Polytope of Type {60,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,4}*1920b
if this polytope has a name.
Group : SmallGroup(1920,237603)
Rank : 3
Schlafli Type : {60,4}
Number of vertices, edges, etc : 240, 480, 16
Order of s0s1s2 : 60
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {30,4}*960a
   4-fold quotients : {60,4}*480b
   5-fold quotients : {12,4}*384b
   8-fold quotients : {30,4}*240b
   10-fold quotients : {6,4}*192a
   16-fold quotients : {15,4}*120
   20-fold quotients : {12,4}*96b
   40-fold quotients : {6,4}*48c
   80-fold quotients : {3,4}*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*s0*s1*s2*s1*s0*s2*s1*s0> of order 2.
      8 facets:
         8 of {60}*120
      140 vertex figures:
         100 of {4}*8
         40 of {2}*4
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s2> of order 2.
      8 facets:
         8 of {60}*120
      120 vertex figures:
         120 of {4}*8
   P/N, where N=<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*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*s2*s1*s0*s1*s0*s1*s2> of order 2.
      8 facets:
         8 of {60}*120
      120 vertex figures:
         120 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s2, 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1> of order 4.
      4 facets:
         4 of {60}*120
      60 vertex figures:
         60 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s2> of order 4.
      4 facets:
         4 of {60}*120
      80 vertex figures:
         40 of {4}*8
         40 of {2}*4
   P/N, where N=<s1*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0> of order 4.
      4 facets:
         4 of {60}*120
      90 vertex figures:
         60 of {2}*4
         30 of {4}*8

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