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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}*1920c
Also Known As : {120,8|2}. if this polytope has another name.
Group : SmallGroup(1920,14515)
Rank : 3
Schlafli Type : {120,8}
Number of vertices, edges, etc : 120, 480, 8
Order of s0s1s2 : 120
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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}*960a, {60,8}*960a
   3-fold quotients : {40,8}*640b
   4-fold quotients : {60,4}*480a, {120,2}*480, {30,8}*480
   5-fold quotients : {24,8}*384b
   6-fold quotients : {40,4}*320a, {20,8}*320a
   8-fold quotients : {60,2}*240, {30,4}*240a
   10-fold quotients : {24,4}*192a, {12,8}*192a
   12-fold quotients : {20,4}*160, {40,2}*160, {10,8}*160
   15-fold quotients : {8,8}*128b
   16-fold quotients : {30,2}*120
   20-fold quotients : {12,4}*96a, {24,2}*96, {6,8}*96
   24-fold quotients : {20,2}*80, {10,4}*80
   30-fold quotients : {4,8}*64a, {8,4}*64a
   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, {8,2}*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 := (  1,721)(  2,725)(  3,724)(  4,723)(  5,722)(  6,731)(  7,735)(  8,734)
(  9,733)( 10,732)( 11,726)( 12,730)( 13,729)( 14,728)( 15,727)( 16,736)
( 17,740)( 18,739)( 19,738)( 20,737)( 21,746)( 22,750)( 23,749)( 24,748)
( 25,747)( 26,741)( 27,745)( 28,744)( 29,743)( 30,742)( 31,751)( 32,755)
( 33,754)( 34,753)( 35,752)( 36,761)( 37,765)( 38,764)( 39,763)( 40,762)
( 41,756)( 42,760)( 43,759)( 44,758)( 45,757)( 46,766)( 47,770)( 48,769)
( 49,768)( 50,767)( 51,776)( 52,780)( 53,779)( 54,778)( 55,777)( 56,771)
( 57,775)( 58,774)( 59,773)( 60,772)( 61,781)( 62,785)( 63,784)( 64,783)
( 65,782)( 66,791)( 67,795)( 68,794)( 69,793)( 70,792)( 71,786)( 72,790)
( 73,789)( 74,788)( 75,787)( 76,796)( 77,800)( 78,799)( 79,798)( 80,797)
( 81,806)( 82,810)( 83,809)( 84,808)( 85,807)( 86,801)( 87,805)( 88,804)
( 89,803)( 90,802)( 91,811)( 92,815)( 93,814)( 94,813)( 95,812)( 96,821)
( 97,825)( 98,824)( 99,823)(100,822)(101,816)(102,820)(103,819)(104,818)
(105,817)(106,826)(107,830)(108,829)(109,828)(110,827)(111,836)(112,840)
(113,839)(114,838)(115,837)(116,831)(117,835)(118,834)(119,833)(120,832)
(121,886)(122,890)(123,889)(124,888)(125,887)(126,896)(127,900)(128,899)
(129,898)(130,897)(131,891)(132,895)(133,894)(134,893)(135,892)(136,871)
(137,875)(138,874)(139,873)(140,872)(141,881)(142,885)(143,884)(144,883)
(145,882)(146,876)(147,880)(148,879)(149,878)(150,877)(151,856)(152,860)
(153,859)(154,858)(155,857)(156,866)(157,870)(158,869)(159,868)(160,867)
(161,861)(162,865)(163,864)(164,863)(165,862)(166,841)(167,845)(168,844)
(169,843)(170,842)(171,851)(172,855)(173,854)(174,853)(175,852)(176,846)
(177,850)(178,849)(179,848)(180,847)(181,946)(182,950)(183,949)(184,948)
(185,947)(186,956)(187,960)(188,959)(189,958)(190,957)(191,951)(192,955)
(193,954)(194,953)(195,952)(196,931)(197,935)(198,934)(199,933)(200,932)
(201,941)(202,945)(203,944)(204,943)(205,942)(206,936)(207,940)(208,939)
(209,938)(210,937)(211,916)(212,920)(213,919)(214,918)(215,917)(216,926)
(217,930)(218,929)(219,928)(220,927)(221,921)(222,925)(223,924)(224,923)
(225,922)(226,901)(227,905)(228,904)(229,903)(230,902)(231,911)(232,915)
(233,914)(234,913)(235,912)(236,906)(237,910)(238,909)(239,908)(240,907)
(241,481)(242,485)(243,484)(244,483)(245,482)(246,491)(247,495)(248,494)
(249,493)(250,492)(251,486)(252,490)(253,489)(254,488)(255,487)(256,496)
(257,500)(258,499)(259,498)(260,497)(261,506)(262,510)(263,509)(264,508)
(265,507)(266,501)(267,505)(268,504)(269,503)(270,502)(271,511)(272,515)
(273,514)(274,513)(275,512)(276,521)(277,525)(278,524)(279,523)(280,522)
(281,516)(282,520)(283,519)(284,518)(285,517)(286,526)(287,530)(288,529)
(289,528)(290,527)(291,536)(292,540)(293,539)(294,538)(295,537)(296,531)
(297,535)(298,534)(299,533)(300,532)(301,541)(302,545)(303,544)(304,543)
(305,542)(306,551)(307,555)(308,554)(309,553)(310,552)(311,546)(312,550)
(313,549)(314,548)(315,547)(316,556)(317,560)(318,559)(319,558)(320,557)
(321,566)(322,570)(323,569)(324,568)(325,567)(326,561)(327,565)(328,564)
(329,563)(330,562)(331,571)(332,575)(333,574)(334,573)(335,572)(336,581)
(337,585)(338,584)(339,583)(340,582)(341,576)(342,580)(343,579)(344,578)
(345,577)(346,586)(347,590)(348,589)(349,588)(350,587)(351,596)(352,600)
(353,599)(354,598)(355,597)(356,591)(357,595)(358,594)(359,593)(360,592)
(361,646)(362,650)(363,649)(364,648)(365,647)(366,656)(367,660)(368,659)
(369,658)(370,657)(371,651)(372,655)(373,654)(374,653)(375,652)(376,631)
(377,635)(378,634)(379,633)(380,632)(381,641)(382,645)(383,644)(384,643)
(385,642)(386,636)(387,640)(388,639)(389,638)(390,637)(391,616)(392,620)
(393,619)(394,618)(395,617)(396,626)(397,630)(398,629)(399,628)(400,627)
(401,621)(402,625)(403,624)(404,623)(405,622)(406,601)(407,605)(408,604)
(409,603)(410,602)(411,611)(412,615)(413,614)(414,613)(415,612)(416,606)
(417,610)(418,609)(419,608)(420,607)(421,706)(422,710)(423,709)(424,708)
(425,707)(426,716)(427,720)(428,719)(429,718)(430,717)(431,711)(432,715)
(433,714)(434,713)(435,712)(436,691)(437,695)(438,694)(439,693)(440,692)
(441,701)(442,705)(443,704)(444,703)(445,702)(446,696)(447,700)(448,699)
(449,698)(450,697)(451,676)(452,680)(453,679)(454,678)(455,677)(456,686)
(457,690)(458,689)(459,688)(460,687)(461,681)(462,685)(463,684)(464,683)
(465,682)(466,661)(467,665)(468,664)(469,663)(470,662)(471,671)(472,675)
(473,674)(474,673)(475,672)(476,666)(477,670)(478,669)(479,668)(480,667);;
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, 82)( 62, 81)( 63, 85)( 64, 84)
( 65, 83)( 66, 77)( 67, 76)( 68, 80)( 69, 79)( 70, 78)( 71, 87)( 72, 86)
( 73, 90)( 74, 89)( 75, 88)( 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)
(181,232)(182,231)(183,235)(184,234)(185,233)(186,227)(187,226)(188,230)
(189,229)(190,228)(191,237)(192,236)(193,240)(194,239)(195,238)(196,217)
(197,216)(198,220)(199,219)(200,218)(201,212)(202,211)(203,215)(204,214)
(205,213)(206,222)(207,221)(208,225)(209,224)(210,223)(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)(541,682)(542,681)(543,685)(544,684)(545,683)(546,677)
(547,676)(548,680)(549,679)(550,678)(551,687)(552,686)(553,690)(554,689)
(555,688)(556,667)(557,666)(558,670)(559,669)(560,668)(561,662)(562,661)
(563,665)(564,664)(565,663)(566,672)(567,671)(568,675)(569,674)(570,673)
(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)(721,922)(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 := (  1,241)(  2,242)(  3,243)(  4,244)(  5,245)(  6,246)(  7,247)(  8,248)
(  9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,256)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)( 24,264)
( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)( 32,272)
( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)( 40,280)
( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)( 48,288)
( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)( 56,296)
( 57,297)( 58,298)( 59,299)( 60,300)( 61,316)( 62,317)( 63,318)( 64,319)
( 65,320)( 66,321)( 67,322)( 68,323)( 69,324)( 70,325)( 71,326)( 72,327)
( 73,328)( 74,329)( 75,330)( 76,301)( 77,302)( 78,303)( 79,304)( 80,305)
( 81,306)( 82,307)( 83,308)( 84,309)( 85,310)( 86,311)( 87,312)( 88,313)
( 89,314)( 90,315)( 91,346)( 92,347)( 93,348)( 94,349)( 95,350)( 96,351)
( 97,352)( 98,353)( 99,354)(100,355)(101,356)(102,357)(103,358)(104,359)
(105,360)(106,331)(107,332)(108,333)(109,334)(110,335)(111,336)(112,337)
(113,338)(114,339)(115,340)(116,341)(117,342)(118,343)(119,344)(120,345)
(121,376)(122,377)(123,378)(124,379)(125,380)(126,381)(127,382)(128,383)
(129,384)(130,385)(131,386)(132,387)(133,388)(134,389)(135,390)(136,361)
(137,362)(138,363)(139,364)(140,365)(141,366)(142,367)(143,368)(144,369)
(145,370)(146,371)(147,372)(148,373)(149,374)(150,375)(151,406)(152,407)
(153,408)(154,409)(155,410)(156,411)(157,412)(158,413)(159,414)(160,415)
(161,416)(162,417)(163,418)(164,419)(165,420)(166,391)(167,392)(168,393)
(169,394)(170,395)(171,396)(172,397)(173,398)(174,399)(175,400)(176,401)
(177,402)(178,403)(179,404)(180,405)(181,421)(182,422)(183,423)(184,424)
(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)(192,432)
(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)(200,440)
(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)(208,448)
(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)(216,456)
(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)(224,464)
(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)(232,472)
(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)(240,480)
(481,721)(482,722)(483,723)(484,724)(485,725)(486,726)(487,727)(488,728)
(489,729)(490,730)(491,731)(492,732)(493,733)(494,734)(495,735)(496,736)
(497,737)(498,738)(499,739)(500,740)(501,741)(502,742)(503,743)(504,744)
(505,745)(506,746)(507,747)(508,748)(509,749)(510,750)(511,751)(512,752)
(513,753)(514,754)(515,755)(516,756)(517,757)(518,758)(519,759)(520,760)
(521,761)(522,762)(523,763)(524,764)(525,765)(526,766)(527,767)(528,768)
(529,769)(530,770)(531,771)(532,772)(533,773)(534,774)(535,775)(536,776)
(537,777)(538,778)(539,779)(540,780)(541,796)(542,797)(543,798)(544,799)
(545,800)(546,801)(547,802)(548,803)(549,804)(550,805)(551,806)(552,807)
(553,808)(554,809)(555,810)(556,781)(557,782)(558,783)(559,784)(560,785)
(561,786)(562,787)(563,788)(564,789)(565,790)(566,791)(567,792)(568,793)
(569,794)(570,795)(571,826)(572,827)(573,828)(574,829)(575,830)(576,831)
(577,832)(578,833)(579,834)(580,835)(581,836)(582,837)(583,838)(584,839)
(585,840)(586,811)(587,812)(588,813)(589,814)(590,815)(591,816)(592,817)
(593,818)(594,819)(595,820)(596,821)(597,822)(598,823)(599,824)(600,825)
(601,856)(602,857)(603,858)(604,859)(605,860)(606,861)(607,862)(608,863)
(609,864)(610,865)(611,866)(612,867)(613,868)(614,869)(615,870)(616,841)
(617,842)(618,843)(619,844)(620,845)(621,846)(622,847)(623,848)(624,849)
(625,850)(626,851)(627,852)(628,853)(629,854)(630,855)(631,886)(632,887)
(633,888)(634,889)(635,890)(636,891)(637,892)(638,893)(639,894)(640,895)
(641,896)(642,897)(643,898)(644,899)(645,900)(646,871)(647,872)(648,873)
(649,874)(650,875)(651,876)(652,877)(653,878)(654,879)(655,880)(656,881)
(657,882)(658,883)(659,884)(660,885)(661,901)(662,902)(663,903)(664,904)
(665,905)(666,906)(667,907)(668,908)(669,909)(670,910)(671,911)(672,912)
(673,913)(674,914)(675,915)(676,916)(677,917)(678,918)(679,919)(680,920)
(681,921)(682,922)(683,923)(684,924)(685,925)(686,926)(687,927)(688,928)
(689,929)(690,930)(691,931)(692,932)(693,933)(694,934)(695,935)(696,936)
(697,937)(698,938)(699,939)(700,940)(701,941)(702,942)(703,943)(704,944)
(705,945)(706,946)(707,947)(708,948)(709,949)(710,950)(711,951)(712,952)
(713,953)(714,954)(715,955)(716,956)(717,957)(718,958)(719,959)(720,960);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)!(  1,721)(  2,725)(  3,724)(  4,723)(  5,722)(  6,731)(  7,735)
(  8,734)(  9,733)( 10,732)( 11,726)( 12,730)( 13,729)( 14,728)( 15,727)
( 16,736)( 17,740)( 18,739)( 19,738)( 20,737)( 21,746)( 22,750)( 23,749)
( 24,748)( 25,747)( 26,741)( 27,745)( 28,744)( 29,743)( 30,742)( 31,751)
( 32,755)( 33,754)( 34,753)( 35,752)( 36,761)( 37,765)( 38,764)( 39,763)
( 40,762)( 41,756)( 42,760)( 43,759)( 44,758)( 45,757)( 46,766)( 47,770)
( 48,769)( 49,768)( 50,767)( 51,776)( 52,780)( 53,779)( 54,778)( 55,777)
( 56,771)( 57,775)( 58,774)( 59,773)( 60,772)( 61,781)( 62,785)( 63,784)
( 64,783)( 65,782)( 66,791)( 67,795)( 68,794)( 69,793)( 70,792)( 71,786)
( 72,790)( 73,789)( 74,788)( 75,787)( 76,796)( 77,800)( 78,799)( 79,798)
( 80,797)( 81,806)( 82,810)( 83,809)( 84,808)( 85,807)( 86,801)( 87,805)
( 88,804)( 89,803)( 90,802)( 91,811)( 92,815)( 93,814)( 94,813)( 95,812)
( 96,821)( 97,825)( 98,824)( 99,823)(100,822)(101,816)(102,820)(103,819)
(104,818)(105,817)(106,826)(107,830)(108,829)(109,828)(110,827)(111,836)
(112,840)(113,839)(114,838)(115,837)(116,831)(117,835)(118,834)(119,833)
(120,832)(121,886)(122,890)(123,889)(124,888)(125,887)(126,896)(127,900)
(128,899)(129,898)(130,897)(131,891)(132,895)(133,894)(134,893)(135,892)
(136,871)(137,875)(138,874)(139,873)(140,872)(141,881)(142,885)(143,884)
(144,883)(145,882)(146,876)(147,880)(148,879)(149,878)(150,877)(151,856)
(152,860)(153,859)(154,858)(155,857)(156,866)(157,870)(158,869)(159,868)
(160,867)(161,861)(162,865)(163,864)(164,863)(165,862)(166,841)(167,845)
(168,844)(169,843)(170,842)(171,851)(172,855)(173,854)(174,853)(175,852)
(176,846)(177,850)(178,849)(179,848)(180,847)(181,946)(182,950)(183,949)
(184,948)(185,947)(186,956)(187,960)(188,959)(189,958)(190,957)(191,951)
(192,955)(193,954)(194,953)(195,952)(196,931)(197,935)(198,934)(199,933)
(200,932)(201,941)(202,945)(203,944)(204,943)(205,942)(206,936)(207,940)
(208,939)(209,938)(210,937)(211,916)(212,920)(213,919)(214,918)(215,917)
(216,926)(217,930)(218,929)(219,928)(220,927)(221,921)(222,925)(223,924)
(224,923)(225,922)(226,901)(227,905)(228,904)(229,903)(230,902)(231,911)
(232,915)(233,914)(234,913)(235,912)(236,906)(237,910)(238,909)(239,908)
(240,907)(241,481)(242,485)(243,484)(244,483)(245,482)(246,491)(247,495)
(248,494)(249,493)(250,492)(251,486)(252,490)(253,489)(254,488)(255,487)
(256,496)(257,500)(258,499)(259,498)(260,497)(261,506)(262,510)(263,509)
(264,508)(265,507)(266,501)(267,505)(268,504)(269,503)(270,502)(271,511)
(272,515)(273,514)(274,513)(275,512)(276,521)(277,525)(278,524)(279,523)
(280,522)(281,516)(282,520)(283,519)(284,518)(285,517)(286,526)(287,530)
(288,529)(289,528)(290,527)(291,536)(292,540)(293,539)(294,538)(295,537)
(296,531)(297,535)(298,534)(299,533)(300,532)(301,541)(302,545)(303,544)
(304,543)(305,542)(306,551)(307,555)(308,554)(309,553)(310,552)(311,546)
(312,550)(313,549)(314,548)(315,547)(316,556)(317,560)(318,559)(319,558)
(320,557)(321,566)(322,570)(323,569)(324,568)(325,567)(326,561)(327,565)
(328,564)(329,563)(330,562)(331,571)(332,575)(333,574)(334,573)(335,572)
(336,581)(337,585)(338,584)(339,583)(340,582)(341,576)(342,580)(343,579)
(344,578)(345,577)(346,586)(347,590)(348,589)(349,588)(350,587)(351,596)
(352,600)(353,599)(354,598)(355,597)(356,591)(357,595)(358,594)(359,593)
(360,592)(361,646)(362,650)(363,649)(364,648)(365,647)(366,656)(367,660)
(368,659)(369,658)(370,657)(371,651)(372,655)(373,654)(374,653)(375,652)
(376,631)(377,635)(378,634)(379,633)(380,632)(381,641)(382,645)(383,644)
(384,643)(385,642)(386,636)(387,640)(388,639)(389,638)(390,637)(391,616)
(392,620)(393,619)(394,618)(395,617)(396,626)(397,630)(398,629)(399,628)
(400,627)(401,621)(402,625)(403,624)(404,623)(405,622)(406,601)(407,605)
(408,604)(409,603)(410,602)(411,611)(412,615)(413,614)(414,613)(415,612)
(416,606)(417,610)(418,609)(419,608)(420,607)(421,706)(422,710)(423,709)
(424,708)(425,707)(426,716)(427,720)(428,719)(429,718)(430,717)(431,711)
(432,715)(433,714)(434,713)(435,712)(436,691)(437,695)(438,694)(439,693)
(440,692)(441,701)(442,705)(443,704)(444,703)(445,702)(446,696)(447,700)
(448,699)(449,698)(450,697)(451,676)(452,680)(453,679)(454,678)(455,677)
(456,686)(457,690)(458,689)(459,688)(460,687)(461,681)(462,685)(463,684)
(464,683)(465,682)(466,661)(467,665)(468,664)(469,663)(470,662)(471,671)
(472,675)(473,674)(474,673)(475,672)(476,666)(477,670)(478,669)(479,668)
(480,667);
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, 82)( 62, 81)( 63, 85)
( 64, 84)( 65, 83)( 66, 77)( 67, 76)( 68, 80)( 69, 79)( 70, 78)( 71, 87)
( 72, 86)( 73, 90)( 74, 89)( 75, 88)( 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)(181,232)(182,231)(183,235)(184,234)(185,233)(186,227)(187,226)
(188,230)(189,229)(190,228)(191,237)(192,236)(193,240)(194,239)(195,238)
(196,217)(197,216)(198,220)(199,219)(200,218)(201,212)(202,211)(203,215)
(204,214)(205,213)(206,222)(207,221)(208,225)(209,224)(210,223)(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)(541,682)(542,681)(543,685)(544,684)(545,683)
(546,677)(547,676)(548,680)(549,679)(550,678)(551,687)(552,686)(553,690)
(554,689)(555,688)(556,667)(557,666)(558,670)(559,669)(560,668)(561,662)
(562,661)(563,665)(564,664)(565,663)(566,672)(567,671)(568,675)(569,674)
(570,673)(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)(721,922)
(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)!(  1,241)(  2,242)(  3,243)(  4,244)(  5,245)(  6,246)(  7,247)
(  8,248)(  9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)
( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)
( 24,264)( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)
( 32,272)( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)
( 40,280)( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)
( 48,288)( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)
( 56,296)( 57,297)( 58,298)( 59,299)( 60,300)( 61,316)( 62,317)( 63,318)
( 64,319)( 65,320)( 66,321)( 67,322)( 68,323)( 69,324)( 70,325)( 71,326)
( 72,327)( 73,328)( 74,329)( 75,330)( 76,301)( 77,302)( 78,303)( 79,304)
( 80,305)( 81,306)( 82,307)( 83,308)( 84,309)( 85,310)( 86,311)( 87,312)
( 88,313)( 89,314)( 90,315)( 91,346)( 92,347)( 93,348)( 94,349)( 95,350)
( 96,351)( 97,352)( 98,353)( 99,354)(100,355)(101,356)(102,357)(103,358)
(104,359)(105,360)(106,331)(107,332)(108,333)(109,334)(110,335)(111,336)
(112,337)(113,338)(114,339)(115,340)(116,341)(117,342)(118,343)(119,344)
(120,345)(121,376)(122,377)(123,378)(124,379)(125,380)(126,381)(127,382)
(128,383)(129,384)(130,385)(131,386)(132,387)(133,388)(134,389)(135,390)
(136,361)(137,362)(138,363)(139,364)(140,365)(141,366)(142,367)(143,368)
(144,369)(145,370)(146,371)(147,372)(148,373)(149,374)(150,375)(151,406)
(152,407)(153,408)(154,409)(155,410)(156,411)(157,412)(158,413)(159,414)
(160,415)(161,416)(162,417)(163,418)(164,419)(165,420)(166,391)(167,392)
(168,393)(169,394)(170,395)(171,396)(172,397)(173,398)(174,399)(175,400)
(176,401)(177,402)(178,403)(179,404)(180,405)(181,421)(182,422)(183,423)
(184,424)(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)
(192,432)(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)
(200,440)(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)
(208,448)(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)
(216,456)(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)
(224,464)(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)
(232,472)(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)
(240,480)(481,721)(482,722)(483,723)(484,724)(485,725)(486,726)(487,727)
(488,728)(489,729)(490,730)(491,731)(492,732)(493,733)(494,734)(495,735)
(496,736)(497,737)(498,738)(499,739)(500,740)(501,741)(502,742)(503,743)
(504,744)(505,745)(506,746)(507,747)(508,748)(509,749)(510,750)(511,751)
(512,752)(513,753)(514,754)(515,755)(516,756)(517,757)(518,758)(519,759)
(520,760)(521,761)(522,762)(523,763)(524,764)(525,765)(526,766)(527,767)
(528,768)(529,769)(530,770)(531,771)(532,772)(533,773)(534,774)(535,775)
(536,776)(537,777)(538,778)(539,779)(540,780)(541,796)(542,797)(543,798)
(544,799)(545,800)(546,801)(547,802)(548,803)(549,804)(550,805)(551,806)
(552,807)(553,808)(554,809)(555,810)(556,781)(557,782)(558,783)(559,784)
(560,785)(561,786)(562,787)(563,788)(564,789)(565,790)(566,791)(567,792)
(568,793)(569,794)(570,795)(571,826)(572,827)(573,828)(574,829)(575,830)
(576,831)(577,832)(578,833)(579,834)(580,835)(581,836)(582,837)(583,838)
(584,839)(585,840)(586,811)(587,812)(588,813)(589,814)(590,815)(591,816)
(592,817)(593,818)(594,819)(595,820)(596,821)(597,822)(598,823)(599,824)
(600,825)(601,856)(602,857)(603,858)(604,859)(605,860)(606,861)(607,862)
(608,863)(609,864)(610,865)(611,866)(612,867)(613,868)(614,869)(615,870)
(616,841)(617,842)(618,843)(619,844)(620,845)(621,846)(622,847)(623,848)
(624,849)(625,850)(626,851)(627,852)(628,853)(629,854)(630,855)(631,886)
(632,887)(633,888)(634,889)(635,890)(636,891)(637,892)(638,893)(639,894)
(640,895)(641,896)(642,897)(643,898)(644,899)(645,900)(646,871)(647,872)
(648,873)(649,874)(650,875)(651,876)(652,877)(653,878)(654,879)(655,880)
(656,881)(657,882)(658,883)(659,884)(660,885)(661,901)(662,902)(663,903)
(664,904)(665,905)(666,906)(667,907)(668,908)(669,909)(670,910)(671,911)
(672,912)(673,913)(674,914)(675,915)(676,916)(677,917)(678,918)(679,919)
(680,920)(681,921)(682,922)(683,923)(684,924)(685,925)(686,926)(687,927)
(688,928)(689,929)(690,930)(691,931)(692,932)(693,933)(694,934)(695,935)
(696,936)(697,937)(698,938)(699,939)(700,940)(701,941)(702,942)(703,943)
(704,944)(705,945)(706,946)(707,947)(708,948)(709,949)(710,950)(711,951)
(712,952)(713,953)(714,954)(715,955)(716,956)(717,957)(718,958)(719,959)
(720,960);
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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