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}*1920g
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}*640c
   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=<s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> 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=<s0*s1*s0*s1*s2*s1*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=<s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2> of order 4.
      84 facets:
         36 of {4}*8
         48 of {2}*4
      4 vertex figures:
         4 of {60}*120
   P/N, where N=<s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*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 := (  1,249)(  2,250)(  3,251)(  4,252)(  5,253)(  6,254)(  7,255)(  8,256)(  9,241)( 10,242)( 11,243)( 12,244)( 13,245)( 14,246)( 15,247)( 16,248)( 17,265)( 18,266)( 19,267)( 20,268)
( 21,269)( 22,270)( 23,271)( 24,272)( 25,257)( 26,258)( 27,259)( 28,260)( 29,261)( 30,262)( 31,263)( 32,264)( 33,281)( 34,282)( 35,283)( 36,284)( 37,285)( 38,286)( 39,287)( 40,288)( 41,273)( 42,274)( 43,275)( 44,276)( 45,277)( 46,278)( 47,279)( 48,280)( 49,297)( 50,298)( 51,299)( 52,300)( 53,301)( 54,302)( 55,303)( 56,304)( 57,289)( 58,290)( 59,291)( 60,292)( 61,293)( 62,294)( 63,295)( 64,296)( 65,313)( 66,314)( 67,315)( 68,316)( 69,317)( 70,318)( 71,319)( 72,320)( 73,305)( 74,306)( 75,307)( 76,308)( 77,309)( 78,310)( 79,311)( 80,312)( 81,329)( 82,330)( 83,331)( 84,332)( 85,333)( 86,334)( 87,335)( 88,336)( 89,321)( 90,322)( 91,323)( 92,324)( 93,325)( 94,326)( 95,327)( 96,328)( 97,345)( 98,346)( 99,347)(100,348)(101,349)(102,350)(103,351)(104,352)(105,337)(106,338)(107,339)(108,340)(109,341)(110,342)(111,343)(112,344)(113,361)(114,362)(115,363)(116,364)(117,365)(118,366)(119,367)(120,368)(121,353)(122,354)(123,355)(124,356)(125,357)(126,358)(127,359)(128,360)(129,377)(130,378)(131,379)(132,380)(133,381)(134,382)(135,383)(136,384)(137,369)(138,370)(139,371)(140,372)(141,373)(142,374)(143,375)(144,376)(145,393)(146,394)(147,395)(148,396)(149,397)(150,398)(151,399)(152,400)(153,385)(154,386)(155,387)(156,388)(157,389)(158,390)(159,391)(160,392)(161,409)(162,410)(163,411)(164,412)(165,413)(166,414)(167,415)(168,416)(169,401)(170,402)(171,403)(172,404)(173,405)(174,406)(175,407)(176,408)(177,425)(178,426)(179,427)(180,428)(181,429)(182,430)(183,431)(184,432)(185,417)(186,418)(187,419)(188,420)(189,421)(190,422)(191,423)(192,424)(193,441)(194,442)(195,443)(196,444)(197,445)(198,446)(199,447)(200,448)(201,433)(202,434)(203,435)(204,436)(205,437)(206,438)(207,439)(208,440)(209,457)(210,458)(211,459)(212,460)(213,461)(214,462)(215,463)(216,464)(217,449)(218,450)(219,451)(220,452)(221,453)(222,454)(223,455)(224,456)(225,473)(226,474)(227,475)(228,476)(229,477)(230,478)(231,479)(232,480)(233,465)(234,466)(235,467)(236,468)(237,469)(238,470)(239,471)(240,472)(481,729)(482,730)(483,731)(484,732)(485,733)(486,734)(487,735)(488,736)(489,721)(490,722)(491,723)(492,724)(493,725)(494,726)(495,727)(496,728)(497,745)(498,746)(499,747)(500,748)(501,749)(502,750)(503,751)(504,752)(505,737)(506,738)(507,739)(508,740)(509,741)(510,742)(511,743)(512,744)(513,761)(514,762)(515,763)(516,764)(517,765)(518,766)(519,767)(520,768)(521,753)(522,754)(523,755)(524,756)(525,757)(526,758)(527,759)(528,760)(529,777)(530,778)(531,779)(532,780)(533,781)(534,782)(535,783)(536,784)(537,769)(538,770)(539,771)(540,772)(541,773)(542,774)(543,775)(544,776)(545,793)(546,794)(547,795)(548,796)(549,797)(550,798)(551,799)(552,800)(553,785)(554,786)(555,787)(556,788)(557,789)(558,790)(559,791)(560,792)(561,809)(562,810)(563,811)(564,812)(565,813)(566,814)(567,815)(568,816)(569,801)(570,802)(571,803)(572,804)(573,805)(574,806)(575,807)(576,808)(577,825)(578,826)(579,827)(580,828)(581,829)(582,830)(583,831)(584,832)(585,817)(586,818)(587,819)(588,820)(589,821)(590,822)(591,823)(592,824)(593,841)(594,842)(595,843)(596,844)(597,845)(598,846)(599,847)(600,848)(601,833)(602,834)(603,835)(604,836)(605,837)(606,838)(607,839)(608,840)(609,857)(610,858)(611,859)(612,860)(613,861)(614,862)(615,863)(616,864)(617,849)(618,850)(619,851)(620,852)(621,853)(622,854)(623,855)(624,856)(625,873)(626,874)(627,875)(628,876)(629,877)(630,878)(631,879)(632,880)(633,865)(634,866)(635,867)(636,868)(637,869)(638,870)(639,871)(640,872)(641,889)(642,890)(643,891)(644,892)(645,893)(646,894)(647,895)(648,896)(649,881)(650,882)(651,883)(652,884)(653,885)(654,886)(655,887)(656,888)(657,905)(658,906)(659,907)(660,908)(661,909)(662,910)(663,911)(664,912)(665,897)(666,898)(667,899)(668,900)(669,901)(670,902)(671,903)(672,904)(673,921)(674,922)(675,923)(676,924)(677,925)(678,926)(679,927)(680,928)(681,913)(682,914)(683,915)(684,916)(685,917)(686,918)(687,919)(688,920)(689,937)(690,938)(691,939)(692,940)(693,941)(694,942)(695,943)(696,944)(697,929)(698,930)(699,931)(700,932)(701,933)(702,934)(703,935)(704,936)(705,953)(706,954)(707,955)(708,956)(709,957)(710,958)(711,959)(712,960)(713,945)(714,946)
(715,947)(716,948)(717,949)(718,950)(719,951)(720,952);;
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, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*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*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {4,60}

Twisty Puzzle