Polytope of Type {15,8}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle