776,871)(777,865)(778,866)(779,868)(780,867)
(781,901)(782,902)(783,904)(784,903)(785,917)(786,918)(787,920)(788,919)
(789,913)(790,914)(791,916)(792,915)(793,909)(794,910)(795,912)(796,911)
(797,905)(798,906)(799,908)(800,907)(801,941)(802,942)(803,944)(804,943)
(805,957)(806,958)(807,960)(808,959)(809,953)(810,954)(811,956)(812,955)
(813,949)(814,950)(815,952)(816,951)(817,945)(818,946)(819,948)(820,947)
(821,921)(822,922)(823,924)(824,923)(825,937)(826,938)(827,940)(828,939)
(829,933)(830,934)(831,936)(832,935)(833,929)(834,930)(835,932)(836,931)
(837,925)(838,926)(839,928)(840,927);;
s2 := (  1,265)(  2,268)(  3,267)(  4,266)(  5,261)(  6,264)(  7,263)(  8,262)
(  9,277)( 10,280)( 11,279)( 12,278)( 13,273)( 14,276)( 15,275)( 16,274)
( 17,269)( 18,272)( 19,271)( 20,270)( 21,245)( 22,248)( 23,247)( 24,246)
( 25,241)( 26,244)( 27,243)( 28,242)( 29,257)( 30,260)( 31,259)( 32,258)
( 33,253)( 34,256)( 35,255)( 36,254)( 37,249)( 38,252)( 39,251)( 40,250)
( 41,285)( 42,288)( 43,287)( 44,286)( 45,281)( 46,284)( 47,283)( 48,282)
( 49,297)( 50,300)( 51,299)( 52,298)( 53,293)( 54,296)( 55,295)( 56,294)
( 57,289)( 58,292)( 59,291)( 60,290)( 61,325)( 62,328)( 63,327)( 64,326)
( 65,321)( 66,324)( 67,323)( 68,322)( 69,337)( 70,340)( 71,339)( 72,338)
( 73,333)( 74,336)( 75,335)( 76,334)( 77,329)( 78,332)( 79,331)( 80,330)
( 81,305)( 82,308)( 83,307)( 84,306)( 85,301)( 86,304)( 87,303)( 88,302)
( 89,317)( 90,320)( 91,319)( 92,318)( 93,313)( 94,316)( 95,315)( 96,314)
( 97,309)( 98,312)( 99,311)(100,310)(101,345)(102,348)(103,347)(104,346)
(105,341)(106,344)(107,343)(108,342)(109,357)(110,360)(111,359)(112,358)
(113,353)(114,356)(115,355)(116,354)(117,349)(118,352)(119,351)(120,350)
(121,445)(122,448)(123,447)(124,446)(125,441)(126,444)(127,443)(128,442)
(129,457)(130,460)(131,459)(132,458)(133,453)(134,456)(135,455)(136,454)
(137,449)(138,452)(139,451)(140,450)(141,425)(142,428)(143,427)(144,426)
(145,421)(146,424)(147,423)(148,422)(149,437)(150,440)(151,439)(152,438)
(153,433)(154,436)(155,435)(156,434)(157,429)(158,432)(159,431)(160,430)
(161,465)(162,468)(163,467)(164,466)(165,461)(166,464)(167,463)(168,462)
(169,477)(170,480)(171,479)(172,478)(173,473)(174,476)(175,475)(176,474)
(177,469)(178,472)(179,471)(180,470)(181,385)(182,388)(183,387)(184,386)
(185,381)(186,384)(187,383)(188,382)(189,397)(190,400)(191,399)(192,398)
(193,393)(194,396)(195,395)(196,394)(197,389)(198,392)(199,391)(200,390)
(201,365)(202,368)(203,367)(204,366)(205,361)(206,364)(207,363)(208,362)
(209,377)(210,380)(211,379)(212,378)(213,373)(214,376)(215,375)(216,374)
(217,369)(218,372)(219,371)(220,370)(221,405)(222,408)(223,407)(224,406)
(225,401)(226,404)(227,403)(228,402)(229,417)(230,420)(231,419)(232,418)
(233,413)(234,416)(235,415)(236,414)(237,409)(238,412)(239,411)(240,410)
(481,745)(482,748)(483,747)(484,746)(485,741)(486,744)(487,743)(488,742)
(489,757)(490,760)(491,759)(492,758)(493,753)(494,756)(495,755)(496,754)
(497,749)(498,752)(499,751)(500,750)(501,725)(502,728)(503,727)(504,726)
(505,721)(506,724)(507,723)(508,722)(509,737)(510,740)(511,739)(512,738)
(513,733)(514,736)(515,735)(516,734)(517,729)(518,732)(519,731)(520,730)
(521,765)(522,768)(523,767)(524,766)(525,761)(526,764)(527,763)(528,762)
(529,777)(530,780)(531,779)(532,778)(533,773)(534,776)(535,775)(536,774)
(537,769)(538,772)(539,771)(540,770)(541,805)(542,808)(543,807)(544,806)
(545,801)(546,804)(547,803)(548,802)(549,817)(550,820)(551,819)(552,818)
(553,813)(554,816)(555,815)(556,814)(557,809)(558,812)(559,811)(560,810)
(561,785)(562,788)(563,787)(564,786)(565,781)(566,784)(567,783)(568,782)
(569,797)(570,800)(571,799)(572,798)(573,793)(574,796)(575,795)(576,794)
(577,789)(578,792)(579,791)(580,790)(581,825)(582,828)(583,827)(584,826)
(585,821)(586,824)(587,823)(588,822)(589,837)(590,840)(591,839)(592,838)
(593,833)(594,836)(595,835)(596,834)(597,829)(598,832)(599,831)(600,830)
(601,925)(602,928)(603,927)(604,926)(605,921)(606,924)(607,923)(608,922)
(609,937)(610,940)(611,939)(612,938)(613,933)(614,936)(615,935)(616,934)
(617,929)(618,932)(619,931)(620,930)(621,905)(622,908)(623,907)(624,906)
(625,901)(626,904)(627,903)(628,902)(629,917)(630,920)(631,919)(632,918)
(633,913)(634,916)(635,915)(636,914)(637,909)(638,912)(639,911)(640,910)
(641,945)(642,948)(643,947)(644,946)(645,941)(646,944)(647,943)(648,942)
(649,957)(650,960)(651,959)(652,958)(653,953)(654,956)(655,955)(656,954)
(657,949)(658,952)(659,951)(660,950)(661,865)(662,868)(663,867)(664,866)
(665,861)(666,864)(667,863)(668,862)(669,877)(670,880)(671,879)(672,878)
(673,873)(674,876)(675,875)(676,874)(677,869)(678,872)(679,871)(680,870)
(681,845)(682,848)(683,847)(684,846)(685,841)(686,844)(687,843)(688,842)
(689,857)(690,860)(691,859)(692,858)(693,853)(694,856)(695,855)(696,854)
(697,849)(698,852)(699,851)(700,850)(701,885)(702,888)(703,887)(704,886)
(705,881)(706,884)(707,883)(708,882)(709,897)(710,900)(711,899)(712,898)
(713,893)(714,896)(715,895)(716,894)(717,889)(718,892)(719,891)(720,890);;
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*s0*s1*s2*s1*s2*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*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)!(  1,483)(  2,484)(  3,481)(  4,482)(  5,487)(  6,488)(  7,485)
(  8,486)(  9,491)( 10,492)( 11,489)( 12,490)( 13,495)( 14,496)( 15,493)
( 16,494)( 17,499)( 18,500)( 19,497)( 20,498)( 21,503)( 22,504)( 23,501)
( 24,502)( 25,507)( 26,508)( 27,505)( 28,506)( 29,511)( 30,512)( 31,509)
( 32,510)( 33,515)( 34,516)( 35,513)( 36,514)( 37,519)( 38,520)( 39,517)
( 40,518)( 41,523)( 42,524)( 43,521)( 44,522)( 45,527)( 46,528)( 47,525)
( 48,526)( 49,531)( 50,532)( 51,529)( 52,530)( 53,535)( 54,536)( 55,533)
( 56,534)( 57,539)( 58,540)( 59,537)( 60,538)( 61,543)( 62,544)( 63,541)
( 64,542)( 65,547)( 66,548)( 67,545)( 68,546)( 69,551)( 70,552)( 71,549)
( 72,550)( 73,555)( 74,556)( 75,553)( 76,554)( 77,559)( 78,560)( 79,557)
( 80,558)( 81,563)( 82,564)( 83,561)( 84,562)( 85,567)( 86,568)( 87,565)
( 88,566)( 89,571)( 90,572)( 91,569)( 92,570)( 93,575)( 94,576)( 95,573)
( 96,574)( 97,579)( 98,580)( 99,577)(100,578)(101,583)(102,584)(103,581)
(104,582)(105,587)(106,588)(107,585)(108,586)(109,591)(110,592)(111,589)
(112,590)(113,595)(114,596)(115,593)(116,594)(117,599)(118,600)(119,597)
(120,598)(121,603)(122,604)(123,601)(124,602)(125,607)(126,608)(127,605)
(128,606)(129,611)(130,612)(131,609)(132,610)(133,615)(134,616)(135,613)
(136,614)(137,619)(138,620)(139,617)(140,618)(141,623)(142,624)(143,621)
(144,622)(145,627)(146,628)(147,625)(148,626)(149,631)(150,632)(151,629)
(152,630)(153,635)(154,636)(155,633)(156,634)(157,639)(158,640)(159,637)
(160,638)(161,643)(162,644)(163,641)(164,642)(165,647)(166,648)(167,645)
(168,646)(169,651)(170,652)(171,649)(172,650)(173,655)(174,656)(175,653)
(176,654)(177,659)(178,660)(179,657)(180,658)(181,663)(182,664)(183,661)
(184,662)(185,667)(186,668)(187,665)(188,666)(189,671)(190,672)(191,669)
(192,670)(193,675)(194,676)(195,673)(196,674)(197,679)(198,680)(199,677)
(200,678)(201,683)(202,684)(203,681)(204,682)(205,687)(206,688)(207,685)
(208,686)(209,691)(210,692)(211,689)(212,690)(213,695)(214,696)(215,693)
(216,694)(217,699)(218,700)(219,697)(220,698)(221,703)(222,704)(223,701)
(224,702)(225,707)(226,708)(227,705)(228,706)(229,711)(230,712)(231,709)
(232,710)(233,715)(234,716)(235,713)(236,714)(237,719)(238,720)(239,717)
(240,718)(241,723)(242,724)(243,721)(244,722)(245,727)(246,728)(247,725)
(248,726)(249,731)(250,732)(251,729)(252,730)(253,735)(254,736)(255,733)
(256,734)(257,739)(258,740)(259,737)(260,738)(261,743)(262,744)(263,741)
(264,742)(265,747)(266,748)(267,745)(268,746)(269,751)(270,752)(271,749)
(272,750)(273,755)(274,756)(275,753)(276,754)(277,759)(278,760)(279,757)
(280,758)(281,763)(282,764)(283,761)(284,762)(285,767)(286,768)(287,765)
(288,766)(289,771)(290,772)(291,769)(292,770)(293,775)(294,776)(295,773)
(296,774)(297,779)(298,780)(299,777)(300,778)(301,783)(302,784)(303,781)
(304,782)(305,787)(306,788)(307,785)(308,786)(309,791)(310,792)(311,789)
(312,790)(313,795)(314,796)(315,793)(316,794)(317,799)(318,800)(319,797)
(320,798)(321,803)(322,804)(323,801)(324,802)(325,807)(326,808)(327,805)
(328,806)(329,811)(330,812)(331,809)(332,810)(333,815)(334,816)(335,813)
(336,814)(337,819)(338,820)(339,817)(340,818)(341,823)(342,824)(343,821)
(344,822)(345,827)(346,828)(347,825)(348,826)(349,831)(350,832)(351,829)
(352,830)(353,835)(354,836)(355,833)(356,834)(357,839)(358,840)(359,837)
(360,838)(361,843)(362,844)(363,841)(364,842)(365,847)(366,848)(367,845)
(368,846)(369,851)(370,852)(371,849)(372,850)(373,855)(374,856)(375,853)
(376,854)(377,859)(378,860)(379,857)(380,858)(381,863)(382,864)(383,861)
(384,862)(385,867)(386,868)(387,865)(388,866)(389,871)(390,872)(391,869)
(392,870)(393,875)(394,876)(395,873)(396,874)(397,879)(398,880)(399,877)
(400,878)(401,883)(402,884)(403,881)(404,882)(405,887)(406,888)(407,885)
(408,886)(409,891)(410,892)(411,889)(412,890)(413,895)(414,896)(415,893)
(416,894)(417,899)(418,900)(419,897)(420,898)(421,903)(422,904)(423,901)
(424,902)(425,907)(426,908)(427,905)(428,906)(429,911)(430,912)(431,909)
(432,910)(433,915)(434,916)(435,913)(436,914)(437,919)(438,920)(439,917)
(440,918)(441,923)(442,924)(443,921)(444,922)(445,927)(446,928)(447,925)
(448,926)(449,931)(450,932)(451,929)(452,930)(453,935)(454,936)(455,933)
(456,934)(457,939)(458,940)(459,937)(460,938)(461,943)(462,944)(463,941)
(464,942)(465,947)(466,948)(467,945)(468,946)(469,951)(470,952)(471,949)
(472,950)(473,955)(474,956)(475,953)(476,954)(477,959)(478,960)(479,957)
(480,958);
s1 := Sym(960)!(  3,  4)(  5, 17)(  6, 18)(  7, 20)(  8, 19)(  9, 13)( 10, 14)
( 11, 16)( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)
( 27, 60)( 28, 59)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)
( 35, 52)( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 63, 64)( 65, 77)
( 66, 78)( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)( 81,101)
( 82,102)( 83,104)( 84,103)( 85,117)( 86,118)( 87,120)( 88,119)( 89,113)
( 90,114)( 91,116)( 92,115)( 93,109)( 94,110)( 95,112)( 96,111)( 97,105)
( 98,106)( 99,108)(100,107)(121,181)(122,182)(123,184)(124,183)(125,197)
(126,198)(127,200)(128,199)(129,193)(130,194)(131,196)(132,195)(133,189)
(134,190)(135,192)(136,191)(137,185)(138,186)(139,188)(140,187)(141,221)
(142,222)(143,224)(144,223)(145,237)(146,238)(147,240)(148,239)(149,233)
(150,234)(151,236)(152,235)(153,229)(154,230)(155,232)(156,231)(157,225)
(158,226)(159,228)(160,227)(161,201)(162,202)(163,204)(164,203)(165,217)
(166,218)(167,220)(168,219)(169,213)(170,214)(171,216)(172,215)(173,209)
(174,210)(175,212)(176,211)(177,205)(178,206)(179,208)(180,207)(241,361)
(242,362)(243,364)(244,363)(245,377)(246,378)(247,380)(248,379)(249,373)
(250,374)(251,376)(252,375)(253,369)(254,370)(255,372)(256,371)(257,365)
(258,366)(259,368)(260,367)(261,401)(262,402)(263,404)(264,403)(265,417)
(266,418)(267,420)(268,419)(269,413)(270,414)(271,416)(272,415)(273,409)
(274,410)(275,412)(276,411)(277,405)(278,406)(279,408)(280,407)(281,381)
(282,382)(283,384)(284,383)(285,397)(286,398)(287,400)(288,399)(289,393)
(290,394)(291,396)(292,395)(293,389)(294,390)(295,392)(296,391)(297,385)
(298,386)(299,388)(300,387)(301,421)(302,422)(303,424)(304,423)(305,437)
(306,438)(307,440)(308,439)(309,433)(310,434)(311,436)(312,435)(313,429)
(314,430)(315,432)(316,431)(317,425)(318,426)(319,428)(320,427)(321,461)
(322,462)(323,464)(324,463)(325,477)(326,478)(327,480)(328,479)(329,473)
(330,474)(331,476)(332,475)(333,469)(334,470)(335,472)(336,471)(337,465)
(338,466)(339,468)(340,467)(341,441)(342,442)(343,444)(344,443)(345,457)
(346,458)(347,460)(348,459)(349,453)(350,454)(351,456)(352,455)(353,449)
(354,450)(355,452)(356,451)(357,445)(358,446)(359,448)(360,447)(483,484)
(485,497)(486,498)(487,500)(488,499)(489,493)(490,494)(491,496)(492,495)
(501,521)(502,522)(503,524)(504,523)(505,537)(506,538)(507,540)(508,539)
(509,533)(510,534)(511,536)(512,535)(513,529)(514,530)(515,532)(516,531)
(517,525)(518,526)(519,528)(520,527)(543,544)(545,557)(546,558)(547,560)
(548,559)(549,553)(550,554)(551,556)(552,555)(561,581)(562,582)(563,584)
(564,583)(565,597)(566,598)(567,600)(568,599)(569,593)(570,594)(571,596)
(572,595)(573,589)(574,590)(575,592)(576,591)(577,585)(578,586)(579,588)
(580,587)(601,661)(602,662)(603,664)(604,663)(605,677)(606,678)(607,680)
(608,679)(609,673)(610,674)(611,676)(612,675)(613,669)(614,670)(615,672)
(616,671)(617,665)(618,666)(619,668)(620,667)(621,701)(622,702)(623,704)
(624,703)(625,717)(626,718)(627,720)(628,719)(629,713)(630,714)(631,716)
(632,715)(633,709)(634,710)(635,712)(636,711)(637,705)(638,706)(639,708)
(640,707)(641,681)(642,682)(643,684)(644,683)(645,697)(646,698)(647,700)
(648,699)(649,693)(650,694)(651,696)(652,695)(653,689)(654,690)(655,692)
(656,691)(657,685)(658,686)(659,688)(660,687)(721,841)(722,842)(723,844)
(724,843)(725,857)(726,858)(727,860)(728,859)(729,853)(730,854)(731,856)
(732,855)(733,849)(734,850)(735,852)(736,851)(737,845)(738,846)(739,848)
(740,847)(741,881)(742,882)(743,884)(744,883)(745,897)(746,898)(747,900)
(748,899)(749,893)(750,894)(751,896)(752,895)(753,889)(754,890)(755,892)
(756,891)(757,885)(758,886)(759,888)(760,887)(761,861)(762,862)(763,864)
(764,863)(765,877)(766,878)(767,880)(768,879)(769,873)(770,874)(771,876)
(772,875)(773,869)(774,870)(775,872)(776,871)(777,865)(778,866)(779,868)
(780,867)(781,901)(782,902)(783,904)(784,903)(785,917)(786,918)(787,920)
(788,919)(789,913)(790,914)(791,916)(792,915)(793,909)(794,910)(795,912)
(796,911)(797,905)(798,906)(799,908)(800,907)(801,941)(802,942)(803,944)
(804,943)(805,957)(806,958)(807,960)(808,959)(809,953)(810,954)(811,956)
(812,955)(813,949)(814,950)(815,952)(816,951)(817,945)(818,946)(819,948)
(820,947)(821,921)(822,922)(823,924)(824,923)(825,937)(826,938)(827,940)
(828,939)(829,933)(830,934)(831,936)(832,935)(833,929)(834,930)(835,932)
(836,931)(837,925)(838,926)(839,928)(840,927);
s2 := Sym(960)!(  1,265)(  2,268)(  3,267)(  4,266)(  5,261)(  6,264)(  7,263)
(  8,262)(  9,277)( 10,280)( 11,279)( 12,278)( 13,273)( 14,276)( 15,275)
( 16,274)( 17,269)( 18,272)( 19,271)( 20,270)( 21,245)( 22,248)( 23,247)
( 24,246)( 25,241)( 26,244)( 27,243)( 28,242)( 29,257)( 30,260)( 31,259)
( 32,258)( 33,253)( 34,256)( 35,255)( 36,254)( 37,249)( 38,252)( 39,251)
( 40,250)( 41,285)( 42,288)( 43,287)( 44,286)( 45,281)( 46,284)( 47,283)
( 48,282)( 49,297)( 50,300)( 51,299)( 52,298)( 53,293)( 54,296)( 55,295)
( 56,294)( 57,289)( 58,292)( 59,291)( 60,290)( 61,325)( 62,328)( 63,327)
( 64,326)( 65,321)( 66,324)( 67,323)( 68,322)( 69,337)( 70,340)( 71,339)
( 72,338)( 73,333)( 74,336)( 75,335)( 76,334)( 77,329)( 78,332)( 79,331)
( 80,330)( 81,305)( 82,308)( 83,307)( 84,306)( 85,301)( 86,304)( 87,303)
( 88,302)( 89,317)( 90,320)( 91,319)( 92,318)( 93,313)( 94,316)( 95,315)
( 96,314)( 97,309)( 98,312)( 99,311)(100,310)(101,345)(102,348)(103,347)
(104,346)(105,341)(106,344)(107,343)(108,342)(109,357)(110,360)(111,359)
(112,358)(113,353)(114,356)(115,355)(116,354)(117,349)(118,352)(119,351)
(120,350)(121,445)(122,448)(123,447)(124,446)(125,441)(126,444)(127,443)
(128,442)(129,457)(130,460)(131,459)(132,458)(133,453)(134,456)(135,455)
(136,454)(137,449)(138,452)(139,451)(140,450)(141,425)(142,428)(143,427)
(144,426)(145,421)(146,424)(147,423)(148,422)(149,437)(150,440)(151,439)
(152,438)(153,433)(154,436)(155,435)(156,434)(157,429)(158,432)(159,431)
(160,430)(161,465)(162,468)(163,467)(164,466)(165,461)(166,464)(167,463)
(168,462)(169,477)(170,480)(171,479)(172,478)(173,473)(174,476)(175,475)
(176,474)(177,469)(178,472)(179,471)(180,470)(181,385)(182,388)(183,387)
(184,386)(185,381)(186,384)(187,383)(188,382)(189,397)(190,400)(191,399)
(192,398)(193,393)(194,396)(195,395)(196,394)(197,389)(198,392)(199,391)
(200,390)(201,365)(202,368)(203,367)(204,366)(205,361)(206,364)(207,363)
(208,362)(209,377)(210,380)(211,379)(212,378)(213,373)(214,376)(215,375)
(216,374)(217,369)(218,372)(219,371)(220,370)(221,405)(222,408)(223,407)
(224,406)(225,401)(226,404)(227,403)(228,402)(229,417)(230,420)(231,419)
(232,418)(233,413)(234,416)(235,415)(236,414)(237,409)(238,412)(239,411)
(240,410)(481,745)(482,748)(483,747)(484,746)(485,741)(486,744)(487,743)
(488,742)(489,757)(490,760)(491,759)(492,758)(493,753)(494,756)(495,755)
(496,754)(497,749)(498,752)(499,751)(500,750)(501,725)(502,728)(503,727)
(504,726)(505,721)(506,724)(507,723)(508,722)(509,737)(510,740)(511,739)
(512,738)(513,733)(514,736)(515,735)(516,734)(517,729)(518,732)(519,731)
(520,730)(521,765)(522,768)(523,767)(524,766)(525,761)(526,764)(527,763)
(528,762)(529,777)(530,780)(531,779)(532,778)(533,773)(534,776)(535,775)
(536,774)(537,769)(538,772)(539,771)(540,770)(541,805)(542,808)(543,807)
(544,806)(545,801)(546,804)(547,803)(548,802)(549,817)(550,820)(551,819)
(552,818)(553,813)(554,816)(555,815)(556,814)(557,809)(558,812)(559,811)
(560,810)(561,785)(562,788)(563,787)(564,786)(565,781)(566,784)(567,783)
(568,782)(569,797)(570,800)(571,799)(572,798)(573,793)(574,796)(575,795)
(576,794)(577,789)(578,792)(579,791)(580,790)(581,825)(582,828)(583,827)
(584,826)(585,821)(586,824)(587,823)(588,822)(589,837)(590,840)(591,839)
(592,838)(593,833)(594,836)(595,835)(596,834)(597,829)(598,832)(599,831)
(600,830)(601,925)(602,928)(603,927)(604,926)(605,921)(606,924)(607,923)
(608,922)(609,937)(610,940)(611,939)(612,938)(613,933)(614,936)(615,935)
(616,934)(617,929)(618,932)(619,931)(620,930)(621,905)(622,908)(623,907)
(624,906)(625,901)(626,904)(627,903)(628,902)(629,917)(630,920)(631,919)
(632,918)(633,913)(634,916)(635,915)(636,914)(637,909)(638,912)(639,911)
(640,910)(641,945)(642,948)(643,947)(644,946)(645,941)(646,944)(647,943)
(648,942)(649,957)(650,960)(651,959)(652,958)(653,953)(654,956)(655,955)
(656,954)(657,949)(658,952)(659,951)(660,950)(661,865)(662,868)(663,867)
(664,866)(665,861)(666,864)(667,863)(668,862)(669,877)(670,880)(671,879)
(672,878)(673,873)(674,876)(675,875)(676,874)(677,869)(678,872)(679,871)
(680,870)(681,845)(682,848)(683,847)(684,846)(685,841)(686,844)(687,843)
(688,842)(689,857)(690,860)(691,859)(692,858)(693,853)(694,856)(695,855)
(696,854)(697,849)(698,852)(699,851)(700,850)(701,885)(702,888)(703,887)
(704,886)(705,881)(706,884)(707,883)(708,882)(709,897)(710,900)(711,899)
(712,898)(713,893)(714,896)(715,895)(716,894)(717,889)(718,892)(719,891)
(720,890);
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*s0*s1*s2*s1*s2*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*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