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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}*1920e
if this polytope has a name.
Group : SmallGroup(1920,239446)
Rank : 3
Schlafli Type : {60,8}
Number of vertices, edges, etc : 120, 480, 16
Order of s0s1s2 : 60
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {60,4}*960b, {30,8}*960b
   4-fold quotients : {60,4}*480b, {60,4}*480c, {15,8}*480, {30,4}*480
   5-fold quotients : {12,8}*384e
   8-fold quotients : {60,2}*240, {15,4}*240, {30,4}*240b, {30,4}*240c
   10-fold quotients : {12,4}*192b, {6,8}*192b
   16-fold quotients : {15,4}*120, {30,2}*120
   20-fold quotients : {12,4}*96b, {12,4}*96c, {3,8}*96, {6,4}*96
   24-fold quotients : {20,2}*80
   32-fold quotients : {15,2}*60
   40-fold quotients : {12,2}*48, {3,4}*48, {6,4}*48b, {6,4}*48c
   48-fold quotients : {10,2}*40
   80-fold quotients : {3,4}*24, {6,2}*24
   96-fold quotients : {5,2}*20
   120-fold quotients : {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 := (  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);;
s1 := (  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);;
s2 := (  1,483)(  2,484)(  3,482)(  4,481)(  5,487)(  6,488)(  7,486)(  8,485)
(  9,491)( 10,492)( 11,490)( 12,489)( 13,495)( 14,496)( 15,494)( 16,493)
( 17,499)( 18,500)( 19,498)( 20,497)( 21,503)( 22,504)( 23,502)( 24,501)
( 25,507)( 26,508)( 27,506)( 28,505)( 29,511)( 30,512)( 31,510)( 32,509)
( 33,515)( 34,516)( 35,514)( 36,513)( 37,519)( 38,520)( 39,518)( 40,517)
( 41,523)( 42,524)( 43,522)( 44,521)( 45,527)( 46,528)( 47,526)( 48,525)
( 49,531)( 50,532)( 51,530)( 52,529)( 53,535)( 54,536)( 55,534)( 56,533)
( 57,539)( 58,540)( 59,538)( 60,537)( 61,543)( 62,544)( 63,542)( 64,541)
( 65,547)( 66,548)( 67,546)( 68,545)( 69,551)( 70,552)( 71,550)( 72,549)
( 73,555)( 74,556)( 75,554)( 76,553)( 77,559)( 78,560)( 79,558)( 80,557)
( 81,563)( 82,564)( 83,562)( 84,561)( 85,567)( 86,568)( 87,566)( 88,565)
( 89,571)( 90,572)( 91,570)( 92,569)( 93,575)( 94,576)( 95,574)( 96,573)
( 97,579)( 98,580)( 99,578)(100,577)(101,583)(102,584)(103,582)(104,581)
(105,587)(106,588)(107,586)(108,585)(109,591)(110,592)(111,590)(112,589)
(113,595)(114,596)(115,594)(116,593)(117,599)(118,600)(119,598)(120,597)
(121,603)(122,604)(123,602)(124,601)(125,607)(126,608)(127,606)(128,605)
(129,611)(130,612)(131,610)(132,609)(133,615)(134,616)(135,614)(136,613)
(137,619)(138,620)(139,618)(140,617)(141,623)(142,624)(143,622)(144,621)
(145,627)(146,628)(147,626)(148,625)(149,631)(150,632)(151,630)(152,629)
(153,635)(154,636)(155,634)(156,633)(157,639)(158,640)(159,638)(160,637)
(161,643)(162,644)(163,642)(164,641)(165,647)(166,648)(167,646)(168,645)
(169,651)(170,652)(171,650)(172,649)(173,655)(174,656)(175,654)(176,653)
(177,659)(178,660)(179,658)(180,657)(181,663)(182,664)(183,662)(184,661)
(185,667)(186,668)(187,666)(188,665)(189,671)(190,672)(191,670)(192,669)
(193,675)(194,676)(195,674)(196,673)(197,679)(198,680)(199,678)(200,677)
(201,683)(202,684)(203,682)(204,681)(205,687)(206,688)(207,686)(208,685)
(209,691)(210,692)(211,690)(212,689)(213,695)(214,696)(215,694)(216,693)
(217,699)(218,700)(219,698)(220,697)(221,703)(222,704)(223,702)(224,701)
(225,707)(226,708)(227,706)(228,705)(229,711)(230,712)(231,710)(232,709)
(233,715)(234,716)(235,714)(236,713)(237,719)(238,720)(239,718)(240,717)
(241,723)(242,724)(243,722)(244,721)(245,727)(246,728)(247,726)(248,725)
(249,731)(250,732)(251,730)(252,729)(253,735)(254,736)(255,734)(256,733)
(257,739)(258,740)(259,738)(260,737)(261,743)(262,744)(263,742)(264,741)
(265,747)(266,748)(267,746)(268,745)(269,751)(270,752)(271,750)(272,749)
(273,755)(274,756)(275,754)(276,753)(277,759)(278,760)(279,758)(280,757)
(281,763)(282,764)(283,762)(284,761)(285,767)(286,768)(287,766)(288,765)
(289,771)(290,772)(291,770)(292,769)(293,775)(294,776)(295,774)(296,773)
(297,779)(298,780)(299,778)(300,777)(301,783)(302,784)(303,782)(304,781)
(305,787)(306,788)(307,786)(308,785)(309,791)(310,792)(311,790)(312,789)
(313,795)(314,796)(315,794)(316,793)(317,799)(318,800)(319,798)(320,797)
(321,803)(322,804)(323,802)(324,801)(325,807)(326,808)(327,806)(328,805)
(329,811)(330,812)(331,810)(332,809)(333,815)(334,816)(335,814)(336,813)
(337,819)(338,820)(339,818)(340,817)(341,823)(342,824)(343,822)(344,821)
(345,827)(346,828)(347,826)(348,825)(349,831)(350,832)(351,830)(352,829)
(353,835)(354,836)(355,834)(356,833)(357,839)(358,840)(359,838)(360,837)
(361,843)(362,844)(363,842)(364,841)(365,847)(366,848)(367,846)(368,845)
(369,851)(370,852)(371,850)(372,849)(373,855)(374,856)(375,854)(376,853)
(377,859)(378,860)(379,858)(380,857)(381,863)(382,864)(383,862)(384,861)
(385,867)(386,868)(387,866)(388,865)(389,871)(390,872)(391,870)(392,869)
(393,875)(394,876)(395,874)(396,873)(397,879)(398,880)(399,878)(400,877)
(401,883)(402,884)(403,882)(404,881)(405,887)(406,888)(407,886)(408,885)
(409,891)(410,892)(411,890)(412,889)(413,895)(414,896)(415,894)(416,893)
(417,899)(418,900)(419,898)(420,897)(421,903)(422,904)(423,902)(424,901)
(425,907)(426,908)(427,906)(428,905)(429,911)(430,912)(431,910)(432,909)
(433,915)(434,916)(435,914)(436,913)(437,919)(438,920)(439,918)(440,917)
(441,923)(442,924)(443,922)(444,921)(445,927)(446,928)(447,926)(448,925)
(449,931)(450,932)(451,930)(452,929)(453,935)(454,936)(455,934)(456,933)
(457,939)(458,940)(459,938)(460,937)(461,943)(462,944)(463,942)(464,941)
(465,947)(466,948)(467,946)(468,945)(469,951)(470,952)(471,950)(472,949)
(473,955)(474,956)(475,954)(476,953)(477,959)(478,960)(479,958)(480,957);;
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*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*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*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := 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);
s1 := 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);
s2 := Sym(960)!(  1,483)(  2,484)(  3,482)(  4,481)(  5,487)(  6,488)(  7,486)
(  8,485)(  9,491)( 10,492)( 11,490)( 12,489)( 13,495)( 14,496)( 15,494)
( 16,493)( 17,499)( 18,500)( 19,498)( 20,497)( 21,503)( 22,504)( 23,502)
( 24,501)( 25,507)( 26,508)( 27,506)( 28,505)( 29,511)( 30,512)( 31,510)
( 32,509)( 33,515)( 34,516)( 35,514)( 36,513)( 37,519)( 38,520)( 39,518)
( 40,517)( 41,523)( 42,524)( 43,522)( 44,521)( 45,527)( 46,528)( 47,526)
( 48,525)( 49,531)( 50,532)( 51,530)( 52,529)( 53,535)( 54,536)( 55,534)
( 56,533)( 57,539)( 58,540)( 59,538)( 60,537)( 61,543)( 62,544)( 63,542)
( 64,541)( 65,547)( 66,548)( 67,546)( 68,545)( 69,551)( 70,552)( 71,550)
( 72,549)( 73,555)( 74,556)( 75,554)( 76,553)( 77,559)( 78,560)( 79,558)
( 80,557)( 81,563)( 82,564)( 83,562)( 84,561)( 85,567)( 86,568)( 87,566)
( 88,565)( 89,571)( 90,572)( 91,570)( 92,569)( 93,575)( 94,576)( 95,574)
( 96,573)( 97,579)( 98,580)( 99,578)(100,577)(101,583)(102,584)(103,582)
(104,581)(105,587)(106,588)(107,586)(108,585)(109,591)(110,592)(111,590)
(112,589)(113,595)(114,596)(115,594)(116,593)(117,599)(118,600)(119,598)
(120,597)(121,603)(122,604)(123,602)(124,601)(125,607)(126,608)(127,606)
(128,605)(129,611)(130,612)(131,610)(132,609)(133,615)(134,616)(135,614)
(136,613)(137,619)(138,620)(139,618)(140,617)(141,623)(142,624)(143,622)
(144,621)(145,627)(146,628)(147,626)(148,625)(149,631)(150,632)(151,630)
(152,629)(153,635)(154,636)(155,634)(156,633)(157,639)(158,640)(159,638)
(160,637)(161,643)(162,644)(163,642)(164,641)(165,647)(166,648)(167,646)
(168,645)(169,651)(170,652)(171,650)(172,649)(173,655)(174,656)(175,654)
(176,653)(177,659)(178,660)(179,658)(180,657)(181,663)(182,664)(183,662)
(184,661)(185,667)(186,668)(187,666)(188,665)(189,671)(190,672)(191,670)
(192,669)(193,675)(194,676)(195,674)(196,673)(197,679)(198,680)(199,678)
(200,677)(201,683)(202,684)(203,682)(204,681)(205,687)(206,688)(207,686)
(208,685)(209,691)(210,692)(211,690)(212,689)(213,695)(214,696)(215,694)
(216,693)(217,699)(218,700)(219,698)(220,697)(221,703)(222,704)(223,702)
(224,701)(225,707)(226,708)(227,706)(228,705)(229,711)(230,712)(231,710)
(232,709)(233,715)(234,716)(235,714)(236,713)(237,719)(238,720)(239,718)
(240,717)(241,723)(242,724)(243,722)(244,721)(245,727)(246,728)(247,726)
(248,725)(249,731)(250,732)(251,730)(252,729)(253,735)(254,736)(255,734)
(256,733)(257,739)(258,740)(259,738)(260,737)(261,743)(262,744)(263,742)
(264,741)(265,747)(266,748)(267,746)(268,745)(269,751)(270,752)(271,750)
(272,749)(273,755)(274,756)(275,754)(276,753)(277,759)(278,760)(279,758)
(280,757)(281,763)(282,764)(283,762)(284,761)(285,767)(286,768)(287,766)
(288,765)(289,771)(290,772)(291,770)(292,769)(293,775)(294,776)(295,774)
(296,773)(297,779)(298,780)(299,778)(300,777)(301,783)(302,784)(303,782)
(304,781)(305,787)(306,788)(307,786)(308,785)(309,791)(310,792)(311,790)
(312,789)(313,795)(314,796)(315,794)(316,793)(317,799)(318,800)(319,798)
(320,797)(321,803)(322,804)(323,802)(324,801)(325,807)(326,808)(327,806)
(328,805)(329,811)(330,812)(331,810)(332,809)(333,815)(334,816)(335,814)
(336,813)(337,819)(338,820)(339,818)(340,817)(341,823)(342,824)(343,822)
(344,821)(345,827)(346,828)(347,826)(348,825)(349,831)(350,832)(351,830)
(352,829)(353,835)(354,836)(355,834)(356,833)(357,839)(358,840)(359,838)
(360,837)(361,843)(362,844)(363,842)(364,841)(365,847)(366,848)(367,846)
(368,845)(369,851)(370,852)(371,850)(372,849)(373,855)(374,856)(375,854)
(376,853)(377,859)(378,860)(379,858)(380,857)(381,863)(382,864)(383,862)
(384,861)(385,867)(386,868)(387,866)(388,865)(389,871)(390,872)(391,870)
(392,869)(393,875)(394,876)(395,874)(396,873)(397,879)(398,880)(399,878)
(400,877)(401,883)(402,884)(403,882)(404,881)(405,887)(406,888)(407,886)
(408,885)(409,891)(410,892)(411,890)(412,889)(413,895)(414,896)(415,894)
(416,893)(417,899)(418,900)(419,898)(420,897)(421,903)(422,904)(423,902)
(424,901)(425,907)(426,908)(427,906)(428,905)(429,911)(430,912)(431,910)
(432,909)(433,915)(434,916)(435,914)(436,913)(437,919)(438,920)(439,918)
(440,917)(441,923)(442,924)(443,922)(444,921)(445,927)(446,928)(447,926)
(448,925)(449,931)(450,932)(451,930)(452,929)(453,935)(454,936)(455,934)
(456,933)(457,939)(458,940)(459,938)(460,937)(461,943)(462,944)(463,942)
(464,941)(465,947)(466,948)(467,946)(468,945)(469,951)(470,952)(471,950)
(472,949)(473,955)(474,956)(475,954)(476,953)(477,959)(478,960)(479,958)
(480,957);
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*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*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*s0*s1 >; 
 
References : None.
to this polytope