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Polytope of Type {120,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {120,8}*1920d
if this polytope has a name.
Group : SmallGroup(1920,16585)
Rank : 3
Schlafli Type : {120,8}
Number of vertices, edges, etc : 120, 480, 8
Order of s0s1s2 : 120
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   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 : {120,4}*960b, {60,8}*960b
   3-fold quotients : {40,8}*640c
   4-fold quotients : {60,4}*480a
   5-fold quotients : {24,8}*384c
   6-fold quotients : {40,4}*320b, {20,8}*320b
   8-fold quotients : {60,2}*240, {30,4}*240a
   10-fold quotients : {24,4}*192b, {12,8}*192b
   12-fold quotients : {20,4}*160
   15-fold quotients : {8,8}*128d
   16-fold quotients : {30,2}*120
   20-fold quotients : {12,4}*96a
   24-fold quotients : {20,2}*80, {10,4}*80
   30-fold quotients : {4,8}*64b, {8,4}*64b
   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
   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)( 61,346)( 62,350)( 63,349)( 64,348)
( 65,347)( 66,356)( 67,360)( 68,359)( 69,358)( 70,357)( 71,351)( 72,355)
( 73,354)( 74,353)( 75,352)( 76,331)( 77,335)( 78,334)( 79,333)( 80,332)
( 81,341)( 82,345)( 83,344)( 84,343)( 85,342)( 86,336)( 87,340)( 88,339)
( 89,338)( 90,337)( 91,316)( 92,320)( 93,319)( 94,318)( 95,317)( 96,326)
( 97,330)( 98,329)( 99,328)(100,327)(101,321)(102,325)(103,324)(104,323)
(105,322)(106,301)(107,305)(108,304)(109,303)(110,302)(111,311)(112,315)
(113,314)(114,313)(115,312)(116,306)(117,310)(118,309)(119,308)(120,307)
(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)(181,451)(182,455)(183,454)(184,453)
(185,452)(186,461)(187,465)(188,464)(189,463)(190,462)(191,456)(192,460)
(193,459)(194,458)(195,457)(196,466)(197,470)(198,469)(199,468)(200,467)
(201,476)(202,480)(203,479)(204,478)(205,477)(206,471)(207,475)(208,474)
(209,473)(210,472)(211,421)(212,425)(213,424)(214,423)(215,422)(216,431)
(217,435)(218,434)(219,433)(220,432)(221,426)(222,430)(223,429)(224,428)
(225,427)(226,436)(227,440)(228,439)(229,438)(230,437)(231,446)(232,450)
(233,449)(234,448)(235,447)(236,441)(237,445)(238,444)(239,443)(240,442)
(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)(541,826)(542,830)(543,829)(544,828)
(545,827)(546,836)(547,840)(548,839)(549,838)(550,837)(551,831)(552,835)
(553,834)(554,833)(555,832)(556,811)(557,815)(558,814)(559,813)(560,812)
(561,821)(562,825)(563,824)(564,823)(565,822)(566,816)(567,820)(568,819)
(569,818)(570,817)(571,796)(572,800)(573,799)(574,798)(575,797)(576,806)
(577,810)(578,809)(579,808)(580,807)(581,801)(582,805)(583,804)(584,803)
(585,802)(586,781)(587,785)(588,784)(589,783)(590,782)(591,791)(592,795)
(593,794)(594,793)(595,792)(596,786)(597,790)(598,789)(599,788)(600,787)
(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)(661,931)(662,935)(663,934)(664,933)
(665,932)(666,941)(667,945)(668,944)(669,943)(670,942)(671,936)(672,940)
(673,939)(674,938)(675,937)(676,946)(677,950)(678,949)(679,948)(680,947)
(681,956)(682,960)(683,959)(684,958)(685,957)(686,951)(687,955)(688,954)
(689,953)(690,952)(691,901)(692,905)(693,904)(694,903)(695,902)(696,911)
(697,915)(698,914)(699,913)(700,912)(701,906)(702,910)(703,909)(704,908)
(705,907)(706,916)(707,920)(708,919)(709,918)(710,917)(711,926)(712,930)
(713,929)(714,928)(715,927)(716,921)(717,925)(718,924)(719,923)(720,922);;
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)( 61,112)( 62,111)( 63,115)( 64,114)
( 65,113)( 66,107)( 67,106)( 68,110)( 69,109)( 70,108)( 71,117)( 72,116)
( 73,120)( 74,119)( 75,118)( 76, 97)( 77, 96)( 78,100)( 79, 99)( 80, 98)
( 81, 92)( 82, 91)( 83, 95)( 84, 94)( 85, 93)( 86,102)( 87,101)( 88,105)
( 89,104)( 90,103)(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)
(181,202)(182,201)(183,205)(184,204)(185,203)(186,197)(187,196)(188,200)
(189,199)(190,198)(191,207)(192,206)(193,210)(194,209)(195,208)(211,232)
(212,231)(213,235)(214,234)(215,233)(216,227)(217,226)(218,230)(219,229)
(220,228)(221,237)(222,236)(223,240)(224,239)(225,238)(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)(541,712)(542,711)(543,715)(544,714)(545,713)(546,707)
(547,706)(548,710)(549,709)(550,708)(551,717)(552,716)(553,720)(554,719)
(555,718)(556,697)(557,696)(558,700)(559,699)(560,698)(561,692)(562,691)
(563,695)(564,694)(565,693)(566,702)(567,701)(568,705)(569,704)(570,703)
(571,682)(572,681)(573,685)(574,684)(575,683)(576,677)(577,676)(578,680)
(579,679)(580,678)(581,687)(582,686)(583,690)(584,689)(585,688)(586,667)
(587,666)(588,670)(589,669)(590,668)(591,662)(592,661)(593,665)(594,664)
(595,663)(596,672)(597,671)(598,675)(599,674)(600,673)(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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*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 ];;
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)( 61,346)( 62,350)( 63,349)
( 64,348)( 65,347)( 66,356)( 67,360)( 68,359)( 69,358)( 70,357)( 71,351)
( 72,355)( 73,354)( 74,353)( 75,352)( 76,331)( 77,335)( 78,334)( 79,333)
( 80,332)( 81,341)( 82,345)( 83,344)( 84,343)( 85,342)( 86,336)( 87,340)
( 88,339)( 89,338)( 90,337)( 91,316)( 92,320)( 93,319)( 94,318)( 95,317)
( 96,326)( 97,330)( 98,329)( 99,328)(100,327)(101,321)(102,325)(103,324)
(104,323)(105,322)(106,301)(107,305)(108,304)(109,303)(110,302)(111,311)
(112,315)(113,314)(114,313)(115,312)(116,306)(117,310)(118,309)(119,308)
(120,307)(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)(181,451)(182,455)(183,454)
(184,453)(185,452)(186,461)(187,465)(188,464)(189,463)(190,462)(191,456)
(192,460)(193,459)(194,458)(195,457)(196,466)(197,470)(198,469)(199,468)
(200,467)(201,476)(202,480)(203,479)(204,478)(205,477)(206,471)(207,475)
(208,474)(209,473)(210,472)(211,421)(212,425)(213,424)(214,423)(215,422)
(216,431)(217,435)(218,434)(219,433)(220,432)(221,426)(222,430)(223,429)
(224,428)(225,427)(226,436)(227,440)(228,439)(229,438)(230,437)(231,446)
(232,450)(233,449)(234,448)(235,447)(236,441)(237,445)(238,444)(239,443)
(240,442)(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)(541,826)(542,830)(543,829)
(544,828)(545,827)(546,836)(547,840)(548,839)(549,838)(550,837)(551,831)
(552,835)(553,834)(554,833)(555,832)(556,811)(557,815)(558,814)(559,813)
(560,812)(561,821)(562,825)(563,824)(564,823)(565,822)(566,816)(567,820)
(568,819)(569,818)(570,817)(571,796)(572,800)(573,799)(574,798)(575,797)
(576,806)(577,810)(578,809)(579,808)(580,807)(581,801)(582,805)(583,804)
(584,803)(585,802)(586,781)(587,785)(588,784)(589,783)(590,782)(591,791)
(592,795)(593,794)(594,793)(595,792)(596,786)(597,790)(598,789)(599,788)
(600,787)(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)(661,931)(662,935)(663,934)
(664,933)(665,932)(666,941)(667,945)(668,944)(669,943)(670,942)(671,936)
(672,940)(673,939)(674,938)(675,937)(676,946)(677,950)(678,949)(679,948)
(680,947)(681,956)(682,960)(683,959)(684,958)(685,957)(686,951)(687,955)
(688,954)(689,953)(690,952)(691,901)(692,905)(693,904)(694,903)(695,902)
(696,911)(697,915)(698,914)(699,913)(700,912)(701,906)(702,910)(703,909)
(704,908)(705,907)(706,916)(707,920)(708,919)(709,918)(710,917)(711,926)
(712,930)(713,929)(714,928)(715,927)(716,921)(717,925)(718,924)(719,923)
(720,922);
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)( 61,112)( 62,111)( 63,115)
( 64,114)( 65,113)( 66,107)( 67,106)( 68,110)( 69,109)( 70,108)( 71,117)
( 72,116)( 73,120)( 74,119)( 75,118)( 76, 97)( 77, 96)( 78,100)( 79, 99)
( 80, 98)( 81, 92)( 82, 91)( 83, 95)( 84, 94)( 85, 93)( 86,102)( 87,101)
( 88,105)( 89,104)( 90,103)(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)(181,202)(182,201)(183,205)(184,204)(185,203)(186,197)(187,196)
(188,200)(189,199)(190,198)(191,207)(192,206)(193,210)(194,209)(195,208)
(211,232)(212,231)(213,235)(214,234)(215,233)(216,227)(217,226)(218,230)
(219,229)(220,228)(221,237)(222,236)(223,240)(224,239)(225,238)(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)(541,712)(542,711)(543,715)(544,714)(545,713)
(546,707)(547,706)(548,710)(549,709)(550,708)(551,717)(552,716)(553,720)
(554,719)(555,718)(556,697)(557,696)(558,700)(559,699)(560,698)(561,692)
(562,691)(563,695)(564,694)(565,693)(566,702)(567,701)(568,705)(569,704)
(570,703)(571,682)(572,681)(573,685)(574,684)(575,683)(576,677)(577,676)
(578,680)(579,679)(580,678)(581,687)(582,686)(583,690)(584,689)(585,688)
(586,667)(587,666)(588,670)(589,669)(590,668)(591,662)(592,661)(593,665)
(594,664)(595,663)(596,672)(597,671)(598,675)(599,674)(600,673)(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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*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 >; 
 
References : None.
to this polytope