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Polytope of Type {30,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,8}*1920a
if this polytope has a name.
Group : SmallGroup(1920,237609)
Rank : 3
Schlafli Type : {30,8}
Number of vertices, edges, etc : 120, 480, 32
Order of s0s1s2 : 60
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {15,8}*960a
   5-fold quotients : {6,8}*384a
   8-fold quotients : {15,4}*240
   10-fold quotients : {3,8}*192
   16-fold quotients : {15,4}*120
   32-fold quotients : {15,2}*60
   40-fold quotients : {3,4}*48
   80-fold quotients : {3,4}*24
   96-fold quotients : {5,2}*20
   160-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  3,  4)(  5,  6)(  9, 15)( 10, 16)( 11, 14)( 12, 13)( 17, 28)( 18, 27)
( 19, 25)( 20, 26)( 21, 31)( 22, 32)( 23, 30)( 24, 29)( 33,129)( 34,130)
( 35,132)( 36,131)( 37,134)( 38,133)( 39,135)( 40,136)( 41,143)( 42,144)
( 43,142)( 44,141)( 45,140)( 46,139)( 47,137)( 48,138)( 49,156)( 50,155)
( 51,153)( 52,154)( 53,159)( 54,160)( 55,158)( 56,157)( 57,147)( 58,148)
( 59,146)( 60,145)( 61,152)( 62,151)( 63,149)( 64,150)( 65, 97)( 66, 98)
( 67,100)( 68, 99)( 69,102)( 70,101)( 71,103)( 72,104)( 73,111)( 74,112)
( 75,110)( 76,109)( 77,108)( 78,107)( 79,105)( 80,106)( 81,124)( 82,123)
( 83,121)( 84,122)( 85,127)( 86,128)( 87,126)( 88,125)( 89,115)( 90,116)
( 91,114)( 92,113)( 93,120)( 94,119)( 95,117)( 96,118)(161,321)(162,322)
(163,324)(164,323)(165,326)(166,325)(167,327)(168,328)(169,335)(170,336)
(171,334)(172,333)(173,332)(174,331)(175,329)(176,330)(177,348)(178,347)
(179,345)(180,346)(181,351)(182,352)(183,350)(184,349)(185,339)(186,340)
(187,338)(188,337)(189,344)(190,343)(191,341)(192,342)(193,449)(194,450)
(195,452)(196,451)(197,454)(198,453)(199,455)(200,456)(201,463)(202,464)
(203,462)(204,461)(205,460)(206,459)(207,457)(208,458)(209,476)(210,475)
(211,473)(212,474)(213,479)(214,480)(215,478)(216,477)(217,467)(218,468)
(219,466)(220,465)(221,472)(222,471)(223,469)(224,470)(225,417)(226,418)
(227,420)(228,419)(229,422)(230,421)(231,423)(232,424)(233,431)(234,432)
(235,430)(236,429)(237,428)(238,427)(239,425)(240,426)(241,444)(242,443)
(243,441)(244,442)(245,447)(246,448)(247,446)(248,445)(249,435)(250,436)
(251,434)(252,433)(253,440)(254,439)(255,437)(256,438)(257,385)(258,386)
(259,388)(260,387)(261,390)(262,389)(263,391)(264,392)(265,399)(266,400)
(267,398)(268,397)(269,396)(270,395)(271,393)(272,394)(273,412)(274,411)
(275,409)(276,410)(277,415)(278,416)(279,414)(280,413)(281,403)(282,404)
(283,402)(284,401)(285,408)(286,407)(287,405)(288,406)(289,353)(290,354)
(291,356)(292,355)(293,358)(294,357)(295,359)(296,360)(297,367)(298,368)
(299,366)(300,365)(301,364)(302,363)(303,361)(304,362)(305,380)(306,379)
(307,377)(308,378)(309,383)(310,384)(311,382)(312,381)(313,371)(314,372)
(315,370)(316,369)(317,376)(318,375)(319,373)(320,374)(481,487)(482,488)
(483,486)(484,485)(491,492)(493,494)(497,510)(498,509)(499,511)(500,512)
(501,505)(502,506)(503,508)(504,507)(513,615)(514,616)(515,614)(516,613)
(517,612)(518,611)(519,609)(520,610)(521,617)(522,618)(523,620)(524,619)
(525,622)(526,621)(527,623)(528,624)(529,638)(530,637)(531,639)(532,640)
(533,633)(534,634)(535,636)(536,635)(537,629)(538,630)(539,632)(540,631)
(541,626)(542,625)(543,627)(544,628)(545,583)(546,584)(547,582)(548,581)
(549,580)(550,579)(551,577)(552,578)(553,585)(554,586)(555,588)(556,587)
(557,590)(558,589)(559,591)(560,592)(561,606)(562,605)(563,607)(564,608)
(565,601)(566,602)(567,604)(568,603)(569,597)(570,598)(571,600)(572,599)
(573,594)(574,593)(575,595)(576,596)(641,807)(642,808)(643,806)(644,805)
(645,804)(646,803)(647,801)(648,802)(649,809)(650,810)(651,812)(652,811)
(653,814)(654,813)(655,815)(656,816)(657,830)(658,829)(659,831)(660,832)
(661,825)(662,826)(663,828)(664,827)(665,821)(666,822)(667,824)(668,823)
(669,818)(670,817)(671,819)(672,820)(673,935)(674,936)(675,934)(676,933)
(677,932)(678,931)(679,929)(680,930)(681,937)(682,938)(683,940)(684,939)
(685,942)(686,941)(687,943)(688,944)(689,958)(690,957)(691,959)(692,960)
(693,953)(694,954)(695,956)(696,955)(697,949)(698,950)(699,952)(700,951)
(701,946)(702,945)(703,947)(704,948)(705,903)(706,904)(707,902)(708,901)
(709,900)(710,899)(711,897)(712,898)(713,905)(714,906)(715,908)(716,907)
(717,910)(718,909)(719,911)(720,912)(721,926)(722,925)(723,927)(724,928)
(725,921)(726,922)(727,924)(728,923)(729,917)(730,918)(731,920)(732,919)
(733,914)(734,913)(735,915)(736,916)(737,871)(738,872)(739,870)(740,869)
(741,868)(742,867)(743,865)(744,866)(745,873)(746,874)(747,876)(748,875)
(749,878)(750,877)(751,879)(752,880)(753,894)(754,893)(755,895)(756,896)
(757,889)(758,890)(759,892)(760,891)(761,885)(762,886)(763,888)(764,887)
(765,882)(766,881)(767,883)(768,884)(769,839)(770,840)(771,838)(772,837)
(773,836)(774,835)(775,833)(776,834)(777,841)(778,842)(779,844)(780,843)
(781,846)(782,845)(783,847)(784,848)(785,862)(786,861)(787,863)(788,864)
(789,857)(790,858)(791,860)(792,859)(793,853)(794,854)(795,856)(796,855)
(797,850)(798,849)(799,851)(800,852);;
s1 := (  1,209)(  2,212)(  3,211)(  4,210)(  5,213)(  6,216)(  7,215)(  8,214)
(  9,201)( 10,204)( 11,203)( 12,202)( 13,205)( 14,208)( 15,207)( 16,206)
( 17,193)( 18,196)( 19,195)( 20,194)( 21,197)( 22,200)( 23,199)( 24,198)
( 25,221)( 26,224)( 27,223)( 28,222)( 29,217)( 30,220)( 31,219)( 32,218)
( 33,177)( 34,180)( 35,179)( 36,178)( 37,181)( 38,184)( 39,183)( 40,182)
( 41,169)( 42,172)( 43,171)( 44,170)( 45,173)( 46,176)( 47,175)( 48,174)
( 49,161)( 50,164)( 51,163)( 52,162)( 53,165)( 54,168)( 55,167)( 56,166)
( 57,189)( 58,192)( 59,191)( 60,190)( 61,185)( 62,188)( 63,187)( 64,186)
( 65,305)( 66,308)( 67,307)( 68,306)( 69,309)( 70,312)( 71,311)( 72,310)
( 73,297)( 74,300)( 75,299)( 76,298)( 77,301)( 78,304)( 79,303)( 80,302)
( 81,289)( 82,292)( 83,291)( 84,290)( 85,293)( 86,296)( 87,295)( 88,294)
( 89,317)( 90,320)( 91,319)( 92,318)( 93,313)( 94,316)( 95,315)( 96,314)
( 97,273)( 98,276)( 99,275)(100,274)(101,277)(102,280)(103,279)(104,278)
(105,265)(106,268)(107,267)(108,266)(109,269)(110,272)(111,271)(112,270)
(113,257)(114,260)(115,259)(116,258)(117,261)(118,264)(119,263)(120,262)
(121,285)(122,288)(123,287)(124,286)(125,281)(126,284)(127,283)(128,282)
(129,241)(130,244)(131,243)(132,242)(133,245)(134,248)(135,247)(136,246)
(137,233)(138,236)(139,235)(140,234)(141,237)(142,240)(143,239)(144,238)
(145,225)(146,228)(147,227)(148,226)(149,229)(150,232)(151,231)(152,230)
(153,253)(154,256)(155,255)(156,254)(157,249)(158,252)(159,251)(160,250)
(321,369)(322,372)(323,371)(324,370)(325,373)(326,376)(327,375)(328,374)
(329,361)(330,364)(331,363)(332,362)(333,365)(334,368)(335,367)(336,366)
(337,353)(338,356)(339,355)(340,354)(341,357)(342,360)(343,359)(344,358)
(345,381)(346,384)(347,383)(348,382)(349,377)(350,380)(351,379)(352,378)
(385,465)(386,468)(387,467)(388,466)(389,469)(390,472)(391,471)(392,470)
(393,457)(394,460)(395,459)(396,458)(397,461)(398,464)(399,463)(400,462)
(401,449)(402,452)(403,451)(404,450)(405,453)(406,456)(407,455)(408,454)
(409,477)(410,480)(411,479)(412,478)(413,473)(414,476)(415,475)(416,474)
(417,433)(418,436)(419,435)(420,434)(421,437)(422,440)(423,439)(424,438)
(426,428)(430,432)(441,445)(442,448)(443,447)(444,446)(481,695)(482,694)
(483,693)(484,696)(485,691)(486,690)(487,689)(488,692)(489,687)(490,686)
(491,685)(492,688)(493,683)(494,682)(495,681)(496,684)(497,679)(498,678)
(499,677)(500,680)(501,675)(502,674)(503,673)(504,676)(505,699)(506,698)
(507,697)(508,700)(509,703)(510,702)(511,701)(512,704)(513,663)(514,662)
(515,661)(516,664)(517,659)(518,658)(519,657)(520,660)(521,655)(522,654)
(523,653)(524,656)(525,651)(526,650)(527,649)(528,652)(529,647)(530,646)
(531,645)(532,648)(533,643)(534,642)(535,641)(536,644)(537,667)(538,666)
(539,665)(540,668)(541,671)(542,670)(543,669)(544,672)(545,791)(546,790)
(547,789)(548,792)(549,787)(550,786)(551,785)(552,788)(553,783)(554,782)
(555,781)(556,784)(557,779)(558,778)(559,777)(560,780)(561,775)(562,774)
(563,773)(564,776)(565,771)(566,770)(567,769)(568,772)(569,795)(570,794)
(571,793)(572,796)(573,799)(574,798)(575,797)(576,800)(577,759)(578,758)
(579,757)(580,760)(581,755)(582,754)(583,753)(584,756)(585,751)(586,750)
(587,749)(588,752)(589,747)(590,746)(591,745)(592,748)(593,743)(594,742)
(595,741)(596,744)(597,739)(598,738)(599,737)(600,740)(601,763)(602,762)
(603,761)(604,764)(605,767)(606,766)(607,765)(608,768)(609,727)(610,726)
(611,725)(612,728)(613,723)(614,722)(615,721)(616,724)(617,719)(618,718)
(619,717)(620,720)(621,715)(622,714)(623,713)(624,716)(625,711)(626,710)
(627,709)(628,712)(629,707)(630,706)(631,705)(632,708)(633,731)(634,730)
(635,729)(636,732)(637,735)(638,734)(639,733)(640,736)(801,855)(802,854)
(803,853)(804,856)(805,851)(806,850)(807,849)(808,852)(809,847)(810,846)
(811,845)(812,848)(813,843)(814,842)(815,841)(816,844)(817,839)(818,838)
(819,837)(820,840)(821,835)(822,834)(823,833)(824,836)(825,859)(826,858)
(827,857)(828,860)(829,863)(830,862)(831,861)(832,864)(865,951)(866,950)
(867,949)(868,952)(869,947)(870,946)(871,945)(872,948)(873,943)(874,942)
(875,941)(876,944)(877,939)(878,938)(879,937)(880,940)(881,935)(882,934)
(883,933)(884,936)(885,931)(886,930)(887,929)(888,932)(889,955)(890,954)
(891,953)(892,956)(893,959)(894,958)(895,957)(896,960)(897,919)(898,918)
(899,917)(900,920)(901,915)(902,914)(903,913)(904,916)(905,911)(906,910)
(907,909)(908,912)(921,923)(925,927);;
s2 := (  1,489)(  2,490)(  3,491)(  4,492)(  5,493)(  6,494)(  7,495)(  8,496)
(  9,487)( 10,488)( 11,485)( 12,486)( 13,483)( 14,484)( 15,481)( 16,482)
( 17,507)( 18,508)( 19,505)( 20,506)( 21,511)( 22,512)( 23,509)( 24,510)
( 25,501)( 26,502)( 27,503)( 28,504)( 29,497)( 30,498)( 31,499)( 32,500)
( 33,521)( 34,522)( 35,523)( 36,524)( 37,525)( 38,526)( 39,527)( 40,528)
( 41,519)( 42,520)( 43,517)( 44,518)( 45,515)( 46,516)( 47,513)( 48,514)
( 49,539)( 50,540)( 51,537)( 52,538)( 53,543)( 54,544)( 55,541)( 56,542)
( 57,533)( 58,534)( 59,535)( 60,536)( 61,529)( 62,530)( 63,531)( 64,532)
( 65,553)( 66,554)( 67,555)( 68,556)( 69,557)( 70,558)( 71,559)( 72,560)
( 73,551)( 74,552)( 75,549)( 76,550)( 77,547)( 78,548)( 79,545)( 80,546)
( 81,571)( 82,572)( 83,569)( 84,570)( 85,575)( 86,576)( 87,573)( 88,574)
( 89,565)( 90,566)( 91,567)( 92,568)( 93,561)( 94,562)( 95,563)( 96,564)
( 97,585)( 98,586)( 99,587)(100,588)(101,589)(102,590)(103,591)(104,592)
(105,583)(106,584)(107,581)(108,582)(109,579)(110,580)(111,577)(112,578)
(113,603)(114,604)(115,601)(116,602)(117,607)(118,608)(119,605)(120,606)
(121,597)(122,598)(123,599)(124,600)(125,593)(126,594)(127,595)(128,596)
(129,617)(130,618)(131,619)(132,620)(133,621)(134,622)(135,623)(136,624)
(137,615)(138,616)(139,613)(140,614)(141,611)(142,612)(143,609)(144,610)
(145,635)(146,636)(147,633)(148,634)(149,639)(150,640)(151,637)(152,638)
(153,629)(154,630)(155,631)(156,632)(157,625)(158,626)(159,627)(160,628)
(161,649)(162,650)(163,651)(164,652)(165,653)(166,654)(167,655)(168,656)
(169,647)(170,648)(171,645)(172,646)(173,643)(174,644)(175,641)(176,642)
(177,667)(178,668)(179,665)(180,666)(181,671)(182,672)(183,669)(184,670)
(185,661)(186,662)(187,663)(188,664)(189,657)(190,658)(191,659)(192,660)
(193,681)(194,682)(195,683)(196,684)(197,685)(198,686)(199,687)(200,688)
(201,679)(202,680)(203,677)(204,678)(205,675)(206,676)(207,673)(208,674)
(209,699)(210,700)(211,697)(212,698)(213,703)(214,704)(215,701)(216,702)
(217,693)(218,694)(219,695)(220,696)(221,689)(222,690)(223,691)(224,692)
(225,713)(226,714)(227,715)(228,716)(229,717)(230,718)(231,719)(232,720)
(233,711)(234,712)(235,709)(236,710)(237,707)(238,708)(239,705)(240,706)
(241,731)(242,732)(243,729)(244,730)(245,735)(246,736)(247,733)(248,734)
(249,725)(250,726)(251,727)(252,728)(253,721)(254,722)(255,723)(256,724)
(257,745)(258,746)(259,747)(260,748)(261,749)(262,750)(263,751)(264,752)
(265,743)(266,744)(267,741)(268,742)(269,739)(270,740)(271,737)(272,738)
(273,763)(274,764)(275,761)(276,762)(277,767)(278,768)(279,765)(280,766)
(281,757)(282,758)(283,759)(284,760)(285,753)(286,754)(287,755)(288,756)
(289,777)(290,778)(291,779)(292,780)(293,781)(294,782)(295,783)(296,784)
(297,775)(298,776)(299,773)(300,774)(301,771)(302,772)(303,769)(304,770)
(305,795)(306,796)(307,793)(308,794)(309,799)(310,800)(311,797)(312,798)
(313,789)(314,790)(315,791)(316,792)(317,785)(318,786)(319,787)(320,788)
(321,809)(322,810)(323,811)(324,812)(325,813)(326,814)(327,815)(328,816)
(329,807)(330,808)(331,805)(332,806)(333,803)(334,804)(335,801)(336,802)
(337,827)(338,828)(339,825)(340,826)(341,831)(342,832)(343,829)(344,830)
(345,821)(346,822)(347,823)(348,824)(349,817)(350,818)(351,819)(352,820)
(353,841)(354,842)(355,843)(356,844)(357,845)(358,846)(359,847)(360,848)
(361,839)(362,840)(363,837)(364,838)(365,835)(366,836)(367,833)(368,834)
(369,859)(370,860)(371,857)(372,858)(373,863)(374,864)(375,861)(376,862)
(377,853)(378,854)(379,855)(380,856)(381,849)(382,850)(383,851)(384,852)
(385,873)(386,874)(387,875)(388,876)(389,877)(390,878)(391,879)(392,880)
(393,871)(394,872)(395,869)(396,870)(397,867)(398,868)(399,865)(400,866)
(401,891)(402,892)(403,889)(404,890)(405,895)(406,896)(407,893)(408,894)
(409,885)(410,886)(411,887)(412,888)(413,881)(414,882)(415,883)(416,884)
(417,905)(418,906)(419,907)(420,908)(421,909)(422,910)(423,911)(424,912)
(425,903)(426,904)(427,901)(428,902)(429,899)(430,900)(431,897)(432,898)
(433,923)(434,924)(435,921)(436,922)(437,927)(438,928)(439,925)(440,926)
(441,917)(442,918)(443,919)(444,920)(445,913)(446,914)(447,915)(448,916)
(449,937)(450,938)(451,939)(452,940)(453,941)(454,942)(455,943)(456,944)
(457,935)(458,936)(459,933)(460,934)(461,931)(462,932)(463,929)(464,930)
(465,955)(466,956)(467,953)(468,954)(469,959)(470,960)(471,957)(472,958)
(473,949)(474,950)(475,951)(476,952)(477,945)(478,946)(479,947)(480,948);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1, 
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s2*s1*s0 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(960)!(  3,  4)(  5,  6)(  9, 15)( 10, 16)( 11, 14)( 12, 13)( 17, 28)
( 18, 27)( 19, 25)( 20, 26)( 21, 31)( 22, 32)( 23, 30)( 24, 29)( 33,129)
( 34,130)( 35,132)( 36,131)( 37,134)( 38,133)( 39,135)( 40,136)( 41,143)
( 42,144)( 43,142)( 44,141)( 45,140)( 46,139)( 47,137)( 48,138)( 49,156)
( 50,155)( 51,153)( 52,154)( 53,159)( 54,160)( 55,158)( 56,157)( 57,147)
( 58,148)( 59,146)( 60,145)( 61,152)( 62,151)( 63,149)( 64,150)( 65, 97)
( 66, 98)( 67,100)( 68, 99)( 69,102)( 70,101)( 71,103)( 72,104)( 73,111)
( 74,112)( 75,110)( 76,109)( 77,108)( 78,107)( 79,105)( 80,106)( 81,124)
( 82,123)( 83,121)( 84,122)( 85,127)( 86,128)( 87,126)( 88,125)( 89,115)
( 90,116)( 91,114)( 92,113)( 93,120)( 94,119)( 95,117)( 96,118)(161,321)
(162,322)(163,324)(164,323)(165,326)(166,325)(167,327)(168,328)(169,335)
(170,336)(171,334)(172,333)(173,332)(174,331)(175,329)(176,330)(177,348)
(178,347)(179,345)(180,346)(181,351)(182,352)(183,350)(184,349)(185,339)
(186,340)(187,338)(188,337)(189,344)(190,343)(191,341)(192,342)(193,449)
(194,450)(195,452)(196,451)(197,454)(198,453)(199,455)(200,456)(201,463)
(202,464)(203,462)(204,461)(205,460)(206,459)(207,457)(208,458)(209,476)
(210,475)(211,473)(212,474)(213,479)(214,480)(215,478)(216,477)(217,467)
(218,468)(219,466)(220,465)(221,472)(222,471)(223,469)(224,470)(225,417)
(226,418)(227,420)(228,419)(229,422)(230,421)(231,423)(232,424)(233,431)
(234,432)(235,430)(236,429)(237,428)(238,427)(239,425)(240,426)(241,444)
(242,443)(243,441)(244,442)(245,447)(246,448)(247,446)(248,445)(249,435)
(250,436)(251,434)(252,433)(253,440)(254,439)(255,437)(256,438)(257,385)
(258,386)(259,388)(260,387)(261,390)(262,389)(263,391)(264,392)(265,399)
(266,400)(267,398)(268,397)(269,396)(270,395)(271,393)(272,394)(273,412)
(274,411)(275,409)(276,410)(277,415)(278,416)(279,414)(280,413)(281,403)
(282,404)(283,402)(284,401)(285,408)(286,407)(287,405)(288,406)(289,353)
(290,354)(291,356)(292,355)(293,358)(294,357)(295,359)(296,360)(297,367)
(298,368)(299,366)(300,365)(301,364)(302,363)(303,361)(304,362)(305,380)
(306,379)(307,377)(308,378)(309,383)(310,384)(311,382)(312,381)(313,371)
(314,372)(315,370)(316,369)(317,376)(318,375)(319,373)(320,374)(481,487)
(482,488)(483,486)(484,485)(491,492)(493,494)(497,510)(498,509)(499,511)
(500,512)(501,505)(502,506)(503,508)(504,507)(513,615)(514,616)(515,614)
(516,613)(517,612)(518,611)(519,609)(520,610)(521,617)(522,618)(523,620)
(524,619)(525,622)(526,621)(527,623)(528,624)(529,638)(530,637)(531,639)
(532,640)(533,633)(534,634)(535,636)(536,635)(537,629)(538,630)(539,632)
(540,631)(541,626)(542,625)(543,627)(544,628)(545,583)(546,584)(547,582)
(548,581)(549,580)(550,579)(551,577)(552,578)(553,585)(554,586)(555,588)
(556,587)(557,590)(558,589)(559,591)(560,592)(561,606)(562,605)(563,607)
(564,608)(565,601)(566,602)(567,604)(568,603)(569,597)(570,598)(571,600)
(572,599)(573,594)(574,593)(575,595)(576,596)(641,807)(642,808)(643,806)
(644,805)(645,804)(646,803)(647,801)(648,802)(649,809)(650,810)(651,812)
(652,811)(653,814)(654,813)(655,815)(656,816)(657,830)(658,829)(659,831)
(660,832)(661,825)(662,826)(663,828)(664,827)(665,821)(666,822)(667,824)
(668,823)(669,818)(670,817)(671,819)(672,820)(673,935)(674,936)(675,934)
(676,933)(677,932)(678,931)(679,929)(680,930)(681,937)(682,938)(683,940)
(684,939)(685,942)(686,941)(687,943)(688,944)(689,958)(690,957)(691,959)
(692,960)(693,953)(694,954)(695,956)(696,955)(697,949)(698,950)(699,952)
(700,951)(701,946)(702,945)(703,947)(704,948)(705,903)(706,904)(707,902)
(708,901)(709,900)(710,899)(711,897)(712,898)(713,905)(714,906)(715,908)
(716,907)(717,910)(718,909)(719,911)(720,912)(721,926)(722,925)(723,927)
(724,928)(725,921)(726,922)(727,924)(728,923)(729,917)(730,918)(731,920)
(732,919)(733,914)(734,913)(735,915)(736,916)(737,871)(738,872)(739,870)
(740,869)(741,868)(742,867)(743,865)(744,866)(745,873)(746,874)(747,876)
(748,875)(749,878)(750,877)(751,879)(752,880)(753,894)(754,893)(755,895)
(756,896)(757,889)(758,890)(759,892)(760,891)(761,885)(762,886)(763,888)
(764,887)(765,882)(766,881)(767,883)(768,884)(769,839)(770,840)(771,838)
(772,837)(773,836)(774,835)(775,833)(776,834)(777,841)(778,842)(779,844)
(780,843)(781,846)(782,845)(783,847)(784,848)(785,862)(786,861)(787,863)
(788,864)(789,857)(790,858)(791,860)(792,859)(793,853)(794,854)(795,856)
(796,855)(797,850)(798,849)(799,851)(800,852);
s1 := Sym(960)!(  1,209)(  2,212)(  3,211)(  4,210)(  5,213)(  6,216)(  7,215)
(  8,214)(  9,201)( 10,204)( 11,203)( 12,202)( 13,205)( 14,208)( 15,207)
( 16,206)( 17,193)( 18,196)( 19,195)( 20,194)( 21,197)( 22,200)( 23,199)
( 24,198)( 25,221)( 26,224)( 27,223)( 28,222)( 29,217)( 30,220)( 31,219)
( 32,218)( 33,177)( 34,180)( 35,179)( 36,178)( 37,181)( 38,184)( 39,183)
( 40,182)( 41,169)( 42,172)( 43,171)( 44,170)( 45,173)( 46,176)( 47,175)
( 48,174)( 49,161)( 50,164)( 51,163)( 52,162)( 53,165)( 54,168)( 55,167)
( 56,166)( 57,189)( 58,192)( 59,191)( 60,190)( 61,185)( 62,188)( 63,187)
( 64,186)( 65,305)( 66,308)( 67,307)( 68,306)( 69,309)( 70,312)( 71,311)
( 72,310)( 73,297)( 74,300)( 75,299)( 76,298)( 77,301)( 78,304)( 79,303)
( 80,302)( 81,289)( 82,292)( 83,291)( 84,290)( 85,293)( 86,296)( 87,295)
( 88,294)( 89,317)( 90,320)( 91,319)( 92,318)( 93,313)( 94,316)( 95,315)
( 96,314)( 97,273)( 98,276)( 99,275)(100,274)(101,277)(102,280)(103,279)
(104,278)(105,265)(106,268)(107,267)(108,266)(109,269)(110,272)(111,271)
(112,270)(113,257)(114,260)(115,259)(116,258)(117,261)(118,264)(119,263)
(120,262)(121,285)(122,288)(123,287)(124,286)(125,281)(126,284)(127,283)
(128,282)(129,241)(130,244)(131,243)(132,242)(133,245)(134,248)(135,247)
(136,246)(137,233)(138,236)(139,235)(140,234)(141,237)(142,240)(143,239)
(144,238)(145,225)(146,228)(147,227)(148,226)(149,229)(150,232)(151,231)
(152,230)(153,253)(154,256)(155,255)(156,254)(157,249)(158,252)(159,251)
(160,250)(321,369)(322,372)(323,371)(324,370)(325,373)(326,376)(327,375)
(328,374)(329,361)(330,364)(331,363)(332,362)(333,365)(334,368)(335,367)
(336,366)(337,353)(338,356)(339,355)(340,354)(341,357)(342,360)(343,359)
(344,358)(345,381)(346,384)(347,383)(348,382)(349,377)(350,380)(351,379)
(352,378)(385,465)(386,468)(387,467)(388,466)(389,469)(390,472)(391,471)
(392,470)(393,457)(394,460)(395,459)(396,458)(397,461)(398,464)(399,463)
(400,462)(401,449)(402,452)(403,451)(404,450)(405,453)(406,456)(407,455)
(408,454)(409,477)(410,480)(411,479)(412,478)(413,473)(414,476)(415,475)
(416,474)(417,433)(418,436)(419,435)(420,434)(421,437)(422,440)(423,439)
(424,438)(426,428)(430,432)(441,445)(442,448)(443,447)(444,446)(481,695)
(482,694)(483,693)(484,696)(485,691)(486,690)(487,689)(488,692)(489,687)
(490,686)(491,685)(492,688)(493,683)(494,682)(495,681)(496,684)(497,679)
(498,678)(499,677)(500,680)(501,675)(502,674)(503,673)(504,676)(505,699)
(506,698)(507,697)(508,700)(509,703)(510,702)(511,701)(512,704)(513,663)
(514,662)(515,661)(516,664)(517,659)(518,658)(519,657)(520,660)(521,655)
(522,654)(523,653)(524,656)(525,651)(526,650)(527,649)(528,652)(529,647)
(530,646)(531,645)(532,648)(533,643)(534,642)(535,641)(536,644)(537,667)
(538,666)(539,665)(540,668)(541,671)(542,670)(543,669)(544,672)(545,791)
(546,790)(547,789)(548,792)(549,787)(550,786)(551,785)(552,788)(553,783)
(554,782)(555,781)(556,784)(557,779)(558,778)(559,777)(560,780)(561,775)
(562,774)(563,773)(564,776)(565,771)(566,770)(567,769)(568,772)(569,795)
(570,794)(571,793)(572,796)(573,799)(574,798)(575,797)(576,800)(577,759)
(578,758)(579,757)(580,760)(581,755)(582,754)(583,753)(584,756)(585,751)
(586,750)(587,749)(588,752)(589,747)(590,746)(591,745)(592,748)(593,743)
(594,742)(595,741)(596,744)(597,739)(598,738)(599,737)(600,740)(601,763)
(602,762)(603,761)(604,764)(605,767)(606,766)(607,765)(608,768)(609,727)
(610,726)(611,725)(612,728)(613,723)(614,722)(615,721)(616,724)(617,719)
(618,718)(619,717)(620,720)(621,715)(622,714)(623,713)(624,716)(625,711)
(626,710)(627,709)(628,712)(629,707)(630,706)(631,705)(632,708)(633,731)
(634,730)(635,729)(636,732)(637,735)(638,734)(639,733)(640,736)(801,855)
(802,854)(803,853)(804,856)(805,851)(806,850)(807,849)(808,852)(809,847)
(810,846)(811,845)(812,848)(813,843)(814,842)(815,841)(816,844)(817,839)
(818,838)(819,837)(820,840)(821,835)(822,834)(823,833)(824,836)(825,859)
(826,858)(827,857)(828,860)(829,863)(830,862)(831,861)(832,864)(865,951)
(866,950)(867,949)(868,952)(869,947)(870,946)(871,945)(872,948)(873,943)
(874,942)(875,941)(876,944)(877,939)(878,938)(879,937)(880,940)(881,935)
(882,934)(883,933)(884,936)(885,931)(886,930)(887,929)(888,932)(889,955)
(890,954)(891,953)(892,956)(893,959)(894,958)(895,957)(896,960)(897,919)
(898,918)(899,917)(900,920)(901,915)(902,914)(903,913)(904,916)(905,911)
(906,910)(907,909)(908,912)(921,923)(925,927);
s2 := Sym(960)!(  1,489)(  2,490)(  3,491)(  4,492)(  5,493)(  6,494)(  7,495)
(  8,496)(  9,487)( 10,488)( 11,485)( 12,486)( 13,483)( 14,484)( 15,481)
( 16,482)( 17,507)( 18,508)( 19,505)( 20,506)( 21,511)( 22,512)( 23,509)
( 24,510)( 25,501)( 26,502)( 27,503)( 28,504)( 29,497)( 30,498)( 31,499)
( 32,500)( 33,521)( 34,522)( 35,523)( 36,524)( 37,525)( 38,526)( 39,527)
( 40,528)( 41,519)( 42,520)( 43,517)( 44,518)( 45,515)( 46,516)( 47,513)
( 48,514)( 49,539)( 50,540)( 51,537)( 52,538)( 53,543)( 54,544)( 55,541)
( 56,542)( 57,533)( 58,534)( 59,535)( 60,536)( 61,529)( 62,530)( 63,531)
( 64,532)( 65,553)( 66,554)( 67,555)( 68,556)( 69,557)( 70,558)( 71,559)
( 72,560)( 73,551)( 74,552)( 75,549)( 76,550)( 77,547)( 78,548)( 79,545)
( 80,546)( 81,571)( 82,572)( 83,569)( 84,570)( 85,575)( 86,576)( 87,573)
( 88,574)( 89,565)( 90,566)( 91,567)( 92,568)( 93,561)( 94,562)( 95,563)
( 96,564)( 97,585)( 98,586)( 99,587)(100,588)(101,589)(102,590)(103,591)
(104,592)(105,583)(106,584)(107,581)(108,582)(109,579)(110,580)(111,577)
(112,578)(113,603)(114,604)(115,601)(116,602)(117,607)(118,608)(119,605)
(120,606)(121,597)(122,598)(123,599)(124,600)(125,593)(126,594)(127,595)
(128,596)(129,617)(130,618)(131,619)(132,620)(133,621)(134,622)(135,623)
(136,624)(137,615)(138,616)(139,613)(140,614)(141,611)(142,612)(143,609)
(144,610)(145,635)(146,636)(147,633)(148,634)(149,639)(150,640)(151,637)
(152,638)(153,629)(154,630)(155,631)(156,632)(157,625)(158,626)(159,627)
(160,628)(161,649)(162,650)(163,651)(164,652)(165,653)(166,654)(167,655)
(168,656)(169,647)(170,648)(171,645)(172,646)(173,643)(174,644)(175,641)
(176,642)(177,667)(178,668)(179,665)(180,666)(181,671)(182,672)(183,669)
(184,670)(185,661)(186,662)(187,663)(188,664)(189,657)(190,658)(191,659)
(192,660)(193,681)(194,682)(195,683)(196,684)(197,685)(198,686)(199,687)
(200,688)(201,679)(202,680)(203,677)(204,678)(205,675)(206,676)(207,673)
(208,674)(209,699)(210,700)(211,697)(212,698)(213,703)(214,704)(215,701)
(216,702)(217,693)(218,694)(219,695)(220,696)(221,689)(222,690)(223,691)
(224,692)(225,713)(226,714)(227,715)(228,716)(229,717)(230,718)(231,719)
(232,720)(233,711)(234,712)(235,709)(236,710)(237,707)(238,708)(239,705)
(240,706)(241,731)(242,732)(243,729)(244,730)(245,735)(246,736)(247,733)
(248,734)(249,725)(250,726)(251,727)(252,728)(253,721)(254,722)(255,723)
(256,724)(257,745)(258,746)(259,747)(260,748)(261,749)(262,750)(263,751)
(264,752)(265,743)(266,744)(267,741)(268,742)(269,739)(270,740)(271,737)
(272,738)(273,763)(274,764)(275,761)(276,762)(277,767)(278,768)(279,765)
(280,766)(281,757)(282,758)(283,759)(284,760)(285,753)(286,754)(287,755)
(288,756)(289,777)(290,778)(291,779)(292,780)(293,781)(294,782)(295,783)
(296,784)(297,775)(298,776)(299,773)(300,774)(301,771)(302,772)(303,769)
(304,770)(305,795)(306,796)(307,793)(308,794)(309,799)(310,800)(311,797)
(312,798)(313,789)(314,790)(315,791)(316,792)(317,785)(318,786)(319,787)
(320,788)(321,809)(322,810)(323,811)(324,812)(325,813)(326,814)(327,815)
(328,816)(329,807)(330,808)(331,805)(332,806)(333,803)(334,804)(335,801)
(336,802)(337,827)(338,828)(339,825)(340,826)(341,831)(342,832)(343,829)
(344,830)(345,821)(346,822)(347,823)(348,824)(349,817)(350,818)(351,819)
(352,820)(353,841)(354,842)(355,843)(356,844)(357,845)(358,846)(359,847)
(360,848)(361,839)(362,840)(363,837)(364,838)(365,835)(366,836)(367,833)
(368,834)(369,859)(370,860)(371,857)(372,858)(373,863)(374,864)(375,861)
(376,862)(377,853)(378,854)(379,855)(380,856)(381,849)(382,850)(383,851)
(384,852)(385,873)(386,874)(387,875)(388,876)(389,877)(390,878)(391,879)
(392,880)(393,871)(394,872)(395,869)(396,870)(397,867)(398,868)(399,865)
(400,866)(401,891)(402,892)(403,889)(404,890)(405,895)(406,896)(407,893)
(408,894)(409,885)(410,886)(411,887)(412,888)(413,881)(414,882)(415,883)
(416,884)(417,905)(418,906)(419,907)(420,908)(421,909)(422,910)(423,911)
(424,912)(425,903)(426,904)(427,901)(428,902)(429,899)(430,900)(431,897)
(432,898)(433,923)(434,924)(435,921)(436,922)(437,927)(438,928)(439,925)
(440,926)(441,917)(442,918)(443,919)(444,920)(445,913)(446,914)(447,915)
(448,916)(449,937)(450,938)(451,939)(452,940)(453,941)(454,942)(455,943)
(456,944)(457,935)(458,936)(459,933)(460,934)(461,931)(462,932)(463,929)
(464,930)(465,955)(466,956)(467,953)(468,954)(469,959)(470,960)(471,957)
(472,958)(473,949)(474,950)(475,951)(476,952)(477,945)(478,946)(479,947)
(480,948);
poly := sub<Sym(960)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1, 
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s2*s1*s0 >; 
 
References : None.
to this polytope