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}*1920c
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}*480c
   5-fold quotients : {12,4}*384c
   8-fold quotients : {30,4}*240b
   10-fold quotients : {6,4}*192a
   16-fold quotients : {15,4}*120
   20-fold quotients : {12,4}*96c
   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=<s1*s0*s1*s0*s1*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> of order 2.
      8 facets:
         8 of {60}*120
      120 vertex figures:
         120 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2> 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*s0*s1*s2*s1*s0*s2*s1*s0> 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 := (  1,245)(  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*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2 ];;
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)!(  1,245)(  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*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2 >;

References : None.
to this polytope

Polytope of Type {60,4}

Twisty Puzzle