Polytope of Type {10,96}

Play with this polytope as a twisty puzzle

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