Polytope of Type {8,15}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,15}*1920a
if this polytope has a name.
Group : SmallGroup(1920,237609)
Rank : 3
Schlafli Type : {8,15}
Number of vertices, edges, etc : 64, 480, 120
Order of s0s1s2 : 60
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {8,15}*960a
   4-fold quotients : {8,15}*480
   5-fold quotients : {8,3}*384
   8-fold quotients : {4,15}*240
   10-fold quotients : {8,3}*192
   16-fold quotients : {4,15}*120
   20-fold quotients : {8,3}*96
   32-fold quotients : {2,15}*60
   40-fold quotients : {4,3}*48
   80-fold quotients : {4,3}*24
   96-fold quotients : {2,5}*20
   160-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2> of order 2.
      60 facets:
         60 of {8}*16
      32 vertex figures:
         32 of {15}*30
   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
      32 vertex figures:
         32 of {15}*30
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      60 facets:
         60 of {8}*16
      32 vertex figures:
         32 of {15}*30
   P/N, where N=<s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
      40 facets:
         20 of {8}*16
         20 of {4}*8
      16 vertex figures:
         16 of {15}*30
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1> of order 4.
      30 facets:
         30 of {8}*16
      16 vertex figures:
         16 of {15}*30
   P/N, where N=<s0*s2*s1*s0*s1*s0*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1> of order 4.
      50 facets:
         10 of {8}*16
         40 of {4}*8
      16 vertex figures:
         16 of {15}*30
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
      50 facets:
         20 of {8}*16
         20 of {2}*4
         10 of {4}*8
      16 vertex figures:
         16 of {15}*30
   P/N, where N=<s0*s2*s1*s0*s1*s0*s2*s1*s0*s1> of order 4.
      40 facets:
         20 of {8}*16
         20 of {4}*8
      16 vertex figures:
         16 of {15}*30
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2> of order 8.
      25 facets:
         10 of {8}*16
         10 of {2}*4
         5 of {4}*8
      8 vertex figures:
         8 of {15}*30
   P/N, where N=<s0*s2*s1*s0*s1*s0*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 8.
      20 facets:
         10 of {8}*16
         10 of {4}*8
      8 vertex figures:
         8 of {15}*30
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s2*s1*s0*s1*s0*s1*s0*s1*s2> of order 8.
      30 facets:
         5 of {8}*16
         15 of {4}*8
         10 of {2}*4
      8 vertex figures:
         8 of {15}*30
   P/N, where N=<s0*s2*s1*s0*s1*s0*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 8.
      25 facets:
         5 of {8}*16
         20 of {4}*8
      8 vertex figures:
         8 of {15}*30

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

Twisty Puzzle