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Polytope of Type {60,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,8}*1920a
if this polytope has a name.
Group : SmallGroup(1920,13384)
Rank : 3
Schlafli Type : {60,8}
Number of vertices, edges, etc : 120, 480, 16
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 : {60,4}*960a, {60,8}*960a, {60,8}*960b
   3-fold quotients : {20,8}*640a
   4-fold quotients : {60,4}*480a, {30,8}*480
   5-fold quotients : {12,8}*384a
   6-fold quotients : {20,4}*320, {20,8}*320a, {20,8}*320b
   8-fold quotients : {60,2}*240, {30,4}*240a
   10-fold quotients : {12,4}*192a, {12,8}*192a, {12,8}*192b
   12-fold quotients : {20,4}*160, {10,8}*160
   15-fold quotients : {4,8}*128a
   16-fold quotients : {30,2}*120
   20-fold quotients : {12,4}*96a, {6,8}*96
   24-fold quotients : {20,2}*80, {10,4}*80
   30-fold quotients : {4,8}*64a, {4,8}*64b, {4,4}*64
   32-fold quotients : {15,2}*60
   40-fold quotients : {12,2}*48, {6,4}*48a
   48-fold quotients : {10,2}*40
   60-fold quotients : {4,4}*32, {2,8}*32
   80-fold quotients : {6,2}*24
   96-fold quotients : {5,2}*20
   120-fold quotients : {2,4}*16, {4,2}*16
   160-fold quotients : {3,2}*12
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,241)(  2,245)(  3,244)(  4,243)(  5,242)(  6,251)(  7,255)(  8,254)
(  9,253)( 10,252)( 11,246)( 12,250)( 13,249)( 14,248)( 15,247)( 16,256)
( 17,260)( 18,259)( 19,258)( 20,257)( 21,266)( 22,270)( 23,269)( 24,268)
( 25,267)( 26,261)( 27,265)( 28,264)( 29,263)( 30,262)( 31,271)( 32,275)
( 33,274)( 34,273)( 35,272)( 36,281)( 37,285)( 38,284)( 39,283)( 40,282)
( 41,276)( 42,280)( 43,279)( 44,278)( 45,277)( 46,286)( 47,290)( 48,289)
( 49,288)( 50,287)( 51,296)( 52,300)( 53,299)( 54,298)( 55,297)( 56,291)
( 57,295)( 58,294)( 59,293)( 60,292)( 61,301)( 62,305)( 63,304)( 64,303)
( 65,302)( 66,311)( 67,315)( 68,314)( 69,313)( 70,312)( 71,306)( 72,310)
( 73,309)( 74,308)( 75,307)( 76,316)( 77,320)( 78,319)( 79,318)( 80,317)
( 81,326)( 82,330)( 83,329)( 84,328)( 85,327)( 86,321)( 87,325)( 88,324)
( 89,323)( 90,322)( 91,331)( 92,335)( 93,334)( 94,333)( 95,332)( 96,341)
( 97,345)( 98,344)( 99,343)(100,342)(101,336)(102,340)(103,339)(104,338)
(105,337)(106,346)(107,350)(108,349)(109,348)(110,347)(111,356)(112,360)
(113,359)(114,358)(115,357)(116,351)(117,355)(118,354)(119,353)(120,352)
(121,376)(122,380)(123,379)(124,378)(125,377)(126,386)(127,390)(128,389)
(129,388)(130,387)(131,381)(132,385)(133,384)(134,383)(135,382)(136,361)
(137,365)(138,364)(139,363)(140,362)(141,371)(142,375)(143,374)(144,373)
(145,372)(146,366)(147,370)(148,369)(149,368)(150,367)(151,406)(152,410)
(153,409)(154,408)(155,407)(156,416)(157,420)(158,419)(159,418)(160,417)
(161,411)(162,415)(163,414)(164,413)(165,412)(166,391)(167,395)(168,394)
(169,393)(170,392)(171,401)(172,405)(173,404)(174,403)(175,402)(176,396)
(177,400)(178,399)(179,398)(180,397)(181,436)(182,440)(183,439)(184,438)
(185,437)(186,446)(187,450)(188,449)(189,448)(190,447)(191,441)(192,445)
(193,444)(194,443)(195,442)(196,421)(197,425)(198,424)(199,423)(200,422)
(201,431)(202,435)(203,434)(204,433)(205,432)(206,426)(207,430)(208,429)
(209,428)(210,427)(211,466)(212,470)(213,469)(214,468)(215,467)(216,476)
(217,480)(218,479)(219,478)(220,477)(221,471)(222,475)(223,474)(224,473)
(225,472)(226,451)(227,455)(228,454)(229,453)(230,452)(231,461)(232,465)
(233,464)(234,463)(235,462)(236,456)(237,460)(238,459)(239,458)(240,457)
(481,721)(482,725)(483,724)(484,723)(485,722)(486,731)(487,735)(488,734)
(489,733)(490,732)(491,726)(492,730)(493,729)(494,728)(495,727)(496,736)
(497,740)(498,739)(499,738)(500,737)(501,746)(502,750)(503,749)(504,748)
(505,747)(506,741)(507,745)(508,744)(509,743)(510,742)(511,751)(512,755)
(513,754)(514,753)(515,752)(516,761)(517,765)(518,764)(519,763)(520,762)
(521,756)(522,760)(523,759)(524,758)(525,757)(526,766)(527,770)(528,769)
(529,768)(530,767)(531,776)(532,780)(533,779)(534,778)(535,777)(536,771)
(537,775)(538,774)(539,773)(540,772)(541,781)(542,785)(543,784)(544,783)
(545,782)(546,791)(547,795)(548,794)(549,793)(550,792)(551,786)(552,790)
(553,789)(554,788)(555,787)(556,796)(557,800)(558,799)(559,798)(560,797)
(561,806)(562,810)(563,809)(564,808)(565,807)(566,801)(567,805)(568,804)
(569,803)(570,802)(571,811)(572,815)(573,814)(574,813)(575,812)(576,821)
(577,825)(578,824)(579,823)(580,822)(581,816)(582,820)(583,819)(584,818)
(585,817)(586,826)(587,830)(588,829)(589,828)(590,827)(591,836)(592,840)
(593,839)(594,838)(595,837)(596,831)(597,835)(598,834)(599,833)(600,832)
(601,856)(602,860)(603,859)(604,858)(605,857)(606,866)(607,870)(608,869)
(609,868)(610,867)(611,861)(612,865)(613,864)(614,863)(615,862)(616,841)
(617,845)(618,844)(619,843)(620,842)(621,851)(622,855)(623,854)(624,853)
(625,852)(626,846)(627,850)(628,849)(629,848)(630,847)(631,886)(632,890)
(633,889)(634,888)(635,887)(636,896)(637,900)(638,899)(639,898)(640,897)
(641,891)(642,895)(643,894)(644,893)(645,892)(646,871)(647,875)(648,874)
(649,873)(650,872)(651,881)(652,885)(653,884)(654,883)(655,882)(656,876)
(657,880)(658,879)(659,878)(660,877)(661,916)(662,920)(663,919)(664,918)
(665,917)(666,926)(667,930)(668,929)(669,928)(670,927)(671,921)(672,925)
(673,924)(674,923)(675,922)(676,901)(677,905)(678,904)(679,903)(680,902)
(681,911)(682,915)(683,914)(684,913)(685,912)(686,906)(687,910)(688,909)
(689,908)(690,907)(691,946)(692,950)(693,949)(694,948)(695,947)(696,956)
(697,960)(698,959)(699,958)(700,957)(701,951)(702,955)(703,954)(704,953)
(705,952)(706,931)(707,935)(708,934)(709,933)(710,932)(711,941)(712,945)
(713,944)(714,943)(715,942)(716,936)(717,940)(718,939)(719,938)(720,937);;
s1 := (  1,  7)(  2,  6)(  3, 10)(  4,  9)(  5,  8)( 11, 12)( 13, 15)( 16, 22)
( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 37)( 32, 36)
( 33, 40)( 34, 39)( 35, 38)( 41, 42)( 43, 45)( 46, 52)( 47, 51)( 48, 55)
( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 67)( 62, 66)( 63, 70)( 64, 69)
( 65, 68)( 71, 72)( 73, 75)( 76, 82)( 77, 81)( 78, 85)( 79, 84)( 80, 83)
( 86, 87)( 88, 90)( 91, 97)( 92, 96)( 93,100)( 94, 99)( 95, 98)(101,102)
(103,105)(106,112)(107,111)(108,115)(109,114)(110,113)(116,117)(118,120)
(121,157)(122,156)(123,160)(124,159)(125,158)(126,152)(127,151)(128,155)
(129,154)(130,153)(131,162)(132,161)(133,165)(134,164)(135,163)(136,172)
(137,171)(138,175)(139,174)(140,173)(141,167)(142,166)(143,170)(144,169)
(145,168)(146,177)(147,176)(148,180)(149,179)(150,178)(181,217)(182,216)
(183,220)(184,219)(185,218)(186,212)(187,211)(188,215)(189,214)(190,213)
(191,222)(192,221)(193,225)(194,224)(195,223)(196,232)(197,231)(198,235)
(199,234)(200,233)(201,227)(202,226)(203,230)(204,229)(205,228)(206,237)
(207,236)(208,240)(209,239)(210,238)(241,307)(242,306)(243,310)(244,309)
(245,308)(246,302)(247,301)(248,305)(249,304)(250,303)(251,312)(252,311)
(253,315)(254,314)(255,313)(256,322)(257,321)(258,325)(259,324)(260,323)
(261,317)(262,316)(263,320)(264,319)(265,318)(266,327)(267,326)(268,330)
(269,329)(270,328)(271,337)(272,336)(273,340)(274,339)(275,338)(276,332)
(277,331)(278,335)(279,334)(280,333)(281,342)(282,341)(283,345)(284,344)
(285,343)(286,352)(287,351)(288,355)(289,354)(290,353)(291,347)(292,346)
(293,350)(294,349)(295,348)(296,357)(297,356)(298,360)(299,359)(300,358)
(361,457)(362,456)(363,460)(364,459)(365,458)(366,452)(367,451)(368,455)
(369,454)(370,453)(371,462)(372,461)(373,465)(374,464)(375,463)(376,472)
(377,471)(378,475)(379,474)(380,473)(381,467)(382,466)(383,470)(384,469)
(385,468)(386,477)(387,476)(388,480)(389,479)(390,478)(391,427)(392,426)
(393,430)(394,429)(395,428)(396,422)(397,421)(398,425)(399,424)(400,423)
(401,432)(402,431)(403,435)(404,434)(405,433)(406,442)(407,441)(408,445)
(409,444)(410,443)(411,437)(412,436)(413,440)(414,439)(415,438)(416,447)
(417,446)(418,450)(419,449)(420,448)(481,607)(482,606)(483,610)(484,609)
(485,608)(486,602)(487,601)(488,605)(489,604)(490,603)(491,612)(492,611)
(493,615)(494,614)(495,613)(496,622)(497,621)(498,625)(499,624)(500,623)
(501,617)(502,616)(503,620)(504,619)(505,618)(506,627)(507,626)(508,630)
(509,629)(510,628)(511,637)(512,636)(513,640)(514,639)(515,638)(516,632)
(517,631)(518,635)(519,634)(520,633)(521,642)(522,641)(523,645)(524,644)
(525,643)(526,652)(527,651)(528,655)(529,654)(530,653)(531,647)(532,646)
(533,650)(534,649)(535,648)(536,657)(537,656)(538,660)(539,659)(540,658)
(541,667)(542,666)(543,670)(544,669)(545,668)(546,662)(547,661)(548,665)
(549,664)(550,663)(551,672)(552,671)(553,675)(554,674)(555,673)(556,682)
(557,681)(558,685)(559,684)(560,683)(561,677)(562,676)(563,680)(564,679)
(565,678)(566,687)(567,686)(568,690)(569,689)(570,688)(571,697)(572,696)
(573,700)(574,699)(575,698)(576,692)(577,691)(578,695)(579,694)(580,693)
(581,702)(582,701)(583,705)(584,704)(585,703)(586,712)(587,711)(588,715)
(589,714)(590,713)(591,707)(592,706)(593,710)(594,709)(595,708)(596,717)
(597,716)(598,720)(599,719)(600,718)(721,922)(722,921)(723,925)(724,924)
(725,923)(726,917)(727,916)(728,920)(729,919)(730,918)(731,927)(732,926)
(733,930)(734,929)(735,928)(736,907)(737,906)(738,910)(739,909)(740,908)
(741,902)(742,901)(743,905)(744,904)(745,903)(746,912)(747,911)(748,915)
(749,914)(750,913)(751,952)(752,951)(753,955)(754,954)(755,953)(756,947)
(757,946)(758,950)(759,949)(760,948)(761,957)(762,956)(763,960)(764,959)
(765,958)(766,937)(767,936)(768,940)(769,939)(770,938)(771,932)(772,931)
(773,935)(774,934)(775,933)(776,942)(777,941)(778,945)(779,944)(780,943)
(781,862)(782,861)(783,865)(784,864)(785,863)(786,857)(787,856)(788,860)
(789,859)(790,858)(791,867)(792,866)(793,870)(794,869)(795,868)(796,847)
(797,846)(798,850)(799,849)(800,848)(801,842)(802,841)(803,845)(804,844)
(805,843)(806,852)(807,851)(808,855)(809,854)(810,853)(811,892)(812,891)
(813,895)(814,894)(815,893)(816,887)(817,886)(818,890)(819,889)(820,888)
(821,897)(822,896)(823,900)(824,899)(825,898)(826,877)(827,876)(828,880)
(829,879)(830,878)(831,872)(832,871)(833,875)(834,874)(835,873)(836,882)
(837,881)(838,885)(839,884)(840,883);;
s2 := (  1,481)(  2,482)(  3,483)(  4,484)(  5,485)(  6,486)(  7,487)(  8,488)
(  9,489)( 10,490)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)( 16,496)
( 17,497)( 18,498)( 19,499)( 20,500)( 21,501)( 22,502)( 23,503)( 24,504)
( 25,505)( 26,506)( 27,507)( 28,508)( 29,509)( 30,510)( 31,511)( 32,512)
( 33,513)( 34,514)( 35,515)( 36,516)( 37,517)( 38,518)( 39,519)( 40,520)
( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,526)( 47,527)( 48,528)
( 49,529)( 50,530)( 51,531)( 52,532)( 53,533)( 54,534)( 55,535)( 56,536)
( 57,537)( 58,538)( 59,539)( 60,540)( 61,556)( 62,557)( 63,558)( 64,559)
( 65,560)( 66,561)( 67,562)( 68,563)( 69,564)( 70,565)( 71,566)( 72,567)
( 73,568)( 74,569)( 75,570)( 76,541)( 77,542)( 78,543)( 79,544)( 80,545)
( 81,546)( 82,547)( 83,548)( 84,549)( 85,550)( 86,551)( 87,552)( 88,553)
( 89,554)( 90,555)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)( 96,591)
( 97,592)( 98,593)( 99,594)(100,595)(101,596)(102,597)(103,598)(104,599)
(105,600)(106,571)(107,572)(108,573)(109,574)(110,575)(111,576)(112,577)
(113,578)(114,579)(115,580)(116,581)(117,582)(118,583)(119,584)(120,585)
(121,631)(122,632)(123,633)(124,634)(125,635)(126,636)(127,637)(128,638)
(129,639)(130,640)(131,641)(132,642)(133,643)(134,644)(135,645)(136,646)
(137,647)(138,648)(139,649)(140,650)(141,651)(142,652)(143,653)(144,654)
(145,655)(146,656)(147,657)(148,658)(149,659)(150,660)(151,601)(152,602)
(153,603)(154,604)(155,605)(156,606)(157,607)(158,608)(159,609)(160,610)
(161,611)(162,612)(163,613)(164,614)(165,615)(166,616)(167,617)(168,618)
(169,619)(170,620)(171,621)(172,622)(173,623)(174,624)(175,625)(176,626)
(177,627)(178,628)(179,629)(180,630)(181,706)(182,707)(183,708)(184,709)
(185,710)(186,711)(187,712)(188,713)(189,714)(190,715)(191,716)(192,717)
(193,718)(194,719)(195,720)(196,691)(197,692)(198,693)(199,694)(200,695)
(201,696)(202,697)(203,698)(204,699)(205,700)(206,701)(207,702)(208,703)
(209,704)(210,705)(211,676)(212,677)(213,678)(214,679)(215,680)(216,681)
(217,682)(218,683)(219,684)(220,685)(221,686)(222,687)(223,688)(224,689)
(225,690)(226,661)(227,662)(228,663)(229,664)(230,665)(231,666)(232,667)
(233,668)(234,669)(235,670)(236,671)(237,672)(238,673)(239,674)(240,675)
(241,721)(242,722)(243,723)(244,724)(245,725)(246,726)(247,727)(248,728)
(249,729)(250,730)(251,731)(252,732)(253,733)(254,734)(255,735)(256,736)
(257,737)(258,738)(259,739)(260,740)(261,741)(262,742)(263,743)(264,744)
(265,745)(266,746)(267,747)(268,748)(269,749)(270,750)(271,751)(272,752)
(273,753)(274,754)(275,755)(276,756)(277,757)(278,758)(279,759)(280,760)
(281,761)(282,762)(283,763)(284,764)(285,765)(286,766)(287,767)(288,768)
(289,769)(290,770)(291,771)(292,772)(293,773)(294,774)(295,775)(296,776)
(297,777)(298,778)(299,779)(300,780)(301,796)(302,797)(303,798)(304,799)
(305,800)(306,801)(307,802)(308,803)(309,804)(310,805)(311,806)(312,807)
(313,808)(314,809)(315,810)(316,781)(317,782)(318,783)(319,784)(320,785)
(321,786)(322,787)(323,788)(324,789)(325,790)(326,791)(327,792)(328,793)
(329,794)(330,795)(331,826)(332,827)(333,828)(334,829)(335,830)(336,831)
(337,832)(338,833)(339,834)(340,835)(341,836)(342,837)(343,838)(344,839)
(345,840)(346,811)(347,812)(348,813)(349,814)(350,815)(351,816)(352,817)
(353,818)(354,819)(355,820)(356,821)(357,822)(358,823)(359,824)(360,825)
(361,871)(362,872)(363,873)(364,874)(365,875)(366,876)(367,877)(368,878)
(369,879)(370,880)(371,881)(372,882)(373,883)(374,884)(375,885)(376,886)
(377,887)(378,888)(379,889)(380,890)(381,891)(382,892)(383,893)(384,894)
(385,895)(386,896)(387,897)(388,898)(389,899)(390,900)(391,841)(392,842)
(393,843)(394,844)(395,845)(396,846)(397,847)(398,848)(399,849)(400,850)
(401,851)(402,852)(403,853)(404,854)(405,855)(406,856)(407,857)(408,858)
(409,859)(410,860)(411,861)(412,862)(413,863)(414,864)(415,865)(416,866)
(417,867)(418,868)(419,869)(420,870)(421,946)(422,947)(423,948)(424,949)
(425,950)(426,951)(427,952)(428,953)(429,954)(430,955)(431,956)(432,957)
(433,958)(434,959)(435,960)(436,931)(437,932)(438,933)(439,934)(440,935)
(441,936)(442,937)(443,938)(444,939)(445,940)(446,941)(447,942)(448,943)
(449,944)(450,945)(451,916)(452,917)(453,918)(454,919)(455,920)(456,921)
(457,922)(458,923)(459,924)(460,925)(461,926)(462,927)(463,928)(464,929)
(465,930)(466,901)(467,902)(468,903)(469,904)(470,905)(471,906)(472,907)
(473,908)(474,909)(475,910)(476,911)(477,912)(478,913)(479,914)(480,915);;
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*s0*s1*s2*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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(960)!(  1,241)(  2,245)(  3,244)(  4,243)(  5,242)(  6,251)(  7,255)
(  8,254)(  9,253)( 10,252)( 11,246)( 12,250)( 13,249)( 14,248)( 15,247)
( 16,256)( 17,260)( 18,259)( 19,258)( 20,257)( 21,266)( 22,270)( 23,269)
( 24,268)( 25,267)( 26,261)( 27,265)( 28,264)( 29,263)( 30,262)( 31,271)
( 32,275)( 33,274)( 34,273)( 35,272)( 36,281)( 37,285)( 38,284)( 39,283)
( 40,282)( 41,276)( 42,280)( 43,279)( 44,278)( 45,277)( 46,286)( 47,290)
( 48,289)( 49,288)( 50,287)( 51,296)( 52,300)( 53,299)( 54,298)( 55,297)
( 56,291)( 57,295)( 58,294)( 59,293)( 60,292)( 61,301)( 62,305)( 63,304)
( 64,303)( 65,302)( 66,311)( 67,315)( 68,314)( 69,313)( 70,312)( 71,306)
( 72,310)( 73,309)( 74,308)( 75,307)( 76,316)( 77,320)( 78,319)( 79,318)
( 80,317)( 81,326)( 82,330)( 83,329)( 84,328)( 85,327)( 86,321)( 87,325)
( 88,324)( 89,323)( 90,322)( 91,331)( 92,335)( 93,334)( 94,333)( 95,332)
( 96,341)( 97,345)( 98,344)( 99,343)(100,342)(101,336)(102,340)(103,339)
(104,338)(105,337)(106,346)(107,350)(108,349)(109,348)(110,347)(111,356)
(112,360)(113,359)(114,358)(115,357)(116,351)(117,355)(118,354)(119,353)
(120,352)(121,376)(122,380)(123,379)(124,378)(125,377)(126,386)(127,390)
(128,389)(129,388)(130,387)(131,381)(132,385)(133,384)(134,383)(135,382)
(136,361)(137,365)(138,364)(139,363)(140,362)(141,371)(142,375)(143,374)
(144,373)(145,372)(146,366)(147,370)(148,369)(149,368)(150,367)(151,406)
(152,410)(153,409)(154,408)(155,407)(156,416)(157,420)(158,419)(159,418)
(160,417)(161,411)(162,415)(163,414)(164,413)(165,412)(166,391)(167,395)
(168,394)(169,393)(170,392)(171,401)(172,405)(173,404)(174,403)(175,402)
(176,396)(177,400)(178,399)(179,398)(180,397)(181,436)(182,440)(183,439)
(184,438)(185,437)(186,446)(187,450)(188,449)(189,448)(190,447)(191,441)
(192,445)(193,444)(194,443)(195,442)(196,421)(197,425)(198,424)(199,423)
(200,422)(201,431)(202,435)(203,434)(204,433)(205,432)(206,426)(207,430)
(208,429)(209,428)(210,427)(211,466)(212,470)(213,469)(214,468)(215,467)
(216,476)(217,480)(218,479)(219,478)(220,477)(221,471)(222,475)(223,474)
(224,473)(225,472)(226,451)(227,455)(228,454)(229,453)(230,452)(231,461)
(232,465)(233,464)(234,463)(235,462)(236,456)(237,460)(238,459)(239,458)
(240,457)(481,721)(482,725)(483,724)(484,723)(485,722)(486,731)(487,735)
(488,734)(489,733)(490,732)(491,726)(492,730)(493,729)(494,728)(495,727)
(496,736)(497,740)(498,739)(499,738)(500,737)(501,746)(502,750)(503,749)
(504,748)(505,747)(506,741)(507,745)(508,744)(509,743)(510,742)(511,751)
(512,755)(513,754)(514,753)(515,752)(516,761)(517,765)(518,764)(519,763)
(520,762)(521,756)(522,760)(523,759)(524,758)(525,757)(526,766)(527,770)
(528,769)(529,768)(530,767)(531,776)(532,780)(533,779)(534,778)(535,777)
(536,771)(537,775)(538,774)(539,773)(540,772)(541,781)(542,785)(543,784)
(544,783)(545,782)(546,791)(547,795)(548,794)(549,793)(550,792)(551,786)
(552,790)(553,789)(554,788)(555,787)(556,796)(557,800)(558,799)(559,798)
(560,797)(561,806)(562,810)(563,809)(564,808)(565,807)(566,801)(567,805)
(568,804)(569,803)(570,802)(571,811)(572,815)(573,814)(574,813)(575,812)
(576,821)(577,825)(578,824)(579,823)(580,822)(581,816)(582,820)(583,819)
(584,818)(585,817)(586,826)(587,830)(588,829)(589,828)(590,827)(591,836)
(592,840)(593,839)(594,838)(595,837)(596,831)(597,835)(598,834)(599,833)
(600,832)(601,856)(602,860)(603,859)(604,858)(605,857)(606,866)(607,870)
(608,869)(609,868)(610,867)(611,861)(612,865)(613,864)(614,863)(615,862)
(616,841)(617,845)(618,844)(619,843)(620,842)(621,851)(622,855)(623,854)
(624,853)(625,852)(626,846)(627,850)(628,849)(629,848)(630,847)(631,886)
(632,890)(633,889)(634,888)(635,887)(636,896)(637,900)(638,899)(639,898)
(640,897)(641,891)(642,895)(643,894)(644,893)(645,892)(646,871)(647,875)
(648,874)(649,873)(650,872)(651,881)(652,885)(653,884)(654,883)(655,882)
(656,876)(657,880)(658,879)(659,878)(660,877)(661,916)(662,920)(663,919)
(664,918)(665,917)(666,926)(667,930)(668,929)(669,928)(670,927)(671,921)
(672,925)(673,924)(674,923)(675,922)(676,901)(677,905)(678,904)(679,903)
(680,902)(681,911)(682,915)(683,914)(684,913)(685,912)(686,906)(687,910)
(688,909)(689,908)(690,907)(691,946)(692,950)(693,949)(694,948)(695,947)
(696,956)(697,960)(698,959)(699,958)(700,957)(701,951)(702,955)(703,954)
(704,953)(705,952)(706,931)(707,935)(708,934)(709,933)(710,932)(711,941)
(712,945)(713,944)(714,943)(715,942)(716,936)(717,940)(718,939)(719,938)
(720,937);
s1 := Sym(960)!(  1,  7)(  2,  6)(  3, 10)(  4,  9)(  5,  8)( 11, 12)( 13, 15)
( 16, 22)( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 37)
( 32, 36)( 33, 40)( 34, 39)( 35, 38)( 41, 42)( 43, 45)( 46, 52)( 47, 51)
( 48, 55)( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 67)( 62, 66)( 63, 70)
( 64, 69)( 65, 68)( 71, 72)( 73, 75)( 76, 82)( 77, 81)( 78, 85)( 79, 84)
( 80, 83)( 86, 87)( 88, 90)( 91, 97)( 92, 96)( 93,100)( 94, 99)( 95, 98)
(101,102)(103,105)(106,112)(107,111)(108,115)(109,114)(110,113)(116,117)
(118,120)(121,157)(122,156)(123,160)(124,159)(125,158)(126,152)(127,151)
(128,155)(129,154)(130,153)(131,162)(132,161)(133,165)(134,164)(135,163)
(136,172)(137,171)(138,175)(139,174)(140,173)(141,167)(142,166)(143,170)
(144,169)(145,168)(146,177)(147,176)(148,180)(149,179)(150,178)(181,217)
(182,216)(183,220)(184,219)(185,218)(186,212)(187,211)(188,215)(189,214)
(190,213)(191,222)(192,221)(193,225)(194,224)(195,223)(196,232)(197,231)
(198,235)(199,234)(200,233)(201,227)(202,226)(203,230)(204,229)(205,228)
(206,237)(207,236)(208,240)(209,239)(210,238)(241,307)(242,306)(243,310)
(244,309)(245,308)(246,302)(247,301)(248,305)(249,304)(250,303)(251,312)
(252,311)(253,315)(254,314)(255,313)(256,322)(257,321)(258,325)(259,324)
(260,323)(261,317)(262,316)(263,320)(264,319)(265,318)(266,327)(267,326)
(268,330)(269,329)(270,328)(271,337)(272,336)(273,340)(274,339)(275,338)
(276,332)(277,331)(278,335)(279,334)(280,333)(281,342)(282,341)(283,345)
(284,344)(285,343)(286,352)(287,351)(288,355)(289,354)(290,353)(291,347)
(292,346)(293,350)(294,349)(295,348)(296,357)(297,356)(298,360)(299,359)
(300,358)(361,457)(362,456)(363,460)(364,459)(365,458)(366,452)(367,451)
(368,455)(369,454)(370,453)(371,462)(372,461)(373,465)(374,464)(375,463)
(376,472)(377,471)(378,475)(379,474)(380,473)(381,467)(382,466)(383,470)
(384,469)(385,468)(386,477)(387,476)(388,480)(389,479)(390,478)(391,427)
(392,426)(393,430)(394,429)(395,428)(396,422)(397,421)(398,425)(399,424)
(400,423)(401,432)(402,431)(403,435)(404,434)(405,433)(406,442)(407,441)
(408,445)(409,444)(410,443)(411,437)(412,436)(413,440)(414,439)(415,438)
(416,447)(417,446)(418,450)(419,449)(420,448)(481,607)(482,606)(483,610)
(484,609)(485,608)(486,602)(487,601)(488,605)(489,604)(490,603)(491,612)
(492,611)(493,615)(494,614)(495,613)(496,622)(497,621)(498,625)(499,624)
(500,623)(501,617)(502,616)(503,620)(504,619)(505,618)(506,627)(507,626)
(508,630)(509,629)(510,628)(511,637)(512,636)(513,640)(514,639)(515,638)
(516,632)(517,631)(518,635)(519,634)(520,633)(521,642)(522,641)(523,645)
(524,644)(525,643)(526,652)(527,651)(528,655)(529,654)(530,653)(531,647)
(532,646)(533,650)(534,649)(535,648)(536,657)(537,656)(538,660)(539,659)
(540,658)(541,667)(542,666)(543,670)(544,669)(545,668)(546,662)(547,661)
(548,665)(549,664)(550,663)(551,672)(552,671)(553,675)(554,674)(555,673)
(556,682)(557,681)(558,685)(559,684)(560,683)(561,677)(562,676)(563,680)
(564,679)(565,678)(566,687)(567,686)(568,690)(569,689)(570,688)(571,697)
(572,696)(573,700)(574,699)(575,698)(576,692)(577,691)(578,695)(579,694)
(580,693)(581,702)(582,701)(583,705)(584,704)(585,703)(586,712)(587,711)
(588,715)(589,714)(590,713)(591,707)(592,706)(593,710)(594,709)(595,708)
(596,717)(597,716)(598,720)(599,719)(600,718)(721,922)(722,921)(723,925)
(724,924)(725,923)(726,917)(727,916)(728,920)(729,919)(730,918)(731,927)
(732,926)(733,930)(734,929)(735,928)(736,907)(737,906)(738,910)(739,909)
(740,908)(741,902)(742,901)(743,905)(744,904)(745,903)(746,912)(747,911)
(748,915)(749,914)(750,913)(751,952)(752,951)(753,955)(754,954)(755,953)
(756,947)(757,946)(758,950)(759,949)(760,948)(761,957)(762,956)(763,960)
(764,959)(765,958)(766,937)(767,936)(768,940)(769,939)(770,938)(771,932)
(772,931)(773,935)(774,934)(775,933)(776,942)(777,941)(778,945)(779,944)
(780,943)(781,862)(782,861)(783,865)(784,864)(785,863)(786,857)(787,856)
(788,860)(789,859)(790,858)(791,867)(792,866)(793,870)(794,869)(795,868)
(796,847)(797,846)(798,850)(799,849)(800,848)(801,842)(802,841)(803,845)
(804,844)(805,843)(806,852)(807,851)(808,855)(809,854)(810,853)(811,892)
(812,891)(813,895)(814,894)(815,893)(816,887)(817,886)(818,890)(819,889)
(820,888)(821,897)(822,896)(823,900)(824,899)(825,898)(826,877)(827,876)
(828,880)(829,879)(830,878)(831,872)(832,871)(833,875)(834,874)(835,873)
(836,882)(837,881)(838,885)(839,884)(840,883);
s2 := Sym(960)!(  1,481)(  2,482)(  3,483)(  4,484)(  5,485)(  6,486)(  7,487)
(  8,488)(  9,489)( 10,490)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)
( 16,496)( 17,497)( 18,498)( 19,499)( 20,500)( 21,501)( 22,502)( 23,503)
( 24,504)( 25,505)( 26,506)( 27,507)( 28,508)( 29,509)( 30,510)( 31,511)
( 32,512)( 33,513)( 34,514)( 35,515)( 36,516)( 37,517)( 38,518)( 39,519)
( 40,520)( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,526)( 47,527)
( 48,528)( 49,529)( 50,530)( 51,531)( 52,532)( 53,533)( 54,534)( 55,535)
( 56,536)( 57,537)( 58,538)( 59,539)( 60,540)( 61,556)( 62,557)( 63,558)
( 64,559)( 65,560)( 66,561)( 67,562)( 68,563)( 69,564)( 70,565)( 71,566)
( 72,567)( 73,568)( 74,569)( 75,570)( 76,541)( 77,542)( 78,543)( 79,544)
( 80,545)( 81,546)( 82,547)( 83,548)( 84,549)( 85,550)( 86,551)( 87,552)
( 88,553)( 89,554)( 90,555)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)
( 96,591)( 97,592)( 98,593)( 99,594)(100,595)(101,596)(102,597)(103,598)
(104,599)(105,600)(106,571)(107,572)(108,573)(109,574)(110,575)(111,576)
(112,577)(113,578)(114,579)(115,580)(116,581)(117,582)(118,583)(119,584)
(120,585)(121,631)(122,632)(123,633)(124,634)(125,635)(126,636)(127,637)
(128,638)(129,639)(130,640)(131,641)(132,642)(133,643)(134,644)(135,645)
(136,646)(137,647)(138,648)(139,649)(140,650)(141,651)(142,652)(143,653)
(144,654)(145,655)(146,656)(147,657)(148,658)(149,659)(150,660)(151,601)
(152,602)(153,603)(154,604)(155,605)(156,606)(157,607)(158,608)(159,609)
(160,610)(161,611)(162,612)(163,613)(164,614)(165,615)(166,616)(167,617)
(168,618)(169,619)(170,620)(171,621)(172,622)(173,623)(174,624)(175,625)
(176,626)(177,627)(178,628)(179,629)(180,630)(181,706)(182,707)(183,708)
(184,709)(185,710)(186,711)(187,712)(188,713)(189,714)(190,715)(191,716)
(192,717)(193,718)(194,719)(195,720)(196,691)(197,692)(198,693)(199,694)
(200,695)(201,696)(202,697)(203,698)(204,699)(205,700)(206,701)(207,702)
(208,703)(209,704)(210,705)(211,676)(212,677)(213,678)(214,679)(215,680)
(216,681)(217,682)(218,683)(219,684)(220,685)(221,686)(222,687)(223,688)
(224,689)(225,690)(226,661)(227,662)(228,663)(229,664)(230,665)(231,666)
(232,667)(233,668)(234,669)(235,670)(236,671)(237,672)(238,673)(239,674)
(240,675)(241,721)(242,722)(243,723)(244,724)(245,725)(246,726)(247,727)
(248,728)(249,729)(250,730)(251,731)(252,732)(253,733)(254,734)(255,735)
(256,736)(257,737)(258,738)(259,739)(260,740)(261,741)(262,742)(263,743)
(264,744)(265,745)(266,746)(267,747)(268,748)(269,749)(270,750)(271,751)
(272,752)(273,753)(274,754)(275,755)(276,756)(277,757)(278,758)(279,759)
(280,760)(281,761)(282,762)(283,763)(284,764)(285,765)(286,766)(287,767)
(288,768)(289,769)(290,770)(291,771)(292,772)(293,773)(294,774)(295,775)
(296,776)(297,777)(298,778)(299,779)(300,780)(301,796)(302,797)(303,798)
(304,799)(305,800)(306,801)(307,802)(308,803)(309,804)(310,805)(311,806)
(312,807)(313,808)(314,809)(315,810)(316,781)(317,782)(318,783)(319,784)
(320,785)(321,786)(322,787)(323,788)(324,789)(325,790)(326,791)(327,792)
(328,793)(329,794)(330,795)(331,826)(332,827)(333,828)(334,829)(335,830)
(336,831)(337,832)(338,833)(339,834)(340,835)(341,836)(342,837)(343,838)
(344,839)(345,840)(346,811)(347,812)(348,813)(349,814)(350,815)(351,816)
(352,817)(353,818)(354,819)(355,820)(356,821)(357,822)(358,823)(359,824)
(360,825)(361,871)(362,872)(363,873)(364,874)(365,875)(366,876)(367,877)
(368,878)(369,879)(370,880)(371,881)(372,882)(373,883)(374,884)(375,885)
(376,886)(377,887)(378,888)(379,889)(380,890)(381,891)(382,892)(383,893)
(384,894)(385,895)(386,896)(387,897)(388,898)(389,899)(390,900)(391,841)
(392,842)(393,843)(394,844)(395,845)(396,846)(397,847)(398,848)(399,849)
(400,850)(401,851)(402,852)(403,853)(404,854)(405,855)(406,856)(407,857)
(408,858)(409,859)(410,860)(411,861)(412,862)(413,863)(414,864)(415,865)
(416,866)(417,867)(418,868)(419,869)(420,870)(421,946)(422,947)(423,948)
(424,949)(425,950)(426,951)(427,952)(428,953)(429,954)(430,955)(431,956)
(432,957)(433,958)(434,959)(435,960)(436,931)(437,932)(438,933)(439,934)
(440,935)(441,936)(442,937)(443,938)(444,939)(445,940)(446,941)(447,942)
(448,943)(449,944)(450,945)(451,916)(452,917)(453,918)(454,919)(455,920)
(456,921)(457,922)(458,923)(459,924)(460,925)(461,926)(462,927)(463,928)
(464,929)(465,930)(466,901)(467,902)(468,903)(469,904)(470,905)(471,906)
(472,907)(473,908)(474,909)(475,910)(476,911)(477,912)(478,913)(479,914)
(480,915);
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*s0*s1*s2*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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope