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}*1920e
if this polytope has a name.
Group : SmallGroup(1920,239568)
Rank : 3
Schlafli Type : {60,4}
Number of vertices, edges, etc : 240, 480, 16
Order of s0s1s2 : 120
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {30,4}*960b
   4-fold quotients : {30,4}*480
   5-fold quotients : {12,4}*384e
   8-fold quotients : {30,4}*240a, {15,4}*240, {30,4}*240b, {30,4}*240c
   10-fold quotients : {6,4}*192b
   16-fold quotients : {15,4}*120, {30,2}*120
   20-fold quotients : {6,4}*96
   24-fold quotients : {10,4}*80
   32-fold quotients : {15,2}*60
   40-fold quotients : {6,4}*48a, {3,4}*48, {6,4}*48b, {6,4}*48c
   48-fold quotients : {10,2}*40
   80-fold quotients : {3,4}*24, {6,2}*24
   96-fold quotients : {5,2}*20
   120-fold quotients : {2,4}*16
   160-fold quotients : {3,2}*12
   240-fold quotients : {2,2}*8
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2> of order 3.
      8 facets:
         4 of {20}*40
         4 of {60}*120
      80 vertex figures:
         80 of {4}*8

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

Twisty Puzzle