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Polytope of Type {60,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,16}*1920a
Also Known As : {60,16|2}. if this polytope has another name.
Group : SmallGroup(1920,41725)
Rank : 3
Schlafli Type : {60,16}
Number of vertices, edges, etc : 60, 480, 16
Order of s0s1s2 : 240
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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 : {60,8}*960a, {30,16}*960
   3-fold quotients : {20,16}*640a
   4-fold quotients : {60,4}*480a, {30,8}*480
   5-fold quotients : {12,16}*384a
   6-fold quotients : {20,8}*320a, {10,16}*320
   8-fold quotients : {60,2}*240, {30,4}*240a
   10-fold quotients : {12,8}*192a, {6,16}*192
   12-fold quotients : {20,4}*160, {10,8}*160
   15-fold quotients : {4,16}*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, {2,16}*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)
(121,361)(122,365)(123,364)(124,363)(125,362)(126,371)(127,375)(128,374)
(129,373)(130,372)(131,366)(132,370)(133,369)(134,368)(135,367)(136,376)
(137,380)(138,379)(139,378)(140,377)(141,386)(142,390)(143,389)(144,388)
(145,387)(146,381)(147,385)(148,384)(149,383)(150,382)(151,391)(152,395)
(153,394)(154,393)(155,392)(156,401)(157,405)(158,404)(159,403)(160,402)
(161,396)(162,400)(163,399)(164,398)(165,397)(166,406)(167,410)(168,409)
(169,408)(170,407)(171,416)(172,420)(173,419)(174,418)(175,417)(176,411)
(177,415)(178,414)(179,413)(180,412)(181,421)(182,425)(183,424)(184,423)
(185,422)(186,431)(187,435)(188,434)(189,433)(190,432)(191,426)(192,430)
(193,429)(194,428)(195,427)(196,436)(197,440)(198,439)(199,438)(200,437)
(201,446)(202,450)(203,449)(204,448)(205,447)(206,441)(207,445)(208,444)
(209,443)(210,442)(211,451)(212,455)(213,454)(214,453)(215,452)(216,461)
(217,465)(218,464)(219,463)(220,462)(221,456)(222,460)(223,459)(224,458)
(225,457)(226,466)(227,470)(228,469)(229,468)(230,467)(231,476)(232,480)
(233,479)(234,478)(235,477)(236,471)(237,475)(238,474)(239,473)(240,472)
(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)
(601,841)(602,845)(603,844)(604,843)(605,842)(606,851)(607,855)(608,854)
(609,853)(610,852)(611,846)(612,850)(613,849)(614,848)(615,847)(616,856)
(617,860)(618,859)(619,858)(620,857)(621,866)(622,870)(623,869)(624,868)
(625,867)(626,861)(627,865)(628,864)(629,863)(630,862)(631,871)(632,875)
(633,874)(634,873)(635,872)(636,881)(637,885)(638,884)(639,883)(640,882)
(641,876)(642,880)(643,879)(644,878)(645,877)(646,886)(647,890)(648,889)
(649,888)(650,887)(651,896)(652,900)(653,899)(654,898)(655,897)(656,891)
(657,895)(658,894)(659,893)(660,892)(661,901)(662,905)(663,904)(664,903)
(665,902)(666,911)(667,915)(668,914)(669,913)(670,912)(671,906)(672,910)
(673,909)(674,908)(675,907)(676,916)(677,920)(678,919)(679,918)(680,917)
(681,926)(682,930)(683,929)(684,928)(685,927)(686,921)(687,925)(688,924)
(689,923)(690,922)(691,931)(692,935)(693,934)(694,933)(695,932)(696,941)
(697,945)(698,944)(699,943)(700,942)(701,936)(702,940)(703,939)(704,938)
(705,937)(706,946)(707,950)(708,949)(709,948)(710,947)(711,956)(712,960)
(713,959)(714,958)(715,957)(716,951)(717,955)(718,954)(719,953)(720,952);;
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, 52)( 32, 51)
( 33, 55)( 34, 54)( 35, 53)( 36, 47)( 37, 46)( 38, 50)( 39, 49)( 40, 48)
( 41, 57)( 42, 56)( 43, 60)( 44, 59)( 45, 58)( 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)( 91,112)( 92,111)( 93,115)( 94,114)( 95,113)
( 96,107)( 97,106)( 98,110)( 99,109)(100,108)(101,117)(102,116)(103,120)
(104,119)(105,118)(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)(271,352)(272,351)(273,355)(274,354)
(275,353)(276,347)(277,346)(278,350)(279,349)(280,348)(281,357)(282,356)
(283,360)(284,359)(285,358)(286,337)(287,336)(288,340)(289,339)(290,338)
(291,332)(292,331)(293,335)(294,334)(295,333)(296,342)(297,341)(298,345)
(299,344)(300,343)(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)(511,652)(512,651)(513,655)(514,654)
(515,653)(516,647)(517,646)(518,650)(519,649)(520,648)(521,657)(522,656)
(523,660)(524,659)(525,658)(526,637)(527,636)(528,640)(529,639)(530,638)
(531,632)(532,631)(533,635)(534,634)(535,633)(536,642)(537,641)(538,645)
(539,644)(540,643)(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)
(571,712)(572,711)(573,715)(574,714)(575,713)(576,707)(577,706)(578,710)
(579,709)(580,708)(581,717)(582,716)(583,720)(584,719)(585,718)(586,697)
(587,696)(588,700)(589,699)(590,698)(591,692)(592,691)(593,695)(594,694)
(595,693)(596,702)(597,701)(598,705)(599,704)(600,703)(721,907)(722,906)
(723,910)(724,909)(725,908)(726,902)(727,901)(728,905)(729,904)(730,903)
(731,912)(732,911)(733,915)(734,914)(735,913)(736,922)(737,921)(738,925)
(739,924)(740,923)(741,917)(742,916)(743,920)(744,919)(745,918)(746,927)
(747,926)(748,930)(749,929)(750,928)(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)(781,847)(782,846)(783,850)(784,849)(785,848)(786,842)
(787,841)(788,845)(789,844)(790,843)(791,852)(792,851)(793,855)(794,854)
(795,853)(796,862)(797,861)(798,865)(799,864)(800,863)(801,857)(802,856)
(803,860)(804,859)(805,858)(806,867)(807,866)(808,870)(809,869)(810,868)
(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)( 31,526)( 32,527)
( 33,528)( 34,529)( 35,530)( 36,531)( 37,532)( 38,533)( 39,534)( 40,535)
( 41,536)( 42,537)( 43,538)( 44,539)( 45,540)( 46,511)( 47,512)( 48,513)
( 49,514)( 50,515)( 51,516)( 52,517)( 53,518)( 54,519)( 55,520)( 56,521)
( 57,522)( 58,523)( 59,524)( 60,525)( 61,541)( 62,542)( 63,543)( 64,544)
( 65,545)( 66,546)( 67,547)( 68,548)( 69,549)( 70,550)( 71,551)( 72,552)
( 73,553)( 74,554)( 75,555)( 76,556)( 77,557)( 78,558)( 79,559)( 80,560)
( 81,561)( 82,562)( 83,563)( 84,564)( 85,565)( 86,566)( 87,567)( 88,568)
( 89,569)( 90,570)( 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)(181,691)(182,692)(183,693)(184,694)
(185,695)(186,696)(187,697)(188,698)(189,699)(190,700)(191,701)(192,702)
(193,703)(194,704)(195,705)(196,706)(197,707)(198,708)(199,709)(200,710)
(201,711)(202,712)(203,713)(204,714)(205,715)(206,716)(207,717)(208,718)
(209,719)(210,720)(211,661)(212,662)(213,663)(214,664)(215,665)(216,666)
(217,667)(218,668)(219,669)(220,670)(221,671)(222,672)(223,673)(224,674)
(225,675)(226,676)(227,677)(228,678)(229,679)(230,680)(231,681)(232,682)
(233,683)(234,684)(235,685)(236,686)(237,687)(238,688)(239,689)(240,690)
(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)(271,766)(272,767)
(273,768)(274,769)(275,770)(276,771)(277,772)(278,773)(279,774)(280,775)
(281,776)(282,777)(283,778)(284,779)(285,780)(286,751)(287,752)(288,753)
(289,754)(290,755)(291,756)(292,757)(293,758)(294,759)(295,760)(296,761)
(297,762)(298,763)(299,764)(300,765)(301,781)(302,782)(303,783)(304,784)
(305,785)(306,786)(307,787)(308,788)(309,789)(310,790)(311,791)(312,792)
(313,793)(314,794)(315,795)(316,796)(317,797)(318,798)(319,799)(320,800)
(321,801)(322,802)(323,803)(324,804)(325,805)(326,806)(327,807)(328,808)
(329,809)(330,810)(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)(421,931)(422,932)(423,933)(424,934)
(425,935)(426,936)(427,937)(428,938)(429,939)(430,940)(431,941)(432,942)
(433,943)(434,944)(435,945)(436,946)(437,947)(438,948)(439,949)(440,950)
(441,951)(442,952)(443,953)(444,954)(445,955)(446,956)(447,957)(448,958)
(449,959)(450,960)(451,901)(452,902)(453,903)(454,904)(455,905)(456,906)
(457,907)(458,908)(459,909)(460,910)(461,911)(462,912)(463,913)(464,914)
(465,915)(466,916)(467,917)(468,918)(469,919)(470,920)(471,921)(472,922)
(473,923)(474,924)(475,925)(476,926)(477,927)(478,928)(479,929)(480,930);;
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*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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)(121,361)(122,365)(123,364)(124,363)(125,362)(126,371)(127,375)
(128,374)(129,373)(130,372)(131,366)(132,370)(133,369)(134,368)(135,367)
(136,376)(137,380)(138,379)(139,378)(140,377)(141,386)(142,390)(143,389)
(144,388)(145,387)(146,381)(147,385)(148,384)(149,383)(150,382)(151,391)
(152,395)(153,394)(154,393)(155,392)(156,401)(157,405)(158,404)(159,403)
(160,402)(161,396)(162,400)(163,399)(164,398)(165,397)(166,406)(167,410)
(168,409)(169,408)(170,407)(171,416)(172,420)(173,419)(174,418)(175,417)
(176,411)(177,415)(178,414)(179,413)(180,412)(181,421)(182,425)(183,424)
(184,423)(185,422)(186,431)(187,435)(188,434)(189,433)(190,432)(191,426)
(192,430)(193,429)(194,428)(195,427)(196,436)(197,440)(198,439)(199,438)
(200,437)(201,446)(202,450)(203,449)(204,448)(205,447)(206,441)(207,445)
(208,444)(209,443)(210,442)(211,451)(212,455)(213,454)(214,453)(215,452)
(216,461)(217,465)(218,464)(219,463)(220,462)(221,456)(222,460)(223,459)
(224,458)(225,457)(226,466)(227,470)(228,469)(229,468)(230,467)(231,476)
(232,480)(233,479)(234,478)(235,477)(236,471)(237,475)(238,474)(239,473)
(240,472)(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)(601,841)(602,845)(603,844)(604,843)(605,842)(606,851)(607,855)
(608,854)(609,853)(610,852)(611,846)(612,850)(613,849)(614,848)(615,847)
(616,856)(617,860)(618,859)(619,858)(620,857)(621,866)(622,870)(623,869)
(624,868)(625,867)(626,861)(627,865)(628,864)(629,863)(630,862)(631,871)
(632,875)(633,874)(634,873)(635,872)(636,881)(637,885)(638,884)(639,883)
(640,882)(641,876)(642,880)(643,879)(644,878)(645,877)(646,886)(647,890)
(648,889)(649,888)(650,887)(651,896)(652,900)(653,899)(654,898)(655,897)
(656,891)(657,895)(658,894)(659,893)(660,892)(661,901)(662,905)(663,904)
(664,903)(665,902)(666,911)(667,915)(668,914)(669,913)(670,912)(671,906)
(672,910)(673,909)(674,908)(675,907)(676,916)(677,920)(678,919)(679,918)
(680,917)(681,926)(682,930)(683,929)(684,928)(685,927)(686,921)(687,925)
(688,924)(689,923)(690,922)(691,931)(692,935)(693,934)(694,933)(695,932)
(696,941)(697,945)(698,944)(699,943)(700,942)(701,936)(702,940)(703,939)
(704,938)(705,937)(706,946)(707,950)(708,949)(709,948)(710,947)(711,956)
(712,960)(713,959)(714,958)(715,957)(716,951)(717,955)(718,954)(719,953)
(720,952);
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, 52)
( 32, 51)( 33, 55)( 34, 54)( 35, 53)( 36, 47)( 37, 46)( 38, 50)( 39, 49)
( 40, 48)( 41, 57)( 42, 56)( 43, 60)( 44, 59)( 45, 58)( 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)( 91,112)( 92,111)( 93,115)( 94,114)
( 95,113)( 96,107)( 97,106)( 98,110)( 99,109)(100,108)(101,117)(102,116)
(103,120)(104,119)(105,118)(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)(271,352)(272,351)(273,355)
(274,354)(275,353)(276,347)(277,346)(278,350)(279,349)(280,348)(281,357)
(282,356)(283,360)(284,359)(285,358)(286,337)(287,336)(288,340)(289,339)
(290,338)(291,332)(292,331)(293,335)(294,334)(295,333)(296,342)(297,341)
(298,345)(299,344)(300,343)(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)(511,652)(512,651)(513,655)
(514,654)(515,653)(516,647)(517,646)(518,650)(519,649)(520,648)(521,657)
(522,656)(523,660)(524,659)(525,658)(526,637)(527,636)(528,640)(529,639)
(530,638)(531,632)(532,631)(533,635)(534,634)(535,633)(536,642)(537,641)
(538,645)(539,644)(540,643)(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)(571,712)(572,711)(573,715)(574,714)(575,713)(576,707)(577,706)
(578,710)(579,709)(580,708)(581,717)(582,716)(583,720)(584,719)(585,718)
(586,697)(587,696)(588,700)(589,699)(590,698)(591,692)(592,691)(593,695)
(594,694)(595,693)(596,702)(597,701)(598,705)(599,704)(600,703)(721,907)
(722,906)(723,910)(724,909)(725,908)(726,902)(727,901)(728,905)(729,904)
(730,903)(731,912)(732,911)(733,915)(734,914)(735,913)(736,922)(737,921)
(738,925)(739,924)(740,923)(741,917)(742,916)(743,920)(744,919)(745,918)
(746,927)(747,926)(748,930)(749,929)(750,928)(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)(781,847)(782,846)(783,850)(784,849)(785,848)
(786,842)(787,841)(788,845)(789,844)(790,843)(791,852)(792,851)(793,855)
(794,854)(795,853)(796,862)(797,861)(798,865)(799,864)(800,863)(801,857)
(802,856)(803,860)(804,859)(805,858)(806,867)(807,866)(808,870)(809,869)
(810,868)(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)( 31,526)
( 32,527)( 33,528)( 34,529)( 35,530)( 36,531)( 37,532)( 38,533)( 39,534)
( 40,535)( 41,536)( 42,537)( 43,538)( 44,539)( 45,540)( 46,511)( 47,512)
( 48,513)( 49,514)( 50,515)( 51,516)( 52,517)( 53,518)( 54,519)( 55,520)
( 56,521)( 57,522)( 58,523)( 59,524)( 60,525)( 61,541)( 62,542)( 63,543)
( 64,544)( 65,545)( 66,546)( 67,547)( 68,548)( 69,549)( 70,550)( 71,551)
( 72,552)( 73,553)( 74,554)( 75,555)( 76,556)( 77,557)( 78,558)( 79,559)
( 80,560)( 81,561)( 82,562)( 83,563)( 84,564)( 85,565)( 86,566)( 87,567)
( 88,568)( 89,569)( 90,570)( 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)(181,691)(182,692)(183,693)
(184,694)(185,695)(186,696)(187,697)(188,698)(189,699)(190,700)(191,701)
(192,702)(193,703)(194,704)(195,705)(196,706)(197,707)(198,708)(199,709)
(200,710)(201,711)(202,712)(203,713)(204,714)(205,715)(206,716)(207,717)
(208,718)(209,719)(210,720)(211,661)(212,662)(213,663)(214,664)(215,665)
(216,666)(217,667)(218,668)(219,669)(220,670)(221,671)(222,672)(223,673)
(224,674)(225,675)(226,676)(227,677)(228,678)(229,679)(230,680)(231,681)
(232,682)(233,683)(234,684)(235,685)(236,686)(237,687)(238,688)(239,689)
(240,690)(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)(271,766)
(272,767)(273,768)(274,769)(275,770)(276,771)(277,772)(278,773)(279,774)
(280,775)(281,776)(282,777)(283,778)(284,779)(285,780)(286,751)(287,752)
(288,753)(289,754)(290,755)(291,756)(292,757)(293,758)(294,759)(295,760)
(296,761)(297,762)(298,763)(299,764)(300,765)(301,781)(302,782)(303,783)
(304,784)(305,785)(306,786)(307,787)(308,788)(309,789)(310,790)(311,791)
(312,792)(313,793)(314,794)(315,795)(316,796)(317,797)(318,798)(319,799)
(320,800)(321,801)(322,802)(323,803)(324,804)(325,805)(326,806)(327,807)
(328,808)(329,809)(330,810)(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)(421,931)(422,932)(423,933)
(424,934)(425,935)(426,936)(427,937)(428,938)(429,939)(430,940)(431,941)
(432,942)(433,943)(434,944)(435,945)(436,946)(437,947)(438,948)(439,949)
(440,950)(441,951)(442,952)(443,953)(444,954)(445,955)(446,956)(447,957)
(448,958)(449,959)(450,960)(451,901)(452,902)(453,903)(454,904)(455,905)
(456,906)(457,907)(458,908)(459,909)(460,910)(461,911)(462,912)(463,913)
(464,914)(465,915)(466,916)(467,917)(468,918)(469,919)(470,920)(471,921)
(472,922)(473,923)(474,924)(475,925)(476,926)(477,927)(478,928)(479,929)
(480,930);
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*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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