Polytope of Type {108,4}

Play with this polytope as a twisty puzzle

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

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