Polytope of Type {4,60}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,60}*1920f
if this polytope has a name.
Group : SmallGroup(1920,240267)
Rank : 3
Schlafli Type : {4,60}
Number of vertices, edges, etc : 16, 480, 240
Order of s0s1s2 : 60
Order of s0s1s2s1 : 4
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 : {4,30}*960c
   3-fold quotients : {4,20}*640b
   4-fold quotients : {4,15}*480
   6-fold quotients : {4,10}*320a
   12-fold quotients : {4,5}*160
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*s2*s1> of order 2.
      144 facets:
         96 of {4}*8
         48 of {2}*4
      8 vertex figures:
         8 of {60}*120
   P/N, where N=<s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2> of order 2.
      120 facets:
         120 of {4}*8
      8 vertex figures:
         8 of {60}*120
   P/N, where N=<s1*s2*s1*s0*s2*s1*s2*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      120 facets:
         120 of {4}*8
      8 vertex figures:
         8 of {60}*120
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 4.
      84 facets:
         36 of {4}*8
         48 of {2}*4
      4 vertex figures:
         4 of {60}*120
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, s1*s0*s2*s1*s2*s1*s0*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*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> of order 4.
      72 facets:
         48 of {4}*8
         24 of {2}*4
      4 vertex figures:
         4 of {60}*120
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s2*s1> of order 4.
      72 facets:
         48 of {4}*8
         24 of {2}*4
      4 vertex figures:
         4 of {60}*120

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

Twisty Puzzle