Polytope of Type {160,4}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle