Polytope of Type {4,60}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,60}*1920c
if this polytope has a name.
Group : SmallGroup(1920,237603)
Rank : 3
Schlafli Type : {4,60}
Number of vertices, edges, etc : 16, 480, 240
Order of s₀s₁s₂ : 60
Order of s₀s₁s₂s₁ : 4
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}*960a
   4-fold quotients : {4,60}*480c
   5-fold quotients : {4,12}*384c
   8-fold quotients : {4,30}*240b
   10-fold quotients : {4,6}*192a
   16-fold quotients : {4,15}*120
   20-fold quotients : {4,12}*96c
   40-fold quotients : {4,6}*48c
   80-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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