Polytope of Type {60,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,4}*1920h
if this polytope has a name.
Group : SmallGroup(1920,240273)
Rank : 3
Schlafli Type : {60,4}
Number of vertices, edges, etc : 240, 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
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {30,4}*960d
   3-fold quotients : {20,4}*640e
   4-fold quotients : {15,4}*480
   6-fold quotients : {10,4}*320b
   12-fold quotients : {5,4}*160
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 2.
      8 facets:
         8 of {60}*120
      120 vertex figures:
         120 of {4}*8

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

Twisty Puzzle