Polytope of Type {15,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,8}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240273)
Rank : 3
Schlafli Type : {15,8}
Number of vertices, edges, etc : 120, 480, 64
Order of s0s1s2 : 60
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 : {15,4}*960
   3-fold quotients : {5,8}*640b
   4-fold quotients : {15,4}*480
   6-fold quotients : {5,4}*320
   12-fold quotients : {5,4}*160
   32-fold quotients : {15,2}*60
   96-fold quotients : {5,2}*20
   160-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s2> of order 2.
      32 facets:
         32 of {15}*30
      60 vertex figures:
         60 of {8}*16
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 2.
      32 facets:
         32 of {15}*30
      60 vertex figures:
         60 of {8}*16
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s2*s1> of order 4.
      16 facets:
         16 of {15}*30
      30 vertex figures:
         30 of {8}*16

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

Twisty Puzzle