Polytope of Type {76,8}

Play with this polytope as a twisty puzzle

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