Polytope of Type {6,160}

Play with this polytope as a twisty puzzle

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

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*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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*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;;
 

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

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*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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*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 >; 
 

Twisty Puzzle