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}*1920g
if this polytope has a name.
Group : SmallGroup(1920,240267)
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}*960c
   3-fold quotients : {20,4}*640c
   4-fold quotients : {15,4}*480
   6-fold quotients : {10,4}*320a
   12-fold quotients : {5,4}*160
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      8 facets:
         8 of {60}*120
      120 vertex figures:
         120 of {4}*8
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1> of order 2.
      8 facets:
         8 of {60}*120
      144 vertex figures:
         96 of {4}*8
         48 of {2}*4
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1> of order 2.
      8 facets:
         8 of {60}*120
      120 vertex figures:
         120 of {4}*8
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1> of order 4.
      4 facets:
         4 of {60}*120
      72 vertex figures:
         48 of {4}*8
         24 of {2}*4
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s2> of order 4.
      4 facets:
         4 of {60}*120
      72 vertex figures:
         48 of {4}*8
         24 of {2}*4
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1> of order 4.
      4 facets:
         4 of {60}*120
      84 vertex figures:
         36 of {4}*8
         48 of {2}*4

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {60,4}

Twisty Puzzle