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

Twisty Puzzle