Polytope of Type {60,8}

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

References : None.
to this polytope