Polytope of Type {4,164}

Play with this polytope as a twisty puzzle

s0 := (  1,329)(  2,330)(  3,331)(  4,332)(  5,333)(  6,334)(  7,335)(  8,336)(  9,337)( 10,338)( 11,339)( 12,340)( 13,341)( 14,342)( 15,343)( 16,344)( 17,345)( 18,346)( 19,347)( 20,348)( 21,349)( 22,350)( 23,351)( 24,352)( 25,353)( 26,354)( 27,355)( 28,356)( 29,357)( 30,358)( 31,359)( 32,360)( 33,361)( 34,362)( 35,363)( 36,364)( 37,365)( 38,366)( 39,367)( 40,368)( 41,369)( 42,370)( 43,371)( 44,372)( 45,373)( 46,374)( 47,375)( 48,376)( 49,377)( 50,378)( 51,379)( 52,380)( 53,381)( 54,382)( 55,383)( 56,384)( 57,385)( 58,386)( 59,387)( 60,388)( 61,389)( 62,390)( 63,391)( 64,392)( 65,393)( 66,394)( 67,395)( 68,396)( 69,397)( 70,398)( 71,399)( 72,400)( 73,401)( 74,402)( 75,403)( 76,404)( 77,405)( 78,406)( 79,407)( 80,408)( 81,409)( 82,410)( 83,411)( 84,412)( 85,413)( 86,414)( 87,415)( 88,416)( 89,417)( 90,418)( 91,419)( 92,420)( 93,421)( 94,422)( 95,423)( 96,424)( 97,425)( 98,426)( 99,427)(100,428)(101,429)(102,430)(103,431)(104,432)(105,433)(106,434)(107,435)(108,436)(109,437)(110,438)(111,439)(112,440)(113,441)(114,442)(115,443)(116,444)(117,445)(118,446)(119,447)(120,448)(121,449)(122,450)(123,451)(124,452)(125,453)(126,454)(127,455)(128,456)(129,457)(130,458)(131,459)(132,460)(133,461)(134,462)(135,463)(136,464)(137,465)(138,466)(139,467)(140,468)(141,469)(142,470)(143,471)(144,472)(145,473)(146,474)(147,475)(148,476)(149,477)(150,478)(151,479)(152,480)(153,481)(154,482)(155,483)(156,484)(157,485)(158,486)(159,487)(160,488)(161,489)(162,490)(163,491)(164,492)(165,493)(166,494)(167,495)(168,496)(169,497)(170,498)(171,499)(172,500)(173,501)(174,502)(175,503)(176,504)(177,505)(178,506)(179,507)(180,508)(181,509)(182,510)(183,511)(184,512)(185,513)(186,514)(187,515)(188,516)(189,517)(190,518)(191,519)(192,520)(193,521)(194,522)(195,523)(196,524)(197,525)(198,526)(199,527)(200,528)(201,529)(202,530)(203,531)(204,532)(205,533)(206,534)(207,535)(208,536)(209,537)(210,538)(211,539)(212,540)(213,541)(214,542)(215,543)(216,544)(217,545)(218,546)(219,547)(220,548)(221,549)(222,550)(223,551)(224,552)(225,553)(226,554)(227,555)(228,556)(229,557)(230,558)(231,559)(232,560)(233,561)(234,562)(235,563)(236,564)(237,565)(238,566)(239,567)(240,568)(241,569)(242,570)(243,571)(244,572)(245,573)(246,574)(247,575)(248,576)(249,577)(250,578)(251,579)(252,580)(253,581)(254,582)(255,583)(256,584)(257,585)(258,586)(259,587)(260,588)(261,589)(262,590)(263,591)(264,592)(265,593)(266,594)(267,595)(268,596)(269,597)(270,598)(271,599)(272,600)(273,601)(274,602)(275,603)(276,604)(277,605)(278,606)(279,607)(280,608)(281,609)(282,610)(283,611)(284,612)(285,613)(286,614)(287,615)(288,616)(289,617)(290,618)(291,619)(292,620)(293,621)(294,622)(295,623)(296,624)(297,625)(298,626)(299,627)(300,628)(301,629)(302,630)(303,631)(304,632)(305,633)(306,634)(307,635)(308,636)(309,637)(310,638)(311,639)(312,640)(313,641)(314,642)(315,643)(316,644)(317,645)(318,646)(319,647)(320,648)(321,649)(322,650)(323,651)(324,652)(325,653)(326,654)(327,655)(328,656);;
s1 := (  2, 41)(  3, 40)(  4, 39)(  5, 38)(  6, 37)(  7, 36)(  8, 35)(  9, 34)( 10, 33)( 11, 32)( 12, 31)( 13, 30)( 14, 29)( 15, 28)( 16, 27)( 17, 26)( 18, 25)( 19, 24)( 20, 23)( 21, 22)( 43, 82)( 44, 81)( 45, 80)( 46, 79)( 47, 78)( 48, 77)( 49, 76)( 50, 75)( 51, 74)( 52, 73)( 53, 72)( 54, 71)( 55, 70)( 56, 69)( 57, 68)( 58, 67)( 59, 66)( 60, 65)( 61, 64)( 62, 63)( 84,123)( 85,122)( 86,121)( 87,120)( 88,119)( 89,118)( 90,117)( 91,116)( 92,115)( 93,114)( 94,113)( 95,112)( 96,111)( 97,110)( 98,109)( 99,108)(100,107)(101,106)(102,105)(103,104)(125,164)(126,163)(127,162)(128,161)(129,160)(130,159)(131,158)(132,157)(133,156)(134,155)(135,154)(136,153)(137,152)(138,151)(139,150)(140,149)(141,148)(142,147)(143,146)(144,145)(165,206)(166,246)(167,245)(168,244)(169,243)(170,242)(171,241)(172,240)(173,239)(174,238)(175,237)(176,236)(177,235)(178,234)(179,233)(180,232)(181,231)(182,230)(183,229)(184,228)(185,227)(186,226)(187,225)(188,224)(189,223)(190,222)(191,221)(192,220)(193,219)(194,218)(195,217)(196,216)(197,215)(198,214)(199,213)(200,212)(201,211)(202,210)(203,209)(204,208)(205,207)(247,288)(248,328)(249,327)(250,326)(251,325)(252,324)(253,323)(254,322)(255,321)(256,320)(257,319)(258,318)(259,317)(260,316)(261,315)(262,314)(263,313)(264,312)(265,311)(266,310)(267,309)(268,308)(269,307)(270,306)(271,305)(272,304)(273,303)(274,302)(275,301)(276,300)(277,299)(278,298)(279,297)(280,296)(281,295)(282,294)(283,293)(284,292)(285,291)(286,290)(287,289)(329,411)(330,451)(331,450)(332,449)(333,448)(334,447)(335,446)(336,445)(337,444)(338,443)(339,442)(340,441)(341,440)(342,439)(343,438)(344,437)(345,436)(346,435)(347,434)(348,433)(349,432)(350,431)(351,430)(352,429)(353,428)(354,427)(355,426)(356,425)(357,424)(358,423)(359,422)(360,421)(361,420)(362,419)(363,418)(364,417)(365,416)(366,415)(367,414)(368,413)(369,412)(370,452)(371,492)(372,491)(373,490)(374,489)(375,488)(376,487)(377,486)(378,485)(379,484)(380,483)(381,482)(382,481)(383,480)(384,479)(385,478)(386,477)(387,476)(388,475)(389,474)(390,473)(391,472)(392,471)(393,470)(394,469)(395,468)(396,467)(397,466)(398,465)(399,464)(400,463)(401,462)(402,461)(403,460)(404,459)(405,458)(406,457)(407,456)(408,455)(409,454)(410,453)(493,616)(494,656)(495,655)(496,654)(497,653)(498,652)(499,651)(500,650)(501,649)(502,648)(503,647)(504,646)(505,645)(506,644)(507,643)(508,642)(509,641)(510,640)(511,639)(512,638)(513,637)(514,636)(515,635)(516,634)(517,633)(518,632)(519,631)(520,630)(521,629)(522,628)(523,627)(524,626)(525,625)(526,624)(527,623)(528,622)(529,621)(530,620)(531,619)(532,618)(533,617)(534,575)(535,615)(536,614)(537,613)(538,612)(539,611)(540,610)(541,609)(542,608)(543,607)(544,606)(545,605)(546,604)(547,603)(548,602)(549,601)(550,600)(551,599)(552,598)(553,597)(554,596)(555,595)(556,594)(557,593)(558,592)(559,591)(560,590)(561,589)(562,588)(563,587)(564,586)(565,585)(566,584)(567,583)(568,582)(569,581)(570,580)(571,579)(572,578)(573,577)(574,576);;
s2 := (  1,166)(  2,165)(  3,205)(  4,204)(  5,203)(  6,202)(  7,201)(  8,200)(  9,199)( 10,198)( 11,197)( 12,196)( 13,195)( 14,194)( 15,193)( 16,192)( 17,191)( 18,190)( 19,189)( 20,188)( 21,187)( 22,186)( 23,185)( 24,184)( 25,183)( 26,182)( 27,181)( 28,180)( 29,179)( 30,178)( 31,177)( 32,176)( 33,175)( 34,174)( 35,173)( 36,172)( 37,171)( 38,170)( 39,169)( 40,168)( 41,167)( 42,207)( 43,206)( 44,246)( 45,245)( 46,244)( 47,243)( 48,242)( 49,241)( 50,240)( 51,239)( 52,238)( 53,237)( 54,236)( 55,235)( 56,234)( 57,233)( 58,232)( 59,231)( 60,230)( 61,229)( 62,228)( 63,227)( 64,226)( 65,225)( 66,224)( 67,223)( 68,222)( 69,221)( 70,220)( 71,219)( 72,218)( 73,217)( 74,216)( 75,215)( 76,214)( 77,213)( 78,212)( 79,211)( 80,210)( 81,209)( 82,208)( 83,248)( 84,247)( 85,287)( 86,286)( 87,285)( 88,284)( 89,283)( 90,282)( 91,281)( 92,280)( 93,279)( 94,278)( 95,277)( 96,276)( 97,275)( 98,274)( 99,273)(100,272)(101,271)(102,270)(103,269)(104,268)(105,267)(106,266)(107,265)(108,264)(109,263)(110,262)(111,261)(112,260)(113,259)(114,258)(115,257)(116,256)(117,255)(118,254)(119,253)(120,252)(121,251)(122,250)(123,249)(124,289)(125,288)(126,328)(127,327)(128,326)(129,325)(130,324)(131,323)(132,322)(133,321)(134,320)(135,319)(136,318)(137,317)(138,316)(139,315)(140,314)(141,313)(142,312)(143,311)(144,310)(145,309)(146,308)(147,307)(148,306)(149,305)(150,304)(151,303)(152,302)(153,301)(154,300)(155,299)(156,298)(157,297)(158,296)(159,295)(160,294)(161,293)(162,292)(163,291)(164,290)(329,494)(330,493)(331,533)(332,532)(333,531)(334,530)(335,529)(336,528)(337,527)(338,526)(339,525)(340,524)(341,523)(342,522)(343,521)(344,520)(345,519)(346,518)(347,517)(348,516)(349,515)(350,514)(351,513)(352,512)(353,511)(354,510)(355,509)(356,508)(357,507)(358,506)(359,505)(360,504)(361,503)(362,502)(363,501)(364,500)(365,499)(366,498)(367,497)(368,496)(369,495)(370,535)(371,534)(372,574)(373,573)(374,572)(375,571)(376,570)(377,569)(378,568)(379,567)(380,566)(381,565)(382,564)(383,563)(384,562)(385,561)(386,560)(387,559)(388,558)(389,557)(390,556)(391,555)(392,554)(393,553)(394,552)(395,551)(396,550)(397,549)(398,548)(399,547)(400,546)(401,545)(402,544)(403,543)(404,542)(405,541)(406,540)(407,539)(408,538)(409,537)(410,536)(411,576)(412,575)(413,615)(414,614)(415,613)(416,612)(417,611)(418,610)(419,609)(420,608)(421,607)(422,606)(423,605)(424,604)(425,603)(426,602)(427,601)(428,600)(429,599)(430,598)(431,597)(432,596)(433,595)(434,594)(435,593)(436,592)(437,591)(438,590)(439,589)(440,588)(441,587)(442,586)(443,585)(444,584)(445,583)(446,582)(447,581)(448,580)(449,579)(450,578)(451,577)(452,617)(453,616)(454,656)(455,655)(456,654)(457,653)(458,652)(459,651)(460,650)(461,649)(462,648)(463,647)(464,646)(465,645)(466,644)(467,643)(468,642)(469,641)(470,640)(471,639)(472,638)(473,637)(474,636)(475,635)(476,634)(477,633)(478,632)(479,631)(480,630)(481,629)(482,628)(483,627)(484,626)(485,625)(486,624)(487,623)(488,622)(489,621)(490,620)(491,619)(492,618);;
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*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(656)!(  1,329)(  2,330)(  3,331)(  4,332)(  5,333)(  6,334)(  7,335)(  8,336)(  9,337)( 10,338)( 11,339)( 12,340)( 13,341)( 14,342)( 15,343)( 16,344)( 17,345)( 18,346)( 19,347)( 20,348)( 21,349)( 22,350)( 23,351)( 24,352)( 25,353)( 26,354)( 27,355)( 28,356)( 29,357)( 30,358)( 31,359)( 32,360)( 33,361)( 34,362)( 35,363)( 36,364)( 37,365)( 38,366)( 39,367)( 40,368)( 41,369)( 42,370)( 43,371)( 44,372)( 45,373)( 46,374)( 47,375)( 48,376)( 49,377)( 50,378)( 51,379)( 52,380)( 53,381)( 54,382)( 55,383)( 56,384)( 57,385)( 58,386)( 59,387)( 60,388)( 61,389)( 62,390)( 63,391)( 64,392)( 65,393)( 66,394)( 67,395)( 68,396)( 69,397)( 70,398)( 71,399)( 72,400)( 73,401)( 74,402)( 75,403)( 76,404)( 77,405)( 78,406)( 79,407)( 80,408)( 81,409)( 82,410)( 83,411)( 84,412)( 85,413)( 86,414)( 87,415)( 88,416)( 89,417)( 90,418)( 91,419)( 92,420)( 93,421)( 94,422)( 95,423)( 96,424)( 97,425)( 98,426)( 99,427)(100,428)(101,429)(102,430)(103,431)(104,432)(105,433)(106,434)(107,435)(108,436)(109,437)(110,438)(111,439)(112,440)(113,441)(114,442)(115,443)(116,444)(117,445)(118,446)(119,447)(120,448)(121,449)(122,450)(123,451)(124,452)(125,453)(126,454)(127,455)(128,456)(129,457)(130,458)(131,459)(132,460)(133,461)(134,462)(135,463)(136,464)(137,465)(138,466)(139,467)(140,468)(141,469)(142,470)(143,471)(144,472)(145,473)(146,474)(147,475)(148,476)(149,477)(150,478)(151,479)(152,480)(153,481)(154,482)(155,483)(156,484)(157,485)(158,486)(159,487)(160,488)(161,489)(162,490)(163,491)(164,492)(165,493)(166,494)(167,495)(168,496)(169,497)(170,498)(171,499)(172,500)(173,501)(174,502)(175,503)(176,504)(177,505)(178,506)(179,507)(180,508)(181,509)(182,510)(183,511)(184,512)(185,513)(186,514)(187,515)(188,516)(189,517)(190,518)(191,519)(192,520)(193,521)(194,522)(195,523)(196,524)(197,525)(198,526)(199,527)(200,528)(201,529)(202,530)(203,531)(204,532)(205,533)(206,534)(207,535)(208,536)(209,537)(210,538)(211,539)(212,540)(213,541)(214,542)(215,543)(216,544)(217,545)(218,546)(219,547)(220,548)(221,549)(222,550)(223,551)(224,552)(225,553)(226,554)(227,555)(228,556)(229,557)(230,558)(231,559)(232,560)(233,561)(234,562)(235,563)(236,564)(237,565)(238,566)(239,567)(240,568)(241,569)(242,570)(243,571)(244,572)(245,573)(246,574)(247,575)(248,576)(249,577)(250,578)(251,579)(252,580)(253,581)(254,582)(255,583)(256,584)(257,585)(258,586)(259,587)(260,588)(261,589)(262,590)(263,591)(264,592)(265,593)(266,594)(267,595)(268,596)(269,597)(270,598)(271,599)(272,600)(273,601)(274,602)(275,603)(276,604)(277,605)(278,606)(279,607)(280,608)(281,609)(282,610)(283,611)(284,612)(285,613)(286,614)(287,615)(288,616)(289,617)(290,618)(291,619)(292,620)(293,621)(294,622)(295,623)(296,624)(297,625)(298,626)(299,627)(300,628)(301,629)(302,630)(303,631)(304,632)(305,633)(306,634)(307,635)(308,636)(309,637)(310,638)(311,639)(312,640)(313,641)(314,642)(315,643)(316,644)(317,645)(318,646)(319,647)(320,648)(321,649)(322,650)(323,651)(324,652)(325,653)(326,654)(327,655)(328,656);
s1 := Sym(656)!(  2, 41)(  3, 40)(  4, 39)(  5, 38)(  6, 37)(  7, 36)(  8, 35)(  9, 34)( 10, 33)( 11, 32)( 12, 31)( 13, 30)( 14, 29)( 15, 28)( 16, 27)( 17, 26)( 18, 25)( 19, 24)( 20, 23)( 21, 22)( 43, 82)( 44, 81)( 45, 80)( 46, 79)( 47, 78)( 48, 77)( 49, 76)( 50, 75)( 51, 74)( 52, 73)( 53, 72)( 54, 71)( 55, 70)( 56, 69)( 57, 68)( 58, 67)( 59, 66)( 60, 65)( 61, 64)( 62, 63)( 84,123)( 85,122)( 86,121)( 87,120)( 88,119)( 89,118)( 90,117)( 91,116)( 92,115)( 93,114)( 94,113)( 95,112)( 96,111)( 97,110)( 98,109)( 99,108)(100,107)(101,106)(102,105)(103,104)(125,164)(126,163)(127,162)(128,161)(129,160)(130,159)(131,158)(132,157)(133,156)(134,155)(135,154)(136,153)(137,152)(138,151)(139,150)(140,149)(141,148)(142,147)(143,146)(144,145)(165,206)(166,246)(167,245)(168,244)(169,243)(170,242)(171,241)(172,240)(173,239)(174,238)(175,237)(176,236)(177,235)(178,234)(179,233)(180,232)(181,231)(182,230)(183,229)(184,228)(185,227)(186,226)(187,225)(188,224)(189,223)(190,222)(191,221)(192,220)(193,219)(194,218)(195,217)(196,216)(197,215)(198,214)(199,213)(200,212)(201,211)(202,210)(203,209)(204,208)(205,207)(247,288)(248,328)(249,327)(250,326)(251,325)(252,324)(253,323)(254,322)(255,321)(256,320)(257,319)(258,318)(259,317)(260,316)(261,315)(262,314)(263,313)(264,312)(265,311)(266,310)(267,309)(268,308)(269,307)(270,306)(271,305)(272,304)(273,303)(274,302)(275,301)(276,300)(277,299)(278,298)(279,297)(280,296)(281,295)(282,294)(283,293)(284,292)(285,291)(286,290)(287,289)(329,411)(330,451)(331,450)(332,449)(333,448)(334,447)(335,446)(336,445)(337,444)(338,443)(339,442)(340,441)(341,440)(342,439)(343,438)(344,437)(345,436)(346,435)(347,434)(348,433)(349,432)(350,431)(351,430)(352,429)(353,428)(354,427)(355,426)(356,425)(357,424)(358,423)(359,422)(360,421)(361,420)(362,419)(363,418)(364,417)(365,416)(366,415)(367,414)(368,413)(369,412)(370,452)(371,492)(372,491)(373,490)(374,489)(375,488)(376,487)(377,486)(378,485)(379,484)(380,483)(381,482)(382,481)(383,480)(384,479)(385,478)(386,477)(387,476)(388,475)(389,474)(390,473)(391,472)(392,471)(393,470)(394,469)(395,468)(396,467)(397,466)(398,465)(399,464)(400,463)(401,462)(402,461)(403,460)(404,459)(405,458)(406,457)(407,456)(408,455)(409,454)(410,453)(493,616)(494,656)(495,655)(496,654)(497,653)(498,652)(499,651)(500,650)(501,649)(502,648)(503,647)(504,646)(505,645)(506,644)(507,643)(508,642)(509,641)(510,640)(511,639)(512,638)(513,637)(514,636)(515,635)(516,634)(517,633)(518,632)(519,631)(520,630)(521,629)(522,628)(523,627)(524,626)(525,625)(526,624)(527,623)(528,622)(529,621)(530,620)(531,619)(532,618)(533,617)(534,575)(535,615)(536,614)(537,613)(538,612)(539,611)(540,610)(541,609)(542,608)(543,607)(544,606)(545,605)(546,604)(547,603)(548,602)(549,601)(550,600)(551,599)(552,598)(553,597)(554,596)(555,595)(556,594)(557,593)(558,592)(559,591)(560,590)(561,589)(562,588)(563,587)(564,586)(565,585)(566,584)(567,583)(568,582)(569,581)(570,580)(571,579)(572,578)(573,577)(574,576);
s2 := Sym(656)!(  1,166)(  2,165)(  3,205)(  4,204)(  5,203)(  6,202)(  7,201)(  8,200)(  9,199)( 10,198)( 11,197)( 12,196)( 13,195)( 14,194)( 15,193)( 16,192)( 17,191)( 18,190)( 19,189)( 20,188)( 21,187)( 22,186)( 23,185)( 24,184)( 25,183)( 26,182)( 27,181)( 28,180)( 29,179)( 30,178)( 31,177)( 32,176)( 33,175)( 34,174)( 35,173)( 36,172)( 37,171)( 38,170)( 39,169)( 40,168)( 41,167)( 42,207)( 43,206)( 44,246)( 45,245)( 46,244)( 47,243)( 48,242)( 49,241)( 50,240)( 51,239)( 52,238)( 53,237)( 54,236)( 55,235)( 56,234)( 57,233)( 58,232)( 59,231)( 60,230)( 61,229)( 62,228)( 63,227)( 64,226)( 65,225)( 66,224)( 67,223)( 68,222)( 69,221)( 70,220)( 71,219)( 72,218)( 73,217)( 74,216)( 75,215)( 76,214)( 77,213)( 78,212)( 79,211)( 80,210)( 81,209)( 82,208)( 83,248)( 84,247)( 85,287)( 86,286)( 87,285)( 88,284)( 89,283)( 90,282)( 91,281)( 92,280)( 93,279)( 94,278)( 95,277)( 96,276)( 97,275)( 98,274)( 99,273)(100,272)(101,271)(102,270)(103,269)(104,268)(105,267)(106,266)(107,265)(108,264)(109,263)(110,262)(111,261)(112,260)(113,259)(114,258)(115,257)(116,256)(117,255)(118,254)(119,253)(120,252)(121,251)(122,250)(123,249)(124,289)(125,288)(126,328)(127,327)(128,326)(129,325)(130,324)(131,323)(132,322)(133,321)(134,320)(135,319)(136,318)(137,317)(138,316)(139,315)(140,314)(141,313)(142,312)(143,311)(144,310)(145,309)(146,308)(147,307)(148,306)(149,305)(150,304)(151,303)(152,302)(153,301)(154,300)(155,299)(156,298)(157,297)(158,296)(159,295)(160,294)(161,293)(162,292)(163,291)(164,290)(329,494)(330,493)(331,533)(332,532)(333,531)(334,530)(335,529)(336,528)(337,527)(338,526)(339,525)(340,524)(341,523)(342,522)(343,521)(344,520)(345,519)(346,518)(347,517)(348,516)(349,515)(350,514)(351,513)(352,512)(353,511)(354,510)(355,509)(356,508)(357,507)(358,506)(359,505)(360,504)(361,503)(362,502)(363,501)(364,500)(365,499)(366,498)(367,497)(368,496)(369,495)(370,535)(371,534)(372,574)(373,573)(374,572)(375,571)(376,570)(377,569)(378,568)(379,567)(380,566)(381,565)(382,564)(383,563)(384,562)(385,561)(386,560)(387,559)(388,558)(389,557)(390,556)(391,555)(392,554)(393,553)(394,552)(395,551)(396,550)(397,549)(398,548)(399,547)(400,546)(401,545)(402,544)(403,543)(404,542)(405,541)(406,540)(407,539)(408,538)(409,537)(410,536)(411,576)(412,575)(413,615)(414,614)(415,613)(416,612)(417,611)(418,610)(419,609)(420,608)(421,607)(422,606)(423,605)(424,604)(425,603)(426,602)(427,601)(428,600)(429,599)(430,598)(431,597)(432,596)(433,595)(434,594)(435,593)(436,592)(437,591)(438,590)(439,589)(440,588)(441,587)(442,586)(443,585)(444,584)(445,583)(446,582)(447,581)(448,580)(449,579)(450,578)(451,577)(452,617)(453,616)(454,656)(455,655)(456,654)(457,653)(458,652)(459,651)(460,650)(461,649)(462,648)(463,647)(464,646)(465,645)(466,644)(467,643)(468,642)(469,641)(470,640)(471,639)(472,638)(473,637)(474,636)(475,635)(476,634)(477,633)(478,632)(479,631)(480,630)(481,629)(482,628)(483,627)(484,626)(485,625)(486,624)(487,623)(488,622)(489,621)(490,620)(491,619)(492,618);
poly := sub<Sym(656)|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*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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