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)( 39,343)( 40,361)( 41,360)( 42,359)( 43,358)( 44,357)( 45,356)( 46,355)( 47,354)( 48,353)( 49,352)( 50,351)( 51,350)( 52,349)( 53,348)( 54,347)( 55,346)( 56,345)( 57,344)( 58,362)( 59,380)( 60,379)( 61,378)( 62,377)( 63,376)( 64,375)( 65,374)( 66,373)( 67,372)( 68,371)( 69,370)( 70,369)( 71,368)( 72,367)( 73,366)( 74,365)( 75,364)( 76,363)( 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)(115,438)(116,456)(117,455)(118,454)(119,453)(120,452)(121,451)(122,450)(123,449)(124,448)(125,447)(126,446)(127,445)(128,444)(129,443)(130,442)(131,441)(132,440)(133,439)(134,419)(135,437)(136,436)(137,435)(138,434)(139,433)(140,432)(141,431)(142,430)(143,429)(144,428)(145,427)(146,426)(147,425)(148,424)(149,423)(150,422)(151,421)(152,420)(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)(191,495)(192,513)(193,512)(194,511)(195,510)(196,509)(197,508)(198,507)(199,506)(200,505)(201,504)(202,503)(203,502)(204,501)(205,500)(206,499)(207,498)(208,497)(209,496)(210,514)(211,532)(212,531)(213,530)(214,529)(215,528)(216,527)(217,526)(218,525)(219,524)(220,523)(221,522)(222,521)(223,520)(224,519)(225,518)(226,517)(227,516)(228,515)(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)(267,590)(268,608)(269,607)(270,606)(271,605)(272,604)(273,603)(274,602)(275,601)(276,600)(277,599)(278,598)(279,597)(280,596)(281,595)(282,594)(283,593)(284,592)(285,591)(286,571)(287,589)(288,588)(289,587)(290,586)(291,585)(292,584)(293,583)(294,582)(295,581)(296,580)(297,579)(298,578)(299,577)(300,576)(301,575)(302,574)(303,573)(304,572);;
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)(457,572)(458,571)(459,589)(460,588)(461,587)(462,586)(463,585)(464,584)(465,583)(466,582)(467,581)(468,580)(469,579)(470,578)(471,577)(472,576)(473,575)(474,574)(475,573)(476,591)(477,590)(478,608)(479,607)(480,606)(481,605)(482,604)(483,603)(484,602)(485,601)(486,600)(487,599)(488,598)(489,597)(490,596)(491,595)(492,594)(493,593)(494,592)(495,534)(496,533)(497,551)(498,550)(499,549)(500,548)(501,547)(502,546)(503,545)(504,544)(505,543)(506,542)(507,541)(508,540)(509,539)(510,538)(511,537)(512,536)(513,535)(514,553)(515,552)(516,570)(517,569)(518,568)(519,567)(520,566)(521,565)(522,564)(523,563)(524,562)(525,561)(526,560)(527,559)(528,558)(529,557)(530,556)(531,555)(532,554);;
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)( 77,229)( 78,230)( 79,231)( 80,232)( 81,233)( 82,234)( 83,235)( 84,236)( 85,237)( 86,238)( 87,239)( 88,240)( 89,241)( 90,242)( 91,243)( 92,244)( 93,245)( 94,246)( 95,247)( 96,248)( 97,249)( 98,250)( 99,251)(100,252)(101,253)(102,254)(103,255)(104,256)(105,257)(106,258)(107,259)(108,260)(109,261)(110,262)(111,263)(112,264)(113,265)(114,266)(115,267)(116,268)(117,269)(118,270)(119,271)(120,272)(121,273)(122,274)(123,275)(124,276)(125,277)(126,278)(127,279)(128,280)(129,281)(130,282)(131,283)(132,284)(133,285)(134,286)(135,287)(136,288)(137,289)(138,290)(139,291)(140,292)(141,293)(142,294)(143,295)(144,296)(145,297)(146,298)(147,299)(148,300)(149,301)(150,302)(151,303)(152,304)(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)(381,533)(382,534)(383,535)(384,536)(385,537)(386,538)(387,539)(388,540)(389,541)(390,542)(391,543)(392,544)(393,545)(394,546)(395,547)(396,548)(397,549)(398,550)(399,551)(400,552)(401,553)(402,554)(403,555)(404,556)(405,557)(406,558)(407,559)(408,560)(409,561)(410,562)(411,563)(412,564)(413,565)(414,566)(415,567)(416,568)(417,569)(418,570)(419,571)(420,572)(421,573)(422,574)(423,575)(424,576)(425,577)(426,578)(427,579)(428,580)(429,581)(430,582)(431,583)(432,584)(433,585)(434,586)(435,587)(436,588)(437,589)(438,590)(439,591)(440,592)(441,593)(442,594)(443,595)(444,596)(445,597)(446,598)(447,599)(448,600)(449,601)(450,602)(451,603)(452,604)(453,605)(454,606)(455,607)(456,608);;
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 ];;
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)( 39,343)( 40,361)( 41,360)( 42,359)( 43,358)( 44,357)( 45,356)( 46,355)( 47,354)( 48,353)( 49,352)( 50,351)( 51,350)( 52,349)( 53,348)( 54,347)( 55,346)( 56,345)( 57,344)( 58,362)( 59,380)( 60,379)( 61,378)( 62,377)( 63,376)( 64,375)( 65,374)( 66,373)( 67,372)( 68,371)( 69,370)( 70,369)( 71,368)( 72,367)( 73,366)( 74,365)( 75,364)( 76,363)( 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)(115,438)(116,456)(117,455)(118,454)(119,453)(120,452)(121,451)(122,450)(123,449)(124,448)(125,447)(126,446)(127,445)(128,444)(129,443)(130,442)(131,441)(132,440)(133,439)(134,419)(135,437)(136,436)(137,435)(138,434)(139,433)(140,432)(141,431)(142,430)(143,429)(144,428)(145,427)(146,426)(147,425)(148,424)(149,423)(150,422)(151,421)(152,420)(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)(191,495)(192,513)(193,512)(194,511)(195,510)(196,509)(197,508)(198,507)(199,506)(200,505)(201,504)(202,503)(203,502)(204,501)(205,500)(206,499)(207,498)(208,497)(209,496)(210,514)(211,532)(212,531)(213,530)(214,529)(215,528)(216,527)(217,526)(218,525)(219,524)(220,523)(221,522)(222,521)(223,520)(224,519)(225,518)(226,517)(227,516)(228,515)(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)(267,590)(268,608)(269,607)(270,606)(271,605)(272,604)(273,603)(274,602)(275,601)(276,600)(277,599)(278,598)(279,597)(280,596)(281,595)(282,594)(283,593)(284,592)(285,591)(286,571)(287,589)(288,588)(289,587)(290,586)(291,585)(292,584)(293,583)(294,582)(295,581)(296,580)(297,579)(298,578)(299,577)(300,576)(301,575)(302,574)(303,573)(304,572);
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)(457,572)(458,571)(459,589)(460,588)(461,587)(462,586)(463,585)(464,584)(465,583)(466,582)(467,581)(468,580)(469,579)(470,578)(471,577)(472,576)(473,575)(474,574)(475,573)(476,591)(477,590)(478,608)(479,607)(480,606)(481,605)(482,604)(483,603)(484,602)(485,601)(486,600)(487,599)(488,598)(489,597)(490,596)(491,595)(492,594)(493,593)(494,592)(495,534)(496,533)(497,551)(498,550)(499,549)(500,548)(501,547)(502,546)(503,545)(504,544)(505,543)(506,542)(507,541)(508,540)(509,539)(510,538)(511,537)(512,536)(513,535)(514,553)(515,552)(516,570)(517,569)(518,568)(519,567)(520,566)(521,565)(522,564)(523,563)(524,562)(525,561)(526,560)(527,559)(528,558)(529,557)(530,556)(531,555)(532,554);
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)( 77,229)( 78,230)( 79,231)( 80,232)( 81,233)( 82,234)( 83,235)( 84,236)( 85,237)( 86,238)( 87,239)( 88,240)( 89,241)( 90,242)( 91,243)( 92,244)( 93,245)( 94,246)( 95,247)( 96,248)( 97,249)( 98,250)( 99,251)(100,252)(101,253)(102,254)(103,255)(104,256)(105,257)(106,258)(107,259)(108,260)(109,261)(110,262)(111,263)(112,264)(113,265)(114,266)(115,267)(116,268)(117,269)(118,270)(119,271)(120,272)(121,273)(122,274)(123,275)(124,276)(125,277)(126,278)(127,279)(128,280)(129,281)(130,282)(131,283)(132,284)(133,285)(134,286)(135,287)(136,288)(137,289)(138,290)(139,291)(140,292)(141,293)(142,294)(143,295)(144,296)(145,297)(146,298)(147,299)(148,300)(149,301)(150,302)(151,303)(152,304)(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)(381,533)(382,534)(383,535)(384,536)(385,537)(386,538)(387,539)(388,540)(389,541)(390,542)(391,543)(392,544)(393,545)(394,546)(395,547)(396,548)(397,549)(398,550)(399,551)(400,552)(401,553)(402,554)(403,555)(404,556)(405,557)(406,558)(407,559)(408,560)(409,561)(410,562)(411,563)(412,564)(413,565)(414,566)(415,567)(416,568)(417,569)(418,570)(419,571)(420,572)(421,573)(422,574)(423,575)(424,576)(425,577)(426,578)(427,579)(428,580)(429,581)(430,582)(431,583)(432,584)(433,585)(434,586)(435,587)(436,588)(437,589)(438,590)(439,591)(440,592)(441,593)(442,594)(443,595)(444,596)(445,597)(446,598)(447,599)(448,600)(449,601)(450,602)(451,603)(452,604)(453,605)(454,606)(455,607)(456,608);
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, 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 >; 
 

Twisty Puzzle