Polytope of Type {8,120}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle