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Polytope of Type {60,8}

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