Polytope of Type {12,80}

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

Twisty Puzzle