Polytope of Type {39,8}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle