Polytope of Type {8,60}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,60}*1920c
if this polytope has a name.
Group : SmallGroup(1920,237609)
Rank : 3
Schlafli Type : {8,60}
Number of vertices, edges, etc : 16, 480, 120
Order of s0s1s2 : 15
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,30}*960a
   5-fold quotients : {8,12}*384c
   8-fold quotients : {4,30}*240c
   10-fold quotients : {8,6}*192a
   16-fold quotients : {4,15}*120
   40-fold quotients : {4,6}*48b
   80-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1> of order 2.
      80 facets:
         40 of {8}*16
         40 of {4}*8
      8 vertex figures:
         8 of {60}*120

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

Twisty Puzzle