Polytope of Type {4,160}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle