Polytope of Type {164,4}

Play with this polytope as a twisty puzzle

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