Polytope of Type {160,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {160,6}*1920
Also Known As : {160,6|2}. if this polytope has another name.
Group : SmallGroup(1920,44852)
Rank : 3
Schlafli Type : {160,6}
Number of vertices, edges, etc : 160, 480, 6
Order of s0s1s2 : 480
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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 : {80,6}*960
   3-fold quotients : {160,2}*640
   4-fold quotients : {40,6}*480
   5-fold quotients : {32,6}*384
   6-fold quotients : {80,2}*320
   8-fold quotients : {20,6}*240a
   10-fold quotients : {16,6}*192
   12-fold quotients : {40,2}*160
   15-fold quotients : {32,2}*128
   16-fold quotients : {10,6}*120
   20-fold quotients : {8,6}*96
   24-fold quotients : {20,2}*80
   30-fold quotients : {16,2}*64
   40-fold quotients : {4,6}*48a
   48-fold quotients : {10,2}*40
   60-fold quotients : {8,2}*32
   80-fold quotients : {2,6}*24
   96-fold quotients : {5,2}*20
   120-fold quotients : {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):
   None.

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