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}*1920b
if this polytope has a name.
Group : SmallGroup(1920,237603)
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}*960a
   4-fold quotients : {4,60}*480b
   5-fold quotients : {4,12}*384b
   8-fold quotients : {4,30}*240b
   10-fold quotients : {4,6}*192a
   16-fold quotients : {4,15}*120
   20-fold quotients : {4,12}*96b
   40-fold quotients : {4,6}*48c
   80-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1> of order 2.
      140 facets:
         100 of {4}*8
         40 of {2}*4
      8 vertex figures:
         8 of {60}*120
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s1*s2*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*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> of order 2.
      120 facets:
         120 of {4}*8
      8 vertex figures:
         8 of {60}*120
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s0*s1*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.
      60 facets:
         60 of {4}*8
      4 vertex figures:
         4 of {60}*120
   P/N, where N=<s0*s1*s0*s1, s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 4.
      80 facets:
         40 of {2}*4
         40 of {4}*8
      4 vertex figures:
         4 of {60}*120
   P/N, where N=<s0*s2*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s2*s1> of order 4.
      90 facets:
         30 of {4}*8
         60 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 := (  1,481)(  2,482)(  3,484)(  4,483)(  5,486)(  6,485)(  7,487)(  8,488)(  9,496)( 10,495)( 11,493)( 12,494)( 13,491)( 14,492)( 15,490)( 16,489)( 17,545)( 18,546)( 19,548)( 20,547)
( 21,550)( 22,549)( 23,551)( 24,552)( 25,560)( 26,559)( 27,557)( 28,558)( 29,555)( 30,556)( 31,554)( 32,553)( 33,529)( 34,530)( 35,532)( 36,531)( 37,534)( 38,533)( 39,535)( 40,536)( 41,544)( 42,543)( 43,541)( 44,542)( 45,539)( 46,540)( 47,538)( 48,537)( 49,513)( 50,514)( 51,516)( 52,515)( 53,518)( 54,517)( 55,519)( 56,520)( 57,528)( 58,527)( 59,525)( 60,526)( 61,523)( 62,524)( 63,522)( 64,521)( 65,497)( 66,498)( 67,500)( 68,499)( 69,502)( 70,501)( 71,503)( 72,504)( 73,512)( 74,511)( 75,509)( 76,510)( 77,507)( 78,508)( 79,506)( 80,505)( 81,641)( 82,642)( 83,644)( 84,643)( 85,646)( 86,645)( 87,647)( 88,648)( 89,656)( 90,655)( 91,653)( 92,654)( 93,651)( 94,652)( 95,650)( 96,649)( 97,705)( 98,706)( 99,708)(100,707)(101,710)(102,709)(103,711)(104,712)(105,720)(106,719)(107,717)(108,718)(109,715)(110,716)(111,714)(112,713)(113,689)(114,690)(115,692)(116,691)(117,694)(118,693)(119,695)(120,696)(121,704)(122,703)(123,701)(124,702)(125,699)(126,700)(127,698)(128,697)(129,673)(130,674)(131,676)(132,675)(133,678)(134,677)(135,679)(136,680)(137,688)(138,687)(139,685)(140,686)(141,683)(142,684)(143,682)(144,681)(145,657)(146,658)(147,660)(148,659)(149,662)(150,661)(151,663)(152,664)(153,672)(154,671)(155,669)(156,670)(157,667)(158,668)(159,666)(160,665)(161,561)(162,562)(163,564)(164,563)(165,566)(166,565)(167,567)(168,568)(169,576)(170,575)(171,573)(172,574)(173,571)(174,572)(175,570)(176,569)(177,625)(178,626)(179,628)(180,627)(181,630)(182,629)(183,631)(184,632)(185,640)(186,639)(187,637)(188,638)(189,635)(190,636)(191,634)(192,633)(193,609)(194,610)(195,612)(196,611)(197,614)(198,613)(199,615)(200,616)(201,624)(202,623)(203,621)(204,622)(205,619)(206,620)(207,618)(208,617)(209,593)(210,594)(211,596)(212,595)(213,598)(214,597)(215,599)(216,600)(217,608)(218,607)(219,605)(220,606)(221,603)(222,604)(223,602)(224,601)(225,577)(226,578)(227,580)(228,579)(229,582)(230,581)(231,583)(232,584)(233,592)(234,591)(235,589)(236,590)(237,587)(238,588)(239,586)(240,585)(241,721)(242,722)(243,724)(244,723)(245,726)(246,725)(247,727)(248,728)(249,736)(250,735)(251,733)(252,734)(253,731)(254,732)(255,730)(256,729)(257,785)(258,786)(259,788)(260,787)(261,790)(262,789)(263,791)(264,792)(265,800)(266,799)(267,797)(268,798)(269,795)(270,796)(271,794)(272,793)(273,769)(274,770)(275,772)(276,771)(277,774)(278,773)(279,775)(280,776)(281,784)(282,783)(283,781)(284,782)(285,779)(286,780)(287,778)(288,777)(289,753)(290,754)(291,756)(292,755)(293,758)(294,757)(295,759)(296,760)(297,768)(298,767)(299,765)(300,766)(301,763)(302,764)(303,762)(304,761)(305,737)(306,738)(307,740)(308,739)(309,742)(310,741)(311,743)(312,744)(313,752)(314,751)(315,749)(316,750)(317,747)(318,748)(319,746)(320,745)(321,881)(322,882)(323,884)(324,883)(325,886)(326,885)(327,887)(328,888)(329,896)(330,895)(331,893)(332,894)(333,891)(334,892)(335,890)(336,889)(337,945)(338,946)(339,948)(340,947)(341,950)(342,949)(343,951)(344,952)(345,960)(346,959)(347,957)(348,958)(349,955)(350,956)(351,954)(352,953)(353,929)(354,930)(355,932)(356,931)(357,934)(358,933)(359,935)(360,936)(361,944)(362,943)(363,941)(364,942)(365,939)(366,940)(367,938)(368,937)(369,913)(370,914)(371,916)(372,915)(373,918)(374,917)(375,919)(376,920)(377,928)(378,927)(379,925)(380,926)(381,923)(382,924)(383,922)(384,921)(385,897)(386,898)(387,900)(388,899)(389,902)(390,901)(391,903)(392,904)(393,912)(394,911)(395,909)(396,910)(397,907)(398,908)(399,906)(400,905)(401,801)(402,802)(403,804)(404,803)(405,806)(406,805)(407,807)(408,808)(409,816)(410,815)(411,813)(412,814)(413,811)(414,812)(415,810)(416,809)(417,865)(418,866)(419,868)(420,867)(421,870)(422,869)(423,871)(424,872)(425,880)(426,879)(427,877)(428,878)(429,875)(430,876)(431,874)(432,873)(433,849)(434,850)(435,852)(436,851)(437,854)(438,853)(439,855)(440,856)(441,864)(442,863)(443,861)(444,862)(445,859)(446,860)(447,858)(448,857)(449,833)(450,834)(451,836)(452,835)(453,838)(454,837)(455,839)(456,840)(457,848)(458,847)(459,845)(460,846)(461,843)(462,844)(463,842)(464,841)(465,817)(466,818)(467,820)(468,819)(469,822)(470,821)(471,823)(472,824)(473,832)(474,831)
(475,829)(476,830)(477,827)(478,828)(479,826)(480,825);;
s2 := (  1, 97)(  2,100)(  3, 99)(  4, 98)(  5,109)(  6,112)(  7,111)(  8,110)(  9,105)( 10,108)( 11,107)( 12,106)( 13,101)( 14,104)( 15,103)( 16,102)( 17, 81)( 18, 84)( 19, 83)( 20, 82)
( 21, 93)( 22, 96)( 23, 95)( 24, 94)( 25, 89)( 26, 92)( 27, 91)( 28, 90)( 29, 85)( 30, 88)( 31, 87)( 32, 86)( 33,145)( 34,148)( 35,147)( 36,146)( 37,157)( 38,160)( 39,159)( 40,158)( 41,153)( 42,156)( 43,155)( 44,154)( 45,149)( 46,152)( 47,151)( 48,150)( 49,129)( 50,132)( 51,131)( 52,130)( 53,141)( 54,144)( 55,143)( 56,142)( 57,137)( 58,140)( 59,139)( 60,138)( 61,133)( 62,136)( 63,135)( 64,134)( 65,113)( 66,116)( 67,115)( 68,114)( 69,125)( 70,128)( 71,127)( 72,126)( 73,121)( 74,124)( 75,123)( 76,122)( 77,117)( 78,120)( 79,119)( 80,118)(161,177)(162,180)(163,179)(164,178)(165,189)(166,192)(167,191)(168,190)(169,185)(170,188)(171,187)(172,186)(173,181)(174,184)(175,183)(176,182)(193,225)(194,228)(195,227)(196,226)(197,237)(198,240)(199,239)(200,238)(201,233)(202,236)(203,235)(204,234)(205,229)(206,232)(207,231)(208,230)(210,212)(213,221)(214,224)(215,223)(216,222)(218,220)(241,337)(242,340)(243,339)(244,338)(245,349)(246,352)(247,351)(248,350)(249,345)(250,348)(251,347)(252,346)(253,341)(254,344)(255,343)(256,342)(257,321)(258,324)(259,323)(260,322)(261,333)(262,336)(263,335)(264,334)(265,329)(266,332)(267,331)(268,330)(269,325)(270,328)(271,327)(272,326)(273,385)(274,388)(275,387)(276,386)(277,397)(278,400)(279,399)(280,398)(281,393)(282,396)(283,395)(284,394)(285,389)(286,392)(287,391)(288,390)(289,369)(290,372)(291,371)(292,370)(293,381)(294,384)(295,383)(296,382)(297,377)(298,380)(299,379)(300,378)(301,373)(302,376)(303,375)(304,374)(305,353)(306,356)(307,355)(308,354)(309,365)(310,368)(311,367)(312,366)(313,361)(314,364)(315,363)(316,362)(317,357)(318,360)(319,359)(320,358)(401,417)(402,420)(403,419)(404,418)(405,429)(406,432)(407,431)(408,430)(409,425)(410,428)(411,427)(412,426)(413,421)(414,424)(415,423)(416,422)(433,465)(434,468)(435,467)(436,466)(437,477)(438,480)(439,479)(440,478)(441,473)(442,476)(443,475)(444,474)(445,469)(446,472)(447,471)(448,470)(450,452)(453,461)(454,464)(455,463)(456,462)(458,460)(481,817)(482,820)(483,819)(484,818)(485,829)(486,832)(487,831)(488,830)(489,825)(490,828)(491,827)(492,826)(493,821)(494,824)(495,823)(496,822)(497,801)(498,804)(499,803)(500,802)(501,813)(502,816)(503,815)(504,814)(505,809)(506,812)(507,811)(508,810)(509,805)(510,808)(511,807)(512,806)(513,865)(514,868)(515,867)(516,866)(517,877)(518,880)(519,879)(520,878)(521,873)(522,876)(523,875)(524,874)(525,869)(526,872)(527,871)(528,870)(529,849)(530,852)(531,851)(532,850)(533,861)(534,864)(535,863)(536,862)(537,857)(538,860)(539,859)(540,858)(541,853)(542,856)(543,855)(544,854)(545,833)(546,836)(547,835)(548,834)(549,845)(550,848)(551,847)(552,846)(553,841)(554,844)(555,843)(556,842)(557,837)(558,840)(559,839)(560,838)(561,737)(562,740)(563,739)(564,738)(565,749)(566,752)(567,751)(568,750)(569,745)(570,748)(571,747)(572,746)(573,741)(574,744)(575,743)(576,742)(577,721)(578,724)(579,723)(580,722)(581,733)(582,736)(583,735)(584,734)(585,729)(586,732)(587,731)(588,730)(589,725)(590,728)(591,727)(592,726)(593,785)(594,788)(595,787)(596,786)(597,797)(598,800)(599,799)(600,798)(601,793)(602,796)(603,795)(604,794)(605,789)(606,792)(607,791)(608,790)(609,769)(610,772)(611,771)(612,770)(613,781)(614,784)(615,783)(616,782)(617,777)(618,780)(619,779)(620,778)(621,773)(622,776)(623,775)(624,774)(625,753)(626,756)(627,755)(628,754)(629,765)(630,768)(631,767)(632,766)(633,761)(634,764)(635,763)(636,762)(637,757)(638,760)(639,759)(640,758)(641,897)(642,900)(643,899)(644,898)(645,909)(646,912)(647,911)(648,910)(649,905)(650,908)(651,907)(652,906)(653,901)(654,904)(655,903)(656,902)(657,881)(658,884)(659,883)(660,882)(661,893)(662,896)(663,895)(664,894)(665,889)(666,892)(667,891)(668,890)(669,885)(670,888)(671,887)(672,886)(673,945)(674,948)(675,947)(676,946)(677,957)(678,960)(679,959)(680,958)(681,953)(682,956)(683,955)(684,954)(685,949)(686,952)(687,951)(688,950)(689,929)(690,932)(691,931)(692,930)(693,941)(694,944)(695,943)(696,942)(697,937)(698,940)(699,939)(700,938)(701,933)(702,936)(703,935)(704,934)(705,913)(706,916)(707,915)(708,914)(709,925)(710,928)(711,927)(712,926)(713,921)(714,924)(715,923)(716,922)(717,917)(718,920)
(719,919)(720,918);;
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, 
s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*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*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)!(  1,481)(  2,482)(  3,484)(  4,483)(  5,486)(  6,485)(  7,487)(  8,488)(  9,496)( 10,495)( 11,493)( 12,494)( 13,491)( 14,492)( 15,490)( 16,489)( 17,545)( 18,546)( 19,548)
( 20,547)( 21,550)( 22,549)( 23,551)( 24,552)( 25,560)( 26,559)( 27,557)( 28,558)( 29,555)( 30,556)( 31,554)( 32,553)( 33,529)( 34,530)( 35,532)( 36,531)( 37,534)( 38,533)( 39,535)( 40,536)( 41,544)( 42,543)( 43,541)( 44,542)( 45,539)( 46,540)( 47,538)( 48,537)( 49,513)( 50,514)( 51,516)( 52,515)( 53,518)( 54,517)( 55,519)( 56,520)( 57,528)( 58,527)( 59,525)( 60,526)( 61,523)( 62,524)( 63,522)( 64,521)( 65,497)( 66,498)( 67,500)( 68,499)( 69,502)( 70,501)( 71,503)( 72,504)( 73,512)( 74,511)( 75,509)( 76,510)( 77,507)( 78,508)( 79,506)( 80,505)( 81,641)( 82,642)( 83,644)( 84,643)( 85,646)( 86,645)( 87,647)( 88,648)( 89,656)( 90,655)( 91,653)( 92,654)( 93,651)( 94,652)( 95,650)( 96,649)( 97,705)( 98,706)( 99,708)(100,707)(101,710)(102,709)(103,711)(104,712)(105,720)(106,719)(107,717)(108,718)(109,715)(110,716)(111,714)(112,713)(113,689)(114,690)(115,692)(116,691)(117,694)(118,693)(119,695)(120,696)(121,704)(122,703)(123,701)(124,702)(125,699)(126,700)(127,698)(128,697)(129,673)(130,674)(131,676)(132,675)(133,678)(134,677)(135,679)(136,680)(137,688)(138,687)(139,685)(140,686)(141,683)(142,684)(143,682)(144,681)(145,657)(146,658)(147,660)(148,659)(149,662)(150,661)(151,663)(152,664)(153,672)(154,671)(155,669)(156,670)(157,667)(158,668)(159,666)(160,665)(161,561)(162,562)(163,564)(164,563)(165,566)(166,565)(167,567)(168,568)(169,576)(170,575)(171,573)(172,574)(173,571)(174,572)(175,570)(176,569)(177,625)(178,626)(179,628)(180,627)(181,630)(182,629)(183,631)(184,632)(185,640)(186,639)(187,637)(188,638)(189,635)(190,636)(191,634)(192,633)(193,609)(194,610)(195,612)(196,611)(197,614)(198,613)(199,615)(200,616)(201,624)(202,623)(203,621)(204,622)(205,619)(206,620)(207,618)(208,617)(209,593)(210,594)(211,596)(212,595)(213,598)(214,597)(215,599)(216,600)(217,608)(218,607)(219,605)(220,606)(221,603)(222,604)(223,602)(224,601)(225,577)(226,578)(227,580)(228,579)(229,582)(230,581)(231,583)(232,584)(233,592)(234,591)(235,589)(236,590)(237,587)(238,588)(239,586)(240,585)(241,721)(242,722)(243,724)(244,723)(245,726)(246,725)(247,727)(248,728)(249,736)(250,735)(251,733)(252,734)(253,731)(254,732)(255,730)(256,729)(257,785)(258,786)(259,788)(260,787)(261,790)(262,789)(263,791)(264,792)(265,800)(266,799)(267,797)(268,798)(269,795)(270,796)(271,794)(272,793)(273,769)(274,770)(275,772)(276,771)(277,774)(278,773)(279,775)(280,776)(281,784)(282,783)(283,781)(284,782)(285,779)(286,780)(287,778)(288,777)(289,753)(290,754)(291,756)(292,755)(293,758)(294,757)(295,759)(296,760)(297,768)(298,767)(299,765)(300,766)(301,763)(302,764)(303,762)(304,761)(305,737)(306,738)(307,740)(308,739)(309,742)(310,741)(311,743)(312,744)(313,752)(314,751)(315,749)(316,750)(317,747)(318,748)(319,746)(320,745)(321,881)(322,882)(323,884)(324,883)(325,886)(326,885)(327,887)(328,888)(329,896)(330,895)(331,893)(332,894)(333,891)(334,892)(335,890)(336,889)(337,945)(338,946)(339,948)(340,947)(341,950)(342,949)(343,951)(344,952)(345,960)(346,959)(347,957)(348,958)(349,955)(350,956)(351,954)(352,953)(353,929)(354,930)(355,932)(356,931)(357,934)(358,933)(359,935)(360,936)(361,944)(362,943)(363,941)(364,942)(365,939)(366,940)(367,938)(368,937)(369,913)(370,914)(371,916)(372,915)(373,918)(374,917)(375,919)(376,920)(377,928)(378,927)(379,925)(380,926)(381,923)(382,924)(383,922)(384,921)(385,897)(386,898)(387,900)(388,899)(389,902)(390,901)(391,903)(392,904)(393,912)(394,911)(395,909)(396,910)(397,907)(398,908)(399,906)(400,905)(401,801)(402,802)(403,804)(404,803)(405,806)(406,805)(407,807)(408,808)(409,816)(410,815)(411,813)(412,814)(413,811)(414,812)(415,810)(416,809)(417,865)(418,866)(419,868)(420,867)(421,870)(422,869)(423,871)(424,872)(425,880)(426,879)(427,877)(428,878)(429,875)(430,876)(431,874)(432,873)(433,849)(434,850)(435,852)(436,851)(437,854)(438,853)(439,855)(440,856)(441,864)(442,863)(443,861)(444,862)(445,859)(446,860)(447,858)(448,857)(449,833)(450,834)(451,836)(452,835)(453,838)(454,837)(455,839)(456,840)(457,848)(458,847)(459,845)(460,846)(461,843)(462,844)(463,842)(464,841)(465,817)(466,818)(467,820)(468,819)(469,822)(470,821)(471,823)(472,824)(473,832)
(474,831)(475,829)(476,830)(477,827)(478,828)(479,826)(480,825);
s2 := Sym(960)!(  1, 97)(  2,100)(  3, 99)(  4, 98)(  5,109)(  6,112)(  7,111)(  8,110)(  9,105)( 10,108)( 11,107)( 12,106)( 13,101)( 14,104)( 15,103)( 16,102)( 17, 81)( 18, 84)( 19, 83)
( 20, 82)( 21, 93)( 22, 96)( 23, 95)( 24, 94)( 25, 89)( 26, 92)( 27, 91)( 28, 90)( 29, 85)( 30, 88)( 31, 87)( 32, 86)( 33,145)( 34,148)( 35,147)( 36,146)( 37,157)( 38,160)( 39,159)( 40,158)( 41,153)( 42,156)( 43,155)( 44,154)( 45,149)( 46,152)( 47,151)( 48,150)( 49,129)( 50,132)( 51,131)( 52,130)( 53,141)( 54,144)( 55,143)( 56,142)( 57,137)( 58,140)( 59,139)( 60,138)( 61,133)( 62,136)( 63,135)( 64,134)( 65,113)( 66,116)( 67,115)( 68,114)( 69,125)( 70,128)( 71,127)( 72,126)( 73,121)( 74,124)( 75,123)( 76,122)( 77,117)( 78,120)( 79,119)( 80,118)(161,177)(162,180)(163,179)(164,178)(165,189)(166,192)(167,191)(168,190)(169,185)(170,188)(171,187)(172,186)(173,181)(174,184)(175,183)(176,182)(193,225)(194,228)(195,227)(196,226)(197,237)(198,240)(199,239)(200,238)(201,233)(202,236)(203,235)(204,234)(205,229)(206,232)(207,231)(208,230)(210,212)(213,221)(214,224)(215,223)(216,222)(218,220)(241,337)(242,340)(243,339)(244,338)(245,349)(246,352)(247,351)(248,350)(249,345)(250,348)(251,347)(252,346)(253,341)(254,344)(255,343)(256,342)(257,321)(258,324)(259,323)(260,322)(261,333)(262,336)(263,335)(264,334)(265,329)(266,332)(267,331)(268,330)(269,325)(270,328)(271,327)(272,326)(273,385)(274,388)(275,387)(276,386)(277,397)(278,400)(279,399)(280,398)(281,393)(282,396)(283,395)(284,394)(285,389)(286,392)(287,391)(288,390)(289,369)(290,372)(291,371)(292,370)(293,381)(294,384)(295,383)(296,382)(297,377)(298,380)(299,379)(300,378)(301,373)(302,376)(303,375)(304,374)(305,353)(306,356)(307,355)(308,354)(309,365)(310,368)(311,367)(312,366)(313,361)(314,364)(315,363)(316,362)(317,357)(318,360)(319,359)(320,358)(401,417)(402,420)(403,419)(404,418)(405,429)(406,432)(407,431)(408,430)(409,425)(410,428)(411,427)(412,426)(413,421)(414,424)(415,423)(416,422)(433,465)(434,468)(435,467)(436,466)(437,477)(438,480)(439,479)(440,478)(441,473)(442,476)(443,475)(444,474)(445,469)(446,472)(447,471)(448,470)(450,452)(453,461)(454,464)(455,463)(456,462)(458,460)(481,817)(482,820)(483,819)(484,818)(485,829)(486,832)(487,831)(488,830)(489,825)(490,828)(491,827)(492,826)(493,821)(494,824)(495,823)(496,822)(497,801)(498,804)(499,803)(500,802)(501,813)(502,816)(503,815)(504,814)(505,809)(506,812)(507,811)(508,810)(509,805)(510,808)(511,807)(512,806)(513,865)(514,868)(515,867)(516,866)(517,877)(518,880)(519,879)(520,878)(521,873)(522,876)(523,875)(524,874)(525,869)(526,872)(527,871)(528,870)(529,849)(530,852)(531,851)(532,850)(533,861)(534,864)(535,863)(536,862)(537,857)(538,860)(539,859)(540,858)(541,853)(542,856)(543,855)(544,854)(545,833)(546,836)(547,835)(548,834)(549,845)(550,848)(551,847)(552,846)(553,841)(554,844)(555,843)(556,842)(557,837)(558,840)(559,839)(560,838)(561,737)(562,740)(563,739)(564,738)(565,749)(566,752)(567,751)(568,750)(569,745)(570,748)(571,747)(572,746)(573,741)(574,744)(575,743)(576,742)(577,721)(578,724)(579,723)(580,722)(581,733)(582,736)(583,735)(584,734)(585,729)(586,732)(587,731)(588,730)(589,725)(590,728)(591,727)(592,726)(593,785)(594,788)(595,787)(596,786)(597,797)(598,800)(599,799)(600,798)(601,793)(602,796)(603,795)(604,794)(605,789)(606,792)(607,791)(608,790)(609,769)(610,772)(611,771)(612,770)(613,781)(614,784)(615,783)(616,782)(617,777)(618,780)(619,779)(620,778)(621,773)(622,776)(623,775)(624,774)(625,753)(626,756)(627,755)(628,754)(629,765)(630,768)(631,767)(632,766)(633,761)(634,764)(635,763)(636,762)(637,757)(638,760)(639,759)(640,758)(641,897)(642,900)(643,899)(644,898)(645,909)(646,912)(647,911)(648,910)(649,905)(650,908)(651,907)(652,906)(653,901)(654,904)(655,903)(656,902)(657,881)(658,884)(659,883)(660,882)(661,893)(662,896)(663,895)(664,894)(665,889)(666,892)(667,891)(668,890)(669,885)(670,888)(671,887)(672,886)(673,945)(674,948)(675,947)(676,946)(677,957)(678,960)(679,959)(680,958)(681,953)(682,956)(683,955)(684,954)(685,949)(686,952)(687,951)(688,950)(689,929)(690,932)(691,931)(692,930)(693,941)(694,944)(695,943)(696,942)(697,937)(698,940)(699,939)(700,938)(701,933)(702,936)(703,935)(704,934)(705,913)(706,916)(707,915)(708,914)(709,925)(710,928)(711,927)(712,926)(713,921)(714,924)(715,923)(716,922)(717,917)
(718,920)(719,919)(720,918);
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, 
s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*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*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