Polytope of Type {166,4}

Play with this polytope as a twisty puzzle

s0 := (  1,167)(  2,249)(  3,248)(  4,247)(  5,246)(  6,245)(  7,244)(  8,243)(  9,242)( 10,241)( 11,240)( 12,239)( 13,238)( 14,237)( 15,236)( 16,235)( 17,234)( 18,233)( 19,232)( 20,231)( 21,230)( 22,229)( 23,228)( 24,227)( 25,226)( 26,225)( 27,224)( 28,223)( 29,222)( 30,221)( 31,220)( 32,219)( 33,218)( 34,217)( 35,216)( 36,215)( 37,214)( 38,213)( 39,212)( 40,211)( 41,210)( 42,209)( 43,208)( 44,207)( 45,206)( 46,205)( 47,204)( 48,203)( 49,202)( 50,201)( 51,200)( 52,199)( 53,198)( 54,197)( 55,196)( 56,195)( 57,194)( 58,193)( 59,192)( 60,191)( 61,190)( 62,189)( 63,188)( 64,187)( 65,186)( 66,185)( 67,184)( 68,183)( 69,182)( 70,181)( 71,180)( 72,179)( 73,178)( 74,177)( 75,176)( 76,175)( 77,174)( 78,173)( 79,172)( 80,171)( 81,170)( 82,169)( 83,168)( 84,250)( 85,332)( 86,331)( 87,330)( 88,329)( 89,328)( 90,327)( 91,326)( 92,325)( 93,324)( 94,323)( 95,322)( 96,321)( 97,320)( 98,319)( 99,318)(100,317)(101,316)(102,315)(103,314)(104,313)(105,312)(106,311)(107,310)(108,309)(109,308)(110,307)(111,306)(112,305)(113,304)(114,303)(115,302)(116,301)(117,300)(118,299)(119,298)(120,297)(121,296)(122,295)(123,294)(124,293)(125,292)(126,291)(127,290)(128,289)(129,288)(130,287)(131,286)(132,285)(133,284)(134,283)(135,282)(136,281)(137,280)(138,279)(139,278)(140,277)(141,276)(142,275)(143,274)(144,273)(145,272)(146,271)(147,270)(148,269)(149,268)(150,267)(151,266)(152,265)(153,264)(154,263)(155,262)(156,261)(157,260)(158,259)(159,258)(160,257)(161,256)(162,255)(163,254)(164,253)(165,252)(166,251)(333,499)(334,581)(335,580)(336,579)(337,578)(338,577)(339,576)(340,575)(341,574)(342,573)(343,572)(344,571)(345,570)(346,569)(347,568)(348,567)(349,566)(350,565)(351,564)(352,563)(353,562)(354,561)(355,560)(356,559)(357,558)(358,557)(359,556)(360,555)(361,554)(362,553)(363,552)(364,551)(365,550)(366,549)(367,548)(368,547)(369,546)(370,545)(371,544)(372,543)(373,542)(374,541)(375,540)(376,539)(377,538)(378,537)(379,536)(380,535)(381,534)(382,533)(383,532)(384,531)(385,530)(386,529)(387,528)(388,527)(389,526)(390,525)(391,524)(392,523)(393,522)(394,521)(395,520)(396,519)(397,518)(398,517)(399,516)(400,515)(401,514)(402,513)(403,512)(404,511)(405,510)(406,509)(407,508)(408,507)(409,506)(410,505)(411,504)(412,503)(413,502)(414,501)(415,500)(416,582)(417,664)(418,663)(419,662)(420,661)(421,660)(422,659)(423,658)(424,657)(425,656)(426,655)(427,654)(428,653)(429,652)(430,651)(431,650)(432,649)(433,648)(434,647)(435,646)(436,645)(437,644)(438,643)(439,642)(440,641)(441,640)(442,639)(443,638)(444,637)(445,636)(446,635)(447,634)(448,633)(449,632)(450,631)(451,630)(452,629)(453,628)(454,627)(455,626)(456,625)(457,624)(458,623)(459,622)(460,621)(461,620)(462,619)(463,618)(464,617)(465,616)(466,615)(467,614)(468,613)(469,612)(470,611)(471,610)(472,609)(473,608)(474,607)(475,606)(476,605)(477,604)(478,603)(479,602)(480,601)(481,600)(482,599)(483,598)(484,597)(485,596)(486,595)(487,594)(488,593)(489,592)(490,591)(491,590)(492,589)(493,588)(494,587)(495,586)(496,585)(497,584)(498,583);;
s1 := (  1,168)(  2,167)(  3,249)(  4,248)(  5,247)(  6,246)(  7,245)(  8,244)(  9,243)( 10,242)( 11,241)( 12,240)( 13,239)( 14,238)( 15,237)( 16,236)( 17,235)( 18,234)( 19,233)( 20,232)( 21,231)( 22,230)( 23,229)( 24,228)( 25,227)( 26,226)( 27,225)( 28,224)( 29,223)( 30,222)( 31,221)( 32,220)( 33,219)( 34,218)( 35,217)( 36,216)( 37,215)( 38,214)( 39,213)( 40,212)( 41,211)( 42,210)( 43,209)( 44,208)( 45,207)( 46,206)( 47,205)( 48,204)( 49,203)( 50,202)( 51,201)( 52,200)( 53,199)( 54,198)( 55,197)( 56,196)( 57,195)( 58,194)( 59,193)( 60,192)( 61,191)( 62,190)( 63,189)( 64,188)( 65,187)( 66,186)( 67,185)( 68,184)( 69,183)( 70,182)( 71,181)( 72,180)( 73,179)( 74,178)( 75,177)( 76,176)( 77,175)( 78,174)( 79,173)( 80,172)( 81,171)( 82,170)( 83,169)( 84,251)( 85,250)( 86,332)( 87,331)( 88,330)( 89,329)( 90,328)( 91,327)( 92,326)( 93,325)( 94,324)( 95,323)( 96,322)( 97,321)( 98,320)( 99,319)(100,318)(101,317)(102,316)(103,315)(104,314)(105,313)(106,312)(107,311)(108,310)(109,309)(110,308)(111,307)(112,306)(113,305)(114,304)(115,303)(116,302)(117,301)(118,300)(119,299)(120,298)(121,297)(122,296)(123,295)(124,294)(125,293)(126,292)(127,291)(128,290)(129,289)(130,288)(131,287)(132,286)(133,285)(134,284)(135,283)(136,282)(137,281)(138,280)(139,279)(140,278)(141,277)(142,276)(143,275)(144,274)(145,273)(146,272)(147,271)(148,270)(149,269)(150,268)(151,267)(152,266)(153,265)(154,264)(155,263)(156,262)(157,261)(158,260)(159,259)(160,258)(161,257)(162,256)(163,255)(164,254)(165,253)(166,252)(333,583)(334,582)(335,664)(336,663)(337,662)(338,661)(339,660)(340,659)(341,658)(342,657)(343,656)(344,655)(345,654)(346,653)(347,652)(348,651)(349,650)(350,649)(351,648)(352,647)(353,646)(354,645)(355,644)(356,643)(357,642)(358,641)(359,640)(360,639)(361,638)(362,637)(363,636)(364,635)(365,634)(366,633)(367,632)(368,631)(369,630)(370,629)(371,628)(372,627)(373,626)(374,625)(375,624)(376,623)(377,622)(378,621)(379,620)(380,619)(381,618)(382,617)(383,616)(384,615)(385,614)(386,613)(387,612)(388,611)(389,610)(390,609)(391,608)(392,607)(393,606)(394,605)(395,604)(396,603)(397,602)(398,601)(399,600)(400,599)(401,598)(402,597)(403,596)(404,595)(405,594)(406,593)(407,592)(408,591)(409,590)(410,589)(411,588)(412,587)(413,586)(414,585)(415,584)(416,500)(417,499)(418,581)(419,580)(420,579)(421,578)(422,577)(423,576)(424,575)(425,574)(426,573)(427,572)(428,571)(429,570)(430,569)(431,568)(432,567)(433,566)(434,565)(435,564)(436,563)(437,562)(438,561)(439,560)(440,559)(441,558)(442,557)(443,556)(444,555)(445,554)(446,553)(447,552)(448,551)(449,550)(450,549)(451,548)(452,547)(453,546)(454,545)(455,544)(456,543)(457,542)(458,541)(459,540)(460,539)(461,538)(462,537)(463,536)(464,535)(465,534)(466,533)(467,532)(468,531)(469,530)(470,529)(471,528)(472,527)(473,526)(474,525)(475,524)(476,523)(477,522)(478,521)(479,520)(480,519)(481,518)(482,517)(483,516)(484,515)(485,514)(486,513)(487,512)(488,511)(489,510)(490,509)(491,508)(492,507)(493,506)(494,505)(495,504)(496,503)(497,502)(498,501);;
s2 := (  1,333)(  2,334)(  3,335)(  4,336)(  5,337)(  6,338)(  7,339)(  8,340)(  9,341)( 10,342)( 11,343)( 12,344)( 13,345)( 14,346)( 15,347)( 16,348)( 17,349)( 18,350)( 19,351)( 20,352)( 21,353)( 22,354)( 23,355)( 24,356)( 25,357)( 26,358)( 27,359)( 28,360)( 29,361)( 30,362)( 31,363)( 32,364)( 33,365)( 34,366)( 35,367)( 36,368)( 37,369)( 38,370)( 39,371)( 40,372)( 41,373)( 42,374)( 43,375)( 44,376)( 45,377)( 46,378)( 47,379)( 48,380)( 49,381)( 50,382)( 51,383)( 52,384)( 53,385)( 54,386)( 55,387)( 56,388)( 57,389)( 58,390)( 59,391)( 60,392)( 61,393)( 62,394)( 63,395)( 64,396)( 65,397)( 66,398)( 67,399)( 68,400)( 69,401)( 70,402)( 71,403)( 72,404)( 73,405)( 74,406)( 75,407)( 76,408)( 77,409)( 78,410)( 79,411)( 80,412)( 81,413)( 82,414)( 83,415)( 84,416)( 85,417)( 86,418)( 87,419)( 88,420)( 89,421)( 90,422)( 91,423)( 92,424)( 93,425)( 94,426)( 95,427)( 96,428)( 97,429)( 98,430)( 99,431)(100,432)(101,433)(102,434)(103,435)(104,436)(105,437)(106,438)(107,439)(108,440)(109,441)(110,442)(111,443)(112,444)(113,445)(114,446)(115,447)(116,448)(117,449)(118,450)(119,451)(120,452)(121,453)(122,454)(123,455)(124,456)(125,457)(126,458)(127,459)(128,460)(129,461)(130,462)(131,463)(132,464)(133,465)(134,466)(135,467)(136,468)(137,469)(138,470)(139,471)(140,472)(141,473)(142,474)(143,475)(144,476)(145,477)(146,478)(147,479)(148,480)(149,481)(150,482)(151,483)(152,484)(153,485)(154,486)(155,487)(156,488)(157,489)(158,490)(159,491)(160,492)(161,493)(162,494)(163,495)(164,496)(165,497)(166,498)(167,499)(168,500)(169,501)(170,502)(171,503)(172,504)(173,505)(174,506)(175,507)(176,508)(177,509)(178,510)(179,511)(180,512)(181,513)(182,514)(183,515)(184,516)(185,517)(186,518)(187,519)(188,520)(189,521)(190,522)(191,523)(192,524)(193,525)(194,526)(195,527)(196,528)(197,529)(198,530)(199,531)(200,532)(201,533)(202,534)(203,535)(204,536)(205,537)(206,538)(207,539)(208,540)(209,541)(210,542)(211,543)(212,544)(213,545)(214,546)(215,547)(216,548)(217,549)(218,550)(219,551)(220,552)(221,553)(222,554)(223,555)(224,556)(225,557)(226,558)(227,559)(228,560)(229,561)(230,562)(231,563)(232,564)(233,565)(234,566)(235,567)(236,568)(237,569)(238,570)(239,571)(240,572)(241,573)(242,574)(243,575)(244,576)(245,577)(246,578)(247,579)(248,580)(249,581)(250,582)(251,583)(252,584)(253,585)(254,586)(255,587)(256,588)(257,589)(258,590)(259,591)(260,592)(261,593)(262,594)(263,595)(264,596)(265,597)(266,598)(267,599)(268,600)(269,601)(270,602)(271,603)(272,604)(273,605)(274,606)(275,607)(276,608)(277,609)(278,610)(279,611)(280,612)(281,613)(282,614)(283,615)(284,616)(285,617)(286,618)(287,619)(288,620)(289,621)(290,622)(291,623)(292,624)(293,625)(294,626)(295,627)(296,628)(297,629)(298,630)(299,631)(300,632)(301,633)(302,634)(303,635)(304,636)(305,637)(306,638)(307,639)(308,640)(309,641)(310,642)(311,643)(312,644)(313,645)(314,646)(315,647)(316,648)(317,649)(318,650)(319,651)(320,652)(321,653)(322,654)(323,655)(324,656)(325,657)(326,658)(327,659)(328,660)(329,661)(330,662)(331,663)(332,664);;
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*s0*s1*s0*s1 ];;
poly := F / rels;;
 

s0 := Sym(664)!(  1,167)(  2,249)(  3,248)(  4,247)(  5,246)(  6,245)(  7,244)(  8,243)(  9,242)( 10,241)( 11,240)( 12,239)( 13,238)( 14,237)( 15,236)( 16,235)( 17,234)( 18,233)( 19,232)( 20,231)( 21,230)( 22,229)( 23,228)( 24,227)( 25,226)( 26,225)( 27,224)( 28,223)( 29,222)( 30,221)( 31,220)( 32,219)( 33,218)( 34,217)( 35,216)( 36,215)( 37,214)( 38,213)( 39,212)( 40,211)( 41,210)( 42,209)( 43,208)( 44,207)( 45,206)( 46,205)( 47,204)( 48,203)( 49,202)( 50,201)( 51,200)( 52,199)( 53,198)( 54,197)( 55,196)( 56,195)( 57,194)( 58,193)( 59,192)( 60,191)( 61,190)( 62,189)( 63,188)( 64,187)( 65,186)( 66,185)( 67,184)( 68,183)( 69,182)( 70,181)( 71,180)( 72,179)( 73,178)( 74,177)( 75,176)( 76,175)( 77,174)( 78,173)( 79,172)( 80,171)( 81,170)( 82,169)( 83,168)( 84,250)( 85,332)( 86,331)( 87,330)( 88,329)( 89,328)( 90,327)( 91,326)( 92,325)( 93,324)( 94,323)( 95,322)( 96,321)( 97,320)( 98,319)( 99,318)(100,317)(101,316)(102,315)(103,314)(104,313)(105,312)(106,311)(107,310)(108,309)(109,308)(110,307)(111,306)(112,305)(113,304)(114,303)(115,302)(116,301)(117,300)(118,299)(119,298)(120,297)(121,296)(122,295)(123,294)(124,293)(125,292)(126,291)(127,290)(128,289)(129,288)(130,287)(131,286)(132,285)(133,284)(134,283)(135,282)(136,281)(137,280)(138,279)(139,278)(140,277)(141,276)(142,275)(143,274)(144,273)(145,272)(146,271)(147,270)(148,269)(149,268)(150,267)(151,266)(152,265)(153,264)(154,263)(155,262)(156,261)(157,260)(158,259)(159,258)(160,257)(161,256)(162,255)(163,254)(164,253)(165,252)(166,251)(333,499)(334,581)(335,580)(336,579)(337,578)(338,577)(339,576)(340,575)(341,574)(342,573)(343,572)(344,571)(345,570)(346,569)(347,568)(348,567)(349,566)(350,565)(351,564)(352,563)(353,562)(354,561)(355,560)(356,559)(357,558)(358,557)(359,556)(360,555)(361,554)(362,553)(363,552)(364,551)(365,550)(366,549)(367,548)(368,547)(369,546)(370,545)(371,544)(372,543)(373,542)(374,541)(375,540)(376,539)(377,538)(378,537)(379,536)(380,535)(381,534)(382,533)(383,532)(384,531)(385,530)(386,529)(387,528)(388,527)(389,526)(390,525)(391,524)(392,523)(393,522)(394,521)(395,520)(396,519)(397,518)(398,517)(399,516)(400,515)(401,514)(402,513)(403,512)(404,511)(405,510)(406,509)(407,508)(408,507)(409,506)(410,505)(411,504)(412,503)(413,502)(414,501)(415,500)(416,582)(417,664)(418,663)(419,662)(420,661)(421,660)(422,659)(423,658)(424,657)(425,656)(426,655)(427,654)(428,653)(429,652)(430,651)(431,650)(432,649)(433,648)(434,647)(435,646)(436,645)(437,644)(438,643)(439,642)(440,641)(441,640)(442,639)(443,638)(444,637)(445,636)(446,635)(447,634)(448,633)(449,632)(450,631)(451,630)(452,629)(453,628)(454,627)(455,626)(456,625)(457,624)(458,623)(459,622)(460,621)(461,620)(462,619)(463,618)(464,617)(465,616)(466,615)(467,614)(468,613)(469,612)(470,611)(471,610)(472,609)(473,608)(474,607)(475,606)(476,605)(477,604)(478,603)(479,602)(480,601)(481,600)(482,599)(483,598)(484,597)(485,596)(486,595)(487,594)(488,593)(489,592)(490,591)(491,590)(492,589)(493,588)(494,587)(495,586)(496,585)(497,584)(498,583);
s1 := Sym(664)!(  1,168)(  2,167)(  3,249)(  4,248)(  5,247)(  6,246)(  7,245)(  8,244)(  9,243)( 10,242)( 11,241)( 12,240)( 13,239)( 14,238)( 15,237)( 16,236)( 17,235)( 18,234)( 19,233)( 20,232)( 21,231)( 22,230)( 23,229)( 24,228)( 25,227)( 26,226)( 27,225)( 28,224)( 29,223)( 30,222)( 31,221)( 32,220)( 33,219)( 34,218)( 35,217)( 36,216)( 37,215)( 38,214)( 39,213)( 40,212)( 41,211)( 42,210)( 43,209)( 44,208)( 45,207)( 46,206)( 47,205)( 48,204)( 49,203)( 50,202)( 51,201)( 52,200)( 53,199)( 54,198)( 55,197)( 56,196)( 57,195)( 58,194)( 59,193)( 60,192)( 61,191)( 62,190)( 63,189)( 64,188)( 65,187)( 66,186)( 67,185)( 68,184)( 69,183)( 70,182)( 71,181)( 72,180)( 73,179)( 74,178)( 75,177)( 76,176)( 77,175)( 78,174)( 79,173)( 80,172)( 81,171)( 82,170)( 83,169)( 84,251)( 85,250)( 86,332)( 87,331)( 88,330)( 89,329)( 90,328)( 91,327)( 92,326)( 93,325)( 94,324)( 95,323)( 96,322)( 97,321)( 98,320)( 99,319)(100,318)(101,317)(102,316)(103,315)(104,314)(105,313)(106,312)(107,311)(108,310)(109,309)(110,308)(111,307)(112,306)(113,305)(114,304)(115,303)(116,302)(117,301)(118,300)(119,299)(120,298)(121,297)(122,296)(123,295)(124,294)(125,293)(126,292)(127,291)(128,290)(129,289)(130,288)(131,287)(132,286)(133,285)(134,284)(135,283)(136,282)(137,281)(138,280)(139,279)(140,278)(141,277)(142,276)(143,275)(144,274)(145,273)(146,272)(147,271)(148,270)(149,269)(150,268)(151,267)(152,266)(153,265)(154,264)(155,263)(156,262)(157,261)(158,260)(159,259)(160,258)(161,257)(162,256)(163,255)(164,254)(165,253)(166,252)(333,583)(334,582)(335,664)(336,663)(337,662)(338,661)(339,660)(340,659)(341,658)(342,657)(343,656)(344,655)(345,654)(346,653)(347,652)(348,651)(349,650)(350,649)(351,648)(352,647)(353,646)(354,645)(355,644)(356,643)(357,642)(358,641)(359,640)(360,639)(361,638)(362,637)(363,636)(364,635)(365,634)(366,633)(367,632)(368,631)(369,630)(370,629)(371,628)(372,627)(373,626)(374,625)(375,624)(376,623)(377,622)(378,621)(379,620)(380,619)(381,618)(382,617)(383,616)(384,615)(385,614)(386,613)(387,612)(388,611)(389,610)(390,609)(391,608)(392,607)(393,606)(394,605)(395,604)(396,603)(397,602)(398,601)(399,600)(400,599)(401,598)(402,597)(403,596)(404,595)(405,594)(406,593)(407,592)(408,591)(409,590)(410,589)(411,588)(412,587)(413,586)(414,585)(415,584)(416,500)(417,499)(418,581)(419,580)(420,579)(421,578)(422,577)(423,576)(424,575)(425,574)(426,573)(427,572)(428,571)(429,570)(430,569)(431,568)(432,567)(433,566)(434,565)(435,564)(436,563)(437,562)(438,561)(439,560)(440,559)(441,558)(442,557)(443,556)(444,555)(445,554)(446,553)(447,552)(448,551)(449,550)(450,549)(451,548)(452,547)(453,546)(454,545)(455,544)(456,543)(457,542)(458,541)(459,540)(460,539)(461,538)(462,537)(463,536)(464,535)(465,534)(466,533)(467,532)(468,531)(469,530)(470,529)(471,528)(472,527)(473,526)(474,525)(475,524)(476,523)(477,522)(478,521)(479,520)(480,519)(481,518)(482,517)(483,516)(484,515)(485,514)(486,513)(487,512)(488,511)(489,510)(490,509)(491,508)(492,507)(493,506)(494,505)(495,504)(496,503)(497,502)(498,501);
s2 := Sym(664)!(  1,333)(  2,334)(  3,335)(  4,336)(  5,337)(  6,338)(  7,339)(  8,340)(  9,341)( 10,342)( 11,343)( 12,344)( 13,345)( 14,346)( 15,347)( 16,348)( 17,349)( 18,350)( 19,351)( 20,352)( 21,353)( 22,354)( 23,355)( 24,356)( 25,357)( 26,358)( 27,359)( 28,360)( 29,361)( 30,362)( 31,363)( 32,364)( 33,365)( 34,366)( 35,367)( 36,368)( 37,369)( 38,370)( 39,371)( 40,372)( 41,373)( 42,374)( 43,375)( 44,376)( 45,377)( 46,378)( 47,379)( 48,380)( 49,381)( 50,382)( 51,383)( 52,384)( 53,385)( 54,386)( 55,387)( 56,388)( 57,389)( 58,390)( 59,391)( 60,392)( 61,393)( 62,394)( 63,395)( 64,396)( 65,397)( 66,398)( 67,399)( 68,400)( 69,401)( 70,402)( 71,403)( 72,404)( 73,405)( 74,406)( 75,407)( 76,408)( 77,409)( 78,410)( 79,411)( 80,412)( 81,413)( 82,414)( 83,415)( 84,416)( 85,417)( 86,418)( 87,419)( 88,420)( 89,421)( 90,422)( 91,423)( 92,424)( 93,425)( 94,426)( 95,427)( 96,428)( 97,429)( 98,430)( 99,431)(100,432)(101,433)(102,434)(103,435)(104,436)(105,437)(106,438)(107,439)(108,440)(109,441)(110,442)(111,443)(112,444)(113,445)(114,446)(115,447)(116,448)(117,449)(118,450)(119,451)(120,452)(121,453)(122,454)(123,455)(124,456)(125,457)(126,458)(127,459)(128,460)(129,461)(130,462)(131,463)(132,464)(133,465)(134,466)(135,467)(136,468)(137,469)(138,470)(139,471)(140,472)(141,473)(142,474)(143,475)(144,476)(145,477)(146,478)(147,479)(148,480)(149,481)(150,482)(151,483)(152,484)(153,485)(154,486)(155,487)(156,488)(157,489)(158,490)(159,491)(160,492)(161,493)(162,494)(163,495)(164,496)(165,497)(166,498)(167,499)(168,500)(169,501)(170,502)(171,503)(172,504)(173,505)(174,506)(175,507)(176,508)(177,509)(178,510)(179,511)(180,512)(181,513)(182,514)(183,515)(184,516)(185,517)(186,518)(187,519)(188,520)(189,521)(190,522)(191,523)(192,524)(193,525)(194,526)(195,527)(196,528)(197,529)(198,530)(199,531)(200,532)(201,533)(202,534)(203,535)(204,536)(205,537)(206,538)(207,539)(208,540)(209,541)(210,542)(211,543)(212,544)(213,545)(214,546)(215,547)(216,548)(217,549)(218,550)(219,551)(220,552)(221,553)(222,554)(223,555)(224,556)(225,557)(226,558)(227,559)(228,560)(229,561)(230,562)(231,563)(232,564)(233,565)(234,566)(235,567)(236,568)(237,569)(238,570)(239,571)(240,572)(241,573)(242,574)(243,575)(244,576)(245,577)(246,578)(247,579)(248,580)(249,581)(250,582)(251,583)(252,584)(253,585)(254,586)(255,587)(256,588)(257,589)(258,590)(259,591)(260,592)(261,593)(262,594)(263,595)(264,596)(265,597)(266,598)(267,599)(268,600)(269,601)(270,602)(271,603)(272,604)(273,605)(274,606)(275,607)(276,608)(277,609)(278,610)(279,611)(280,612)(281,613)(282,614)(283,615)(284,616)(285,617)(286,618)(287,619)(288,620)(289,621)(290,622)(291,623)(292,624)(293,625)(294,626)(295,627)(296,628)(297,629)(298,630)(299,631)(300,632)(301,633)(302,634)(303,635)(304,636)(305,637)(306,638)(307,639)(308,640)(309,641)(310,642)(311,643)(312,644)(313,645)(314,646)(315,647)(316,648)(317,649)(318,650)(319,651)(320,652)(321,653)(322,654)(323,655)(324,656)(325,657)(326,658)(327,659)(328,660)(329,661)(330,662)(331,663)(332,664);
poly := sub<Sym(664)|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*s0*s1*s0*s1 >; 
 

Twisty Puzzle