Polytope of Type {8,76}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle