Polytope of Type {152,4}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle