Polytope of Type {57,8}

Play with this polytope as a twisty puzzle

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

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

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

Twisty Puzzle