Polytope of Type {8,60}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,60}*1920e
if this polytope has a name.
Group : SmallGroup(1920,239446)
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}*960b
   4-fold quotients : {4,60}*480b, {4,60}*480c, {8,15}*480, {4,30}*480
   5-fold quotients : {8,12}*384e
   8-fold quotients : {2,60}*240, {4,15}*240, {4,30}*240b, {4,30}*240c
   10-fold quotients : {4,12}*192b, {8,6}*192b
   16-fold quotients : {4,15}*120, {2,30}*120
   20-fold quotients : {4,12}*96b, {4,12}*96c, {8,3}*96, {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 := (  1,485)(  2,486)(  3,488)(  4,487)(  5,482)(  6,481)(  7,483)(  8,484)
(  9,493)( 10,494)( 11,496)( 12,495)( 13,490)( 14,489)( 15,491)( 16,492)
( 17,501)( 18,502)( 19,504)( 20,503)( 21,498)( 22,497)( 23,499)( 24,500)
( 25,509)( 26,510)( 27,512)( 28,511)( 29,506)( 30,505)( 31,507)( 32,508)
( 33,517)( 34,518)( 35,520)( 36,519)( 37,514)( 38,513)( 39,515)( 40,516)
( 41,525)( 42,526)( 43,528)( 44,527)( 45,522)( 46,521)( 47,523)( 48,524)
( 49,533)( 50,534)( 51,536)( 52,535)( 53,530)( 54,529)( 55,531)( 56,532)
( 57,541)( 58,542)( 59,544)( 60,543)( 61,538)( 62,537)( 63,539)( 64,540)
( 65,549)( 66,550)( 67,552)( 68,551)( 69,546)( 70,545)( 71,547)( 72,548)
( 73,557)( 74,558)( 75,560)( 76,559)( 77,554)( 78,553)( 79,555)( 80,556)
( 81,565)( 82,566)( 83,568)( 84,567)( 85,562)( 86,561)( 87,563)( 88,564)
( 89,573)( 90,574)( 91,576)( 92,575)( 93,570)( 94,569)( 95,571)( 96,572)
( 97,581)( 98,582)( 99,584)(100,583)(101,578)(102,577)(103,579)(104,580)
(105,589)(106,590)(107,592)(108,591)(109,586)(110,585)(111,587)(112,588)
(113,597)(114,598)(115,600)(116,599)(117,594)(118,593)(119,595)(120,596)
(121,605)(122,606)(123,608)(124,607)(125,602)(126,601)(127,603)(128,604)
(129,613)(130,614)(131,616)(132,615)(133,610)(134,609)(135,611)(136,612)
(137,621)(138,622)(139,624)(140,623)(141,618)(142,617)(143,619)(144,620)
(145,629)(146,630)(147,632)(148,631)(149,626)(150,625)(151,627)(152,628)
(153,637)(154,638)(155,640)(156,639)(157,634)(158,633)(159,635)(160,636)
(161,645)(162,646)(163,648)(164,647)(165,642)(166,641)(167,643)(168,644)
(169,653)(170,654)(171,656)(172,655)(173,650)(174,649)(175,651)(176,652)
(177,661)(178,662)(179,664)(180,663)(181,658)(182,657)(183,659)(184,660)
(185,669)(186,670)(187,672)(188,671)(189,666)(190,665)(191,667)(192,668)
(193,677)(194,678)(195,680)(196,679)(197,674)(198,673)(199,675)(200,676)
(201,685)(202,686)(203,688)(204,687)(205,682)(206,681)(207,683)(208,684)
(209,693)(210,694)(211,696)(212,695)(213,690)(214,689)(215,691)(216,692)
(217,701)(218,702)(219,704)(220,703)(221,698)(222,697)(223,699)(224,700)
(225,709)(226,710)(227,712)(228,711)(229,706)(230,705)(231,707)(232,708)
(233,717)(234,718)(235,720)(236,719)(237,714)(238,713)(239,715)(240,716)
(241,725)(242,726)(243,728)(244,727)(245,722)(246,721)(247,723)(248,724)
(249,733)(250,734)(251,736)(252,735)(253,730)(254,729)(255,731)(256,732)
(257,741)(258,742)(259,744)(260,743)(261,738)(262,737)(263,739)(264,740)
(265,749)(266,750)(267,752)(268,751)(269,746)(270,745)(271,747)(272,748)
(273,757)(274,758)(275,760)(276,759)(277,754)(278,753)(279,755)(280,756)
(281,765)(282,766)(283,768)(284,767)(285,762)(286,761)(287,763)(288,764)
(289,773)(290,774)(291,776)(292,775)(293,770)(294,769)(295,771)(296,772)
(297,781)(298,782)(299,784)(300,783)(301,778)(302,777)(303,779)(304,780)
(305,789)(306,790)(307,792)(308,791)(309,786)(310,785)(311,787)(312,788)
(313,797)(314,798)(315,800)(316,799)(317,794)(318,793)(319,795)(320,796)
(321,805)(322,806)(323,808)(324,807)(325,802)(326,801)(327,803)(328,804)
(329,813)(330,814)(331,816)(332,815)(333,810)(334,809)(335,811)(336,812)
(337,821)(338,822)(339,824)(340,823)(341,818)(342,817)(343,819)(344,820)
(345,829)(346,830)(347,832)(348,831)(349,826)(350,825)(351,827)(352,828)
(353,837)(354,838)(355,840)(356,839)(357,834)(358,833)(359,835)(360,836)
(361,845)(362,846)(363,848)(364,847)(365,842)(366,841)(367,843)(368,844)
(369,853)(370,854)(371,856)(372,855)(373,850)(374,849)(375,851)(376,852)
(377,861)(378,862)(379,864)(380,863)(381,858)(382,857)(383,859)(384,860)
(385,869)(386,870)(387,872)(388,871)(389,866)(390,865)(391,867)(392,868)
(393,877)(394,878)(395,880)(396,879)(397,874)(398,873)(399,875)(400,876)
(401,885)(402,886)(403,888)(404,887)(405,882)(406,881)(407,883)(408,884)
(409,893)(410,894)(411,896)(412,895)(413,890)(414,889)(415,891)(416,892)
(417,901)(418,902)(419,904)(420,903)(421,898)(422,897)(423,899)(424,900)
(425,909)(426,910)(427,912)(428,911)(429,906)(430,905)(431,907)(432,908)
(433,917)(434,918)(435,920)(436,919)(437,914)(438,913)(439,915)(440,916)
(441,925)(442,926)(443,928)(444,927)(445,922)(446,921)(447,923)(448,924)
(449,933)(450,934)(451,936)(452,935)(453,930)(454,929)(455,931)(456,932)
(457,941)(458,942)(459,944)(460,943)(461,938)(462,937)(463,939)(464,940)
(465,949)(466,950)(467,952)(468,951)(469,946)(470,945)(471,947)(472,948)
(473,957)(474,958)(475,960)(476,959)(477,954)(478,953)(479,955)(480,956);;
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)(481,482)(485,488)
(486,487)(489,514)(490,513)(491,515)(492,516)(493,520)(494,519)(495,518)
(496,517)(497,506)(498,505)(499,507)(500,508)(501,512)(502,511)(503,510)
(504,509)(521,562)(522,561)(523,563)(524,564)(525,568)(526,567)(527,566)
(528,565)(529,594)(530,593)(531,595)(532,596)(533,600)(534,599)(535,598)
(536,597)(537,586)(538,585)(539,587)(540,588)(541,592)(542,591)(543,590)
(544,589)(545,578)(546,577)(547,579)(548,580)(549,584)(550,583)(551,582)
(552,581)(553,570)(554,569)(555,571)(556,572)(557,576)(558,575)(559,574)
(560,573)(601,602)(605,608)(606,607)(609,634)(610,633)(611,635)(612,636)
(613,640)(614,639)(615,638)(616,637)(617,626)(618,625)(619,627)(620,628)
(621,632)(622,631)(623,630)(624,629)(641,682)(642,681)(643,683)(644,684)
(645,688)(646,687)(647,686)(648,685)(649,714)(650,713)(651,715)(652,716)
(653,720)(654,719)(655,718)(656,717)(657,706)(658,705)(659,707)(660,708)
(661,712)(662,711)(663,710)(664,709)(665,698)(666,697)(667,699)(668,700)
(669,704)(670,703)(671,702)(672,701)(673,690)(674,689)(675,691)(676,692)
(677,696)(678,695)(679,694)(680,693)(721,842)(722,841)(723,843)(724,844)
(725,848)(726,847)(727,846)(728,845)(729,874)(730,873)(731,875)(732,876)
(733,880)(734,879)(735,878)(736,877)(737,866)(738,865)(739,867)(740,868)
(741,872)(742,871)(743,870)(744,869)(745,858)(746,857)(747,859)(748,860)
(749,864)(750,863)(751,862)(752,861)(753,850)(754,849)(755,851)(756,852)
(757,856)(758,855)(759,854)(760,853)(761,922)(762,921)(763,923)(764,924)
(765,928)(766,927)(767,926)(768,925)(769,954)(770,953)(771,955)(772,956)
(773,960)(774,959)(775,958)(776,957)(777,946)(778,945)(779,947)(780,948)
(781,952)(782,951)(783,950)(784,949)(785,938)(786,937)(787,939)(788,940)
(789,944)(790,943)(791,942)(792,941)(793,930)(794,929)(795,931)(796,932)
(797,936)(798,935)(799,934)(800,933)(801,882)(802,881)(803,883)(804,884)
(805,888)(806,887)(807,886)(808,885)(809,914)(810,913)(811,915)(812,916)
(813,920)(814,919)(815,918)(816,917)(817,906)(818,905)(819,907)(820,908)
(821,912)(822,911)(823,910)(824,909)(825,898)(826,897)(827,899)(828,900)
(829,904)(830,903)(831,902)(832,901)(833,890)(834,889)(835,891)(836,892)
(837,896)(838,895)(839,894)(840,893);;
s2 := (  1,289)(  2,290)(  3,295)(  4,296)(  5,294)(  6,293)(  7,291)(  8,292)
(  9,281)( 10,282)( 11,287)( 12,288)( 13,286)( 14,285)( 15,283)( 16,284)
( 17,313)( 18,314)( 19,319)( 20,320)( 21,318)( 22,317)( 23,315)( 24,316)
( 25,305)( 26,306)( 27,311)( 28,312)( 29,310)( 30,309)( 31,307)( 32,308)
( 33,297)( 34,298)( 35,303)( 36,304)( 37,302)( 38,301)( 39,299)( 40,300)
( 41,249)( 42,250)( 43,255)( 44,256)( 45,254)( 46,253)( 47,251)( 48,252)
( 49,241)( 50,242)( 51,247)( 52,248)( 53,246)( 54,245)( 55,243)( 56,244)
( 57,273)( 58,274)( 59,279)( 60,280)( 61,278)( 62,277)( 63,275)( 64,276)
( 65,265)( 66,266)( 67,271)( 68,272)( 69,270)( 70,269)( 71,267)( 72,268)
( 73,257)( 74,258)( 75,263)( 76,264)( 77,262)( 78,261)( 79,259)( 80,260)
( 81,329)( 82,330)( 83,335)( 84,336)( 85,334)( 86,333)( 87,331)( 88,332)
( 89,321)( 90,322)( 91,327)( 92,328)( 93,326)( 94,325)( 95,323)( 96,324)
( 97,353)( 98,354)( 99,359)(100,360)(101,358)(102,357)(103,355)(104,356)
(105,345)(106,346)(107,351)(108,352)(109,350)(110,349)(111,347)(112,348)
(113,337)(114,338)(115,343)(116,344)(117,342)(118,341)(119,339)(120,340)
(121,409)(122,410)(123,415)(124,416)(125,414)(126,413)(127,411)(128,412)
(129,401)(130,402)(131,407)(132,408)(133,406)(134,405)(135,403)(136,404)
(137,433)(138,434)(139,439)(140,440)(141,438)(142,437)(143,435)(144,436)
(145,425)(146,426)(147,431)(148,432)(149,430)(150,429)(151,427)(152,428)
(153,417)(154,418)(155,423)(156,424)(157,422)(158,421)(159,419)(160,420)
(161,369)(162,370)(163,375)(164,376)(165,374)(166,373)(167,371)(168,372)
(169,361)(170,362)(171,367)(172,368)(173,366)(174,365)(175,363)(176,364)
(177,393)(178,394)(179,399)(180,400)(181,398)(182,397)(183,395)(184,396)
(185,385)(186,386)(187,391)(188,392)(189,390)(190,389)(191,387)(192,388)
(193,377)(194,378)(195,383)(196,384)(197,382)(198,381)(199,379)(200,380)
(201,449)(202,450)(203,455)(204,456)(205,454)(206,453)(207,451)(208,452)
(209,441)(210,442)(211,447)(212,448)(213,446)(214,445)(215,443)(216,444)
(217,473)(218,474)(219,479)(220,480)(221,478)(222,477)(223,475)(224,476)
(225,465)(226,466)(227,471)(228,472)(229,470)(230,469)(231,467)(232,468)
(233,457)(234,458)(235,463)(236,464)(237,462)(238,461)(239,459)(240,460)
(481,770)(482,769)(483,776)(484,775)(485,773)(486,774)(487,772)(488,771)
(489,762)(490,761)(491,768)(492,767)(493,765)(494,766)(495,764)(496,763)
(497,794)(498,793)(499,800)(500,799)(501,797)(502,798)(503,796)(504,795)
(505,786)(506,785)(507,792)(508,791)(509,789)(510,790)(511,788)(512,787)
(513,778)(514,777)(515,784)(516,783)(517,781)(518,782)(519,780)(520,779)
(521,730)(522,729)(523,736)(524,735)(525,733)(526,734)(527,732)(528,731)
(529,722)(530,721)(531,728)(532,727)(533,725)(534,726)(535,724)(536,723)
(537,754)(538,753)(539,760)(540,759)(541,757)(542,758)(543,756)(544,755)
(545,746)(546,745)(547,752)(548,751)(549,749)(550,750)(551,748)(552,747)
(553,738)(554,737)(555,744)(556,743)(557,741)(558,742)(559,740)(560,739)
(561,810)(562,809)(563,816)(564,815)(565,813)(566,814)(567,812)(568,811)
(569,802)(570,801)(571,808)(572,807)(573,805)(574,806)(575,804)(576,803)
(577,834)(578,833)(579,840)(580,839)(581,837)(582,838)(583,836)(584,835)
(585,826)(586,825)(587,832)(588,831)(589,829)(590,830)(591,828)(592,827)
(593,818)(594,817)(595,824)(596,823)(597,821)(598,822)(599,820)(600,819)
(601,890)(602,889)(603,896)(604,895)(605,893)(606,894)(607,892)(608,891)
(609,882)(610,881)(611,888)(612,887)(613,885)(614,886)(615,884)(616,883)
(617,914)(618,913)(619,920)(620,919)(621,917)(622,918)(623,916)(624,915)
(625,906)(626,905)(627,912)(628,911)(629,909)(630,910)(631,908)(632,907)
(633,898)(634,897)(635,904)(636,903)(637,901)(638,902)(639,900)(640,899)
(641,850)(642,849)(643,856)(644,855)(645,853)(646,854)(647,852)(648,851)
(649,842)(650,841)(651,848)(652,847)(653,845)(654,846)(655,844)(656,843)
(657,874)(658,873)(659,880)(660,879)(661,877)(662,878)(663,876)(664,875)
(665,866)(666,865)(667,872)(668,871)(669,869)(670,870)(671,868)(672,867)
(673,858)(674,857)(675,864)(676,863)(677,861)(678,862)(679,860)(680,859)
(681,930)(682,929)(683,936)(684,935)(685,933)(686,934)(687,932)(688,931)
(689,922)(690,921)(691,928)(692,927)(693,925)(694,926)(695,924)(696,923)
(697,954)(698,953)(699,960)(700,959)(701,957)(702,958)(703,956)(704,955)
(705,946)(706,945)(707,952)(708,951)(709,949)(710,950)(711,948)(712,947)
(713,938)(714,937)(715,944)(716,943)(717,941)(718,942)(719,940)(720,939);;
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*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)!(  1,485)(  2,486)(  3,488)(  4,487)(  5,482)(  6,481)(  7,483)
(  8,484)(  9,493)( 10,494)( 11,496)( 12,495)( 13,490)( 14,489)( 15,491)
( 16,492)( 17,501)( 18,502)( 19,504)( 20,503)( 21,498)( 22,497)( 23,499)
( 24,500)( 25,509)( 26,510)( 27,512)( 28,511)( 29,506)( 30,505)( 31,507)
( 32,508)( 33,517)( 34,518)( 35,520)( 36,519)( 37,514)( 38,513)( 39,515)
( 40,516)( 41,525)( 42,526)( 43,528)( 44,527)( 45,522)( 46,521)( 47,523)
( 48,524)( 49,533)( 50,534)( 51,536)( 52,535)( 53,530)( 54,529)( 55,531)
( 56,532)( 57,541)( 58,542)( 59,544)( 60,543)( 61,538)( 62,537)( 63,539)
( 64,540)( 65,549)( 66,550)( 67,552)( 68,551)( 69,546)( 70,545)( 71,547)
( 72,548)( 73,557)( 74,558)( 75,560)( 76,559)( 77,554)( 78,553)( 79,555)
( 80,556)( 81,565)( 82,566)( 83,568)( 84,567)( 85,562)( 86,561)( 87,563)
( 88,564)( 89,573)( 90,574)( 91,576)( 92,575)( 93,570)( 94,569)( 95,571)
( 96,572)( 97,581)( 98,582)( 99,584)(100,583)(101,578)(102,577)(103,579)
(104,580)(105,589)(106,590)(107,592)(108,591)(109,586)(110,585)(111,587)
(112,588)(113,597)(114,598)(115,600)(116,599)(117,594)(118,593)(119,595)
(120,596)(121,605)(122,606)(123,608)(124,607)(125,602)(126,601)(127,603)
(128,604)(129,613)(130,614)(131,616)(132,615)(133,610)(134,609)(135,611)
(136,612)(137,621)(138,622)(139,624)(140,623)(141,618)(142,617)(143,619)
(144,620)(145,629)(146,630)(147,632)(148,631)(149,626)(150,625)(151,627)
(152,628)(153,637)(154,638)(155,640)(156,639)(157,634)(158,633)(159,635)
(160,636)(161,645)(162,646)(163,648)(164,647)(165,642)(166,641)(167,643)
(168,644)(169,653)(170,654)(171,656)(172,655)(173,650)(174,649)(175,651)
(176,652)(177,661)(178,662)(179,664)(180,663)(181,658)(182,657)(183,659)
(184,660)(185,669)(186,670)(187,672)(188,671)(189,666)(190,665)(191,667)
(192,668)(193,677)(194,678)(195,680)(196,679)(197,674)(198,673)(199,675)
(200,676)(201,685)(202,686)(203,688)(204,687)(205,682)(206,681)(207,683)
(208,684)(209,693)(210,694)(211,696)(212,695)(213,690)(214,689)(215,691)
(216,692)(217,701)(218,702)(219,704)(220,703)(221,698)(222,697)(223,699)
(224,700)(225,709)(226,710)(227,712)(228,711)(229,706)(230,705)(231,707)
(232,708)(233,717)(234,718)(235,720)(236,719)(237,714)(238,713)(239,715)
(240,716)(241,725)(242,726)(243,728)(244,727)(245,722)(246,721)(247,723)
(248,724)(249,733)(250,734)(251,736)(252,735)(253,730)(254,729)(255,731)
(256,732)(257,741)(258,742)(259,744)(260,743)(261,738)(262,737)(263,739)
(264,740)(265,749)(266,750)(267,752)(268,751)(269,746)(270,745)(271,747)
(272,748)(273,757)(274,758)(275,760)(276,759)(277,754)(278,753)(279,755)
(280,756)(281,765)(282,766)(283,768)(284,767)(285,762)(286,761)(287,763)
(288,764)(289,773)(290,774)(291,776)(292,775)(293,770)(294,769)(295,771)
(296,772)(297,781)(298,782)(299,784)(300,783)(301,778)(302,777)(303,779)
(304,780)(305,789)(306,790)(307,792)(308,791)(309,786)(310,785)(311,787)
(312,788)(313,797)(314,798)(315,800)(316,799)(317,794)(318,793)(319,795)
(320,796)(321,805)(322,806)(323,808)(324,807)(325,802)(326,801)(327,803)
(328,804)(329,813)(330,814)(331,816)(332,815)(333,810)(334,809)(335,811)
(336,812)(337,821)(338,822)(339,824)(340,823)(341,818)(342,817)(343,819)
(344,820)(345,829)(346,830)(347,832)(348,831)(349,826)(350,825)(351,827)
(352,828)(353,837)(354,838)(355,840)(356,839)(357,834)(358,833)(359,835)
(360,836)(361,845)(362,846)(363,848)(364,847)(365,842)(366,841)(367,843)
(368,844)(369,853)(370,854)(371,856)(372,855)(373,850)(374,849)(375,851)
(376,852)(377,861)(378,862)(379,864)(380,863)(381,858)(382,857)(383,859)
(384,860)(385,869)(386,870)(387,872)(388,871)(389,866)(390,865)(391,867)
(392,868)(393,877)(394,878)(395,880)(396,879)(397,874)(398,873)(399,875)
(400,876)(401,885)(402,886)(403,888)(404,887)(405,882)(406,881)(407,883)
(408,884)(409,893)(410,894)(411,896)(412,895)(413,890)(414,889)(415,891)
(416,892)(417,901)(418,902)(419,904)(420,903)(421,898)(422,897)(423,899)
(424,900)(425,909)(426,910)(427,912)(428,911)(429,906)(430,905)(431,907)
(432,908)(433,917)(434,918)(435,920)(436,919)(437,914)(438,913)(439,915)
(440,916)(441,925)(442,926)(443,928)(444,927)(445,922)(446,921)(447,923)
(448,924)(449,933)(450,934)(451,936)(452,935)(453,930)(454,929)(455,931)
(456,932)(457,941)(458,942)(459,944)(460,943)(461,938)(462,937)(463,939)
(464,940)(465,949)(466,950)(467,952)(468,951)(469,946)(470,945)(471,947)
(472,948)(473,957)(474,958)(475,960)(476,959)(477,954)(478,953)(479,955)
(480,956);
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)(481,482)
(485,488)(486,487)(489,514)(490,513)(491,515)(492,516)(493,520)(494,519)
(495,518)(496,517)(497,506)(498,505)(499,507)(500,508)(501,512)(502,511)
(503,510)(504,509)(521,562)(522,561)(523,563)(524,564)(525,568)(526,567)
(527,566)(528,565)(529,594)(530,593)(531,595)(532,596)(533,600)(534,599)
(535,598)(536,597)(537,586)(538,585)(539,587)(540,588)(541,592)(542,591)
(543,590)(544,589)(545,578)(546,577)(547,579)(548,580)(549,584)(550,583)
(551,582)(552,581)(553,570)(554,569)(555,571)(556,572)(557,576)(558,575)
(559,574)(560,573)(601,602)(605,608)(606,607)(609,634)(610,633)(611,635)
(612,636)(613,640)(614,639)(615,638)(616,637)(617,626)(618,625)(619,627)
(620,628)(621,632)(622,631)(623,630)(624,629)(641,682)(642,681)(643,683)
(644,684)(645,688)(646,687)(647,686)(648,685)(649,714)(650,713)(651,715)
(652,716)(653,720)(654,719)(655,718)(656,717)(657,706)(658,705)(659,707)
(660,708)(661,712)(662,711)(663,710)(664,709)(665,698)(666,697)(667,699)
(668,700)(669,704)(670,703)(671,702)(672,701)(673,690)(674,689)(675,691)
(676,692)(677,696)(678,695)(679,694)(680,693)(721,842)(722,841)(723,843)
(724,844)(725,848)(726,847)(727,846)(728,845)(729,874)(730,873)(731,875)
(732,876)(733,880)(734,879)(735,878)(736,877)(737,866)(738,865)(739,867)
(740,868)(741,872)(742,871)(743,870)(744,869)(745,858)(746,857)(747,859)
(748,860)(749,864)(750,863)(751,862)(752,861)(753,850)(754,849)(755,851)
(756,852)(757,856)(758,855)(759,854)(760,853)(761,922)(762,921)(763,923)
(764,924)(765,928)(766,927)(767,926)(768,925)(769,954)(770,953)(771,955)
(772,956)(773,960)(774,959)(775,958)(776,957)(777,946)(778,945)(779,947)
(780,948)(781,952)(782,951)(783,950)(784,949)(785,938)(786,937)(787,939)
(788,940)(789,944)(790,943)(791,942)(792,941)(793,930)(794,929)(795,931)
(796,932)(797,936)(798,935)(799,934)(800,933)(801,882)(802,881)(803,883)
(804,884)(805,888)(806,887)(807,886)(808,885)(809,914)(810,913)(811,915)
(812,916)(813,920)(814,919)(815,918)(816,917)(817,906)(818,905)(819,907)
(820,908)(821,912)(822,911)(823,910)(824,909)(825,898)(826,897)(827,899)
(828,900)(829,904)(830,903)(831,902)(832,901)(833,890)(834,889)(835,891)
(836,892)(837,896)(838,895)(839,894)(840,893);
s2 := Sym(960)!(  1,289)(  2,290)(  3,295)(  4,296)(  5,294)(  6,293)(  7,291)
(  8,292)(  9,281)( 10,282)( 11,287)( 12,288)( 13,286)( 14,285)( 15,283)
( 16,284)( 17,313)( 18,314)( 19,319)( 20,320)( 21,318)( 22,317)( 23,315)
( 24,316)( 25,305)( 26,306)( 27,311)( 28,312)( 29,310)( 30,309)( 31,307)
( 32,308)( 33,297)( 34,298)( 35,303)( 36,304)( 37,302)( 38,301)( 39,299)
( 40,300)( 41,249)( 42,250)( 43,255)( 44,256)( 45,254)( 46,253)( 47,251)
( 48,252)( 49,241)( 50,242)( 51,247)( 52,248)( 53,246)( 54,245)( 55,243)
( 56,244)( 57,273)( 58,274)( 59,279)( 60,280)( 61,278)( 62,277)( 63,275)
( 64,276)( 65,265)( 66,266)( 67,271)( 68,272)( 69,270)( 70,269)( 71,267)
( 72,268)( 73,257)( 74,258)( 75,263)( 76,264)( 77,262)( 78,261)( 79,259)
( 80,260)( 81,329)( 82,330)( 83,335)( 84,336)( 85,334)( 86,333)( 87,331)
( 88,332)( 89,321)( 90,322)( 91,327)( 92,328)( 93,326)( 94,325)( 95,323)
( 96,324)( 97,353)( 98,354)( 99,359)(100,360)(101,358)(102,357)(103,355)
(104,356)(105,345)(106,346)(107,351)(108,352)(109,350)(110,349)(111,347)
(112,348)(113,337)(114,338)(115,343)(116,344)(117,342)(118,341)(119,339)
(120,340)(121,409)(122,410)(123,415)(124,416)(125,414)(126,413)(127,411)
(128,412)(129,401)(130,402)(131,407)(132,408)(133,406)(134,405)(135,403)
(136,404)(137,433)(138,434)(139,439)(140,440)(141,438)(142,437)(143,435)
(144,436)(145,425)(146,426)(147,431)(148,432)(149,430)(150,429)(151,427)
(152,428)(153,417)(154,418)(155,423)(156,424)(157,422)(158,421)(159,419)
(160,420)(161,369)(162,370)(163,375)(164,376)(165,374)(166,373)(167,371)
(168,372)(169,361)(170,362)(171,367)(172,368)(173,366)(174,365)(175,363)
(176,364)(177,393)(178,394)(179,399)(180,400)(181,398)(182,397)(183,395)
(184,396)(185,385)(186,386)(187,391)(188,392)(189,390)(190,389)(191,387)
(192,388)(193,377)(194,378)(195,383)(196,384)(197,382)(198,381)(199,379)
(200,380)(201,449)(202,450)(203,455)(204,456)(205,454)(206,453)(207,451)
(208,452)(209,441)(210,442)(211,447)(212,448)(213,446)(214,445)(215,443)
(216,444)(217,473)(218,474)(219,479)(220,480)(221,478)(222,477)(223,475)
(224,476)(225,465)(226,466)(227,471)(228,472)(229,470)(230,469)(231,467)
(232,468)(233,457)(234,458)(235,463)(236,464)(237,462)(238,461)(239,459)
(240,460)(481,770)(482,769)(483,776)(484,775)(485,773)(486,774)(487,772)
(488,771)(489,762)(490,761)(491,768)(492,767)(493,765)(494,766)(495,764)
(496,763)(497,794)(498,793)(499,800)(500,799)(501,797)(502,798)(503,796)
(504,795)(505,786)(506,785)(507,792)(508,791)(509,789)(510,790)(511,788)
(512,787)(513,778)(514,777)(515,784)(516,783)(517,781)(518,782)(519,780)
(520,779)(521,730)(522,729)(523,736)(524,735)(525,733)(526,734)(527,732)
(528,731)(529,722)(530,721)(531,728)(532,727)(533,725)(534,726)(535,724)
(536,723)(537,754)(538,753)(539,760)(540,759)(541,757)(542,758)(543,756)
(544,755)(545,746)(546,745)(547,752)(548,751)(549,749)(550,750)(551,748)
(552,747)(553,738)(554,737)(555,744)(556,743)(557,741)(558,742)(559,740)
(560,739)(561,810)(562,809)(563,816)(564,815)(565,813)(566,814)(567,812)
(568,811)(569,802)(570,801)(571,808)(572,807)(573,805)(574,806)(575,804)
(576,803)(577,834)(578,833)(579,840)(580,839)(581,837)(582,838)(583,836)
(584,835)(585,826)(586,825)(587,832)(588,831)(589,829)(590,830)(591,828)
(592,827)(593,818)(594,817)(595,824)(596,823)(597,821)(598,822)(599,820)
(600,819)(601,890)(602,889)(603,896)(604,895)(605,893)(606,894)(607,892)
(608,891)(609,882)(610,881)(611,888)(612,887)(613,885)(614,886)(615,884)
(616,883)(617,914)(618,913)(619,920)(620,919)(621,917)(622,918)(623,916)
(624,915)(625,906)(626,905)(627,912)(628,911)(629,909)(630,910)(631,908)
(632,907)(633,898)(634,897)(635,904)(636,903)(637,901)(638,902)(639,900)
(640,899)(641,850)(642,849)(643,856)(644,855)(645,853)(646,854)(647,852)
(648,851)(649,842)(650,841)(651,848)(652,847)(653,845)(654,846)(655,844)
(656,843)(657,874)(658,873)(659,880)(660,879)(661,877)(662,878)(663,876)
(664,875)(665,866)(666,865)(667,872)(668,871)(669,869)(670,870)(671,868)
(672,867)(673,858)(674,857)(675,864)(676,863)(677,861)(678,862)(679,860)
(680,859)(681,930)(682,929)(683,936)(684,935)(685,933)(686,934)(687,932)
(688,931)(689,922)(690,921)(691,928)(692,927)(693,925)(694,926)(695,924)
(696,923)(697,954)(698,953)(699,960)(700,959)(701,957)(702,958)(703,956)
(704,955)(705,946)(706,945)(707,952)(708,951)(709,949)(710,950)(711,948)
(712,947)(713,938)(714,937)(715,944)(716,943)(717,941)(718,942)(719,940)
(720,939);
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*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