Polytope of Type {8,60}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,60}*1920a
if this polytope has a name.
Group : SmallGroup(1920,13384)
Rank : 3
Schlafli Type : {8,60}
Number of vertices, edges, etc : 16, 480, 120
Order of s0s1s2 : 120
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {4,60}*960a, {8,60}*960a, {8,60}*960b
   3-fold quotients : {8,20}*640a
   4-fold quotients : {4,60}*480a, {8,30}*480
   5-fold quotients : {8,12}*384a
   6-fold quotients : {4,20}*320, {8,20}*320a, {8,20}*320b
   8-fold quotients : {2,60}*240, {4,30}*240a
   10-fold quotients : {4,12}*192a, {8,12}*192a, {8,12}*192b
   12-fold quotients : {4,20}*160, {8,10}*160
   15-fold quotients : {8,4}*128a
   16-fold quotients : {2,30}*120
   20-fold quotients : {4,12}*96a, {8,6}*96
   24-fold quotients : {2,20}*80, {4,10}*80
   30-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64
   32-fold quotients : {2,15}*60
   40-fold quotients : {2,12}*48, {4,6}*48a
   48-fold quotients : {2,10}*40
   60-fold quotients : {4,4}*32, {8,2}*32
   80-fold quotients : {2,6}*24
   96-fold quotients : {2,5}*20
   120-fold quotients : {2,4}*16, {4,2}*16
   160-fold quotients : {2,3}*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=<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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      60 facets:
         60 of {8}*16
      12 vertex figures:
         8 of {30}*60
         4 of {60}*120

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

Twisty Puzzle