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