Polytope of Type {168,4}

Play with this polytope as a twisty puzzle

s0 := (  3,  4)(  5, 25)(  6, 26)(  7, 28)(  8, 27)(  9, 21)( 10, 22)( 11, 24)( 12, 23)( 13, 17)( 14, 18)( 15, 20)( 16, 19)( 29, 57)( 30, 58)( 31, 60)( 32, 59)( 33, 81)( 34, 82)( 35, 84)( 36, 83)( 37, 77)( 38, 78)( 39, 80)( 40, 79)( 41, 73)( 42, 74)( 43, 76)( 44, 75)( 45, 69)( 46, 70)( 47, 72)( 48, 71)( 49, 65)( 50, 66)( 51, 68)( 52, 67)( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 87, 88)( 89,109)( 90,110)( 91,112)( 92,111)( 93,105)( 94,106)( 95,108)( 96,107)( 97,101)( 98,102)( 99,104)(100,103)(113,141)(114,142)(115,144)(116,143)(117,165)(118,166)(119,168)(120,167)(121,161)(122,162)(123,164)(124,163)(125,157)(126,158)(127,160)(128,159)(129,153)(130,154)(131,156)(132,155)(133,149)(134,150)(135,152)(136,151)(137,145)(138,146)(139,148)(140,147)(169,253)(170,254)(171,256)(172,255)(173,277)(174,278)(175,280)(176,279)(177,273)(178,274)(179,276)(180,275)(181,269)(182,270)(183,272)(184,271)(185,265)(186,266)(187,268)(188,267)(189,261)(190,262)(191,264)(192,263)(193,257)(194,258)(195,260)(196,259)(197,309)(198,310)(199,312)(200,311)(201,333)(202,334)(203,336)(204,335)(205,329)(206,330)(207,332)(208,331)(209,325)(210,326)(211,328)(212,327)(213,321)(214,322)(215,324)(216,323)(217,317)(218,318)(219,320)(220,319)(221,313)(222,314)(223,316)(224,315)(225,281)(226,282)(227,284)(228,283)(229,305)(230,306)(231,308)(232,307)(233,301)(234,302)(235,304)(236,303)(237,297)(238,298)(239,300)(240,299)(241,293)(242,294)(243,296)(244,295)(245,289)(246,290)(247,292)(248,291)(249,285)(250,286)(251,288)(252,287)(337,505)(338,506)(339,508)(340,507)(341,529)(342,530)(343,532)(344,531)(345,525)(346,526)(347,528)(348,527)(349,521)(350,522)(351,524)(352,523)(353,517)(354,518)(355,520)(356,519)(357,513)(358,514)(359,516)(360,515)(361,509)(362,510)(363,512)(364,511)(365,561)(366,562)(367,564)(368,563)(369,585)(370,586)(371,588)(372,587)(373,581)(374,582)(375,584)(376,583)(377,577)(378,578)(379,580)(380,579)(381,573)(382,574)(383,576)(384,575)(385,569)(386,570)(387,572)(388,571)(389,565)(390,566)(391,568)(392,567)(393,533)(394,534)(395,536)(396,535)(397,557)(398,558)(399,560)(400,559)(401,553)(402,554)(403,556)(404,555)(405,549)(406,550)(407,552)(408,551)(409,545)(410,546)(411,548)(412,547)(413,541)(414,542)(415,544)(416,543)(417,537)(418,538)(419,540)(420,539)(421,589)(422,590)(423,592)(424,591)(425,613)(426,614)(427,616)(428,615)(429,609)(430,610)(431,612)(432,611)(433,605)(434,606)(435,608)(436,607)(437,601)(438,602)(439,604)(440,603)(441,597)(442,598)(443,600)(444,599)(445,593)(446,594)(447,596)(448,595)(449,645)(450,646)(451,648)(452,647)(453,669)(454,670)(455,672)(456,671)(457,665)(458,666)(459,668)(460,667)(461,661)(462,662)(463,664)(464,663)(465,657)(466,658)(467,660)(468,659)(469,653)(470,654)(471,656)(472,655)(473,649)(474,650)(475,652)(476,651)(477,617)(478,618)(479,620)(480,619)(481,641)(482,642)(483,644)(484,643)(485,637)(486,638)(487,640)(488,639)(489,633)(490,634)(491,636)(492,635)(493,629)(494,630)(495,632)(496,631)(497,625)(498,626)(499,628)(500,627)(501,621)(502,622)(503,624)(504,623);;
s1 := (  1,369)(  2,372)(  3,371)(  4,370)(  5,365)(  6,368)(  7,367)(  8,366)(  9,389)( 10,392)( 11,391)( 12,390)( 13,385)( 14,388)( 15,387)( 16,386)( 17,381)( 18,384)( 19,383)( 20,382)( 21,377)( 22,380)( 23,379)( 24,378)( 25,373)( 26,376)( 27,375)( 28,374)( 29,341)( 30,344)( 31,343)( 32,342)( 33,337)( 34,340)( 35,339)( 36,338)( 37,361)( 38,364)( 39,363)( 40,362)( 41,357)( 42,360)( 43,359)( 44,358)( 45,353)( 46,356)( 47,355)( 48,354)( 49,349)( 50,352)( 51,351)( 52,350)( 53,345)( 54,348)( 55,347)( 56,346)( 57,397)( 58,400)( 59,399)( 60,398)( 61,393)( 62,396)( 63,395)( 64,394)( 65,417)( 66,420)( 67,419)( 68,418)( 69,413)( 70,416)( 71,415)( 72,414)( 73,409)( 74,412)( 75,411)( 76,410)( 77,405)( 78,408)( 79,407)( 80,406)( 81,401)( 82,404)( 83,403)( 84,402)( 85,453)( 86,456)( 87,455)( 88,454)( 89,449)( 90,452)( 91,451)( 92,450)( 93,473)( 94,476)( 95,475)( 96,474)( 97,469)( 98,472)( 99,471)(100,470)(101,465)(102,468)(103,467)(104,466)(105,461)(106,464)(107,463)(108,462)(109,457)(110,460)(111,459)(112,458)(113,425)(114,428)(115,427)(116,426)(117,421)(118,424)(119,423)(120,422)(121,445)(122,448)(123,447)(124,446)(125,441)(126,444)(127,443)(128,442)(129,437)(130,440)(131,439)(132,438)(133,433)(134,436)(135,435)(136,434)(137,429)(138,432)(139,431)(140,430)(141,481)(142,484)(143,483)(144,482)(145,477)(146,480)(147,479)(148,478)(149,501)(150,504)(151,503)(152,502)(153,497)(154,500)(155,499)(156,498)(157,493)(158,496)(159,495)(160,494)(161,489)(162,492)(163,491)(164,490)(165,485)(166,488)(167,487)(168,486)(169,621)(170,624)(171,623)(172,622)(173,617)(174,620)(175,619)(176,618)(177,641)(178,644)(179,643)(180,642)(181,637)(182,640)(183,639)(184,638)(185,633)(186,636)(187,635)(188,634)(189,629)(190,632)(191,631)(192,630)(193,625)(194,628)(195,627)(196,626)(197,593)(198,596)(199,595)(200,594)(201,589)(202,592)(203,591)(204,590)(205,613)(206,616)(207,615)(208,614)(209,609)(210,612)(211,611)(212,610)(213,605)(214,608)(215,607)(216,606)(217,601)(218,604)(219,603)(220,602)(221,597)(222,600)(223,599)(224,598)(225,649)(226,652)(227,651)(228,650)(229,645)(230,648)(231,647)(232,646)(233,669)(234,672)(235,671)(236,670)(237,665)(238,668)(239,667)(240,666)(241,661)(242,664)(243,663)(244,662)(245,657)(246,660)(247,659)(248,658)(249,653)(250,656)(251,655)(252,654)(253,537)(254,540)(255,539)(256,538)(257,533)(258,536)(259,535)(260,534)(261,557)(262,560)(263,559)(264,558)(265,553)(266,556)(267,555)(268,554)(269,549)(270,552)(271,551)(272,550)(273,545)(274,548)(275,547)(276,546)(277,541)(278,544)(279,543)(280,542)(281,509)(282,512)(283,511)(284,510)(285,505)(286,508)(287,507)(288,506)(289,529)(290,532)(291,531)(292,530)(293,525)(294,528)(295,527)(296,526)(297,521)(298,524)(299,523)(300,522)(301,517)(302,520)(303,519)(304,518)(305,513)(306,516)(307,515)(308,514)(309,565)(310,568)(311,567)(312,566)(313,561)(314,564)(315,563)(316,562)(317,585)(318,588)(319,587)(320,586)(321,581)(322,584)(323,583)(324,582)(325,577)(326,580)(327,579)(328,578)(329,573)(330,576)(331,575)(332,574)(333,569)(334,572)(335,571)(336,570);;
s2 := (  1, 86)(  2, 85)(  3, 88)(  4, 87)(  5, 90)(  6, 89)(  7, 92)(  8, 91)(  9, 94)( 10, 93)( 11, 96)( 12, 95)( 13, 98)( 14, 97)( 15,100)( 16, 99)( 17,102)( 18,101)( 19,104)( 20,103)( 21,106)( 22,105)( 23,108)( 24,107)( 25,110)( 26,109)( 27,112)( 28,111)( 29,114)( 30,113)( 31,116)( 32,115)( 33,118)( 34,117)( 35,120)( 36,119)( 37,122)( 38,121)( 39,124)( 40,123)( 41,126)( 42,125)( 43,128)( 44,127)( 45,130)( 46,129)( 47,132)( 48,131)( 49,134)( 50,133)( 51,136)( 52,135)( 53,138)( 54,137)( 55,140)( 56,139)( 57,142)( 58,141)( 59,144)( 60,143)( 61,146)( 62,145)( 63,148)( 64,147)( 65,150)( 66,149)( 67,152)( 68,151)( 69,154)( 70,153)( 71,156)( 72,155)( 73,158)( 74,157)( 75,160)( 76,159)( 77,162)( 78,161)( 79,164)( 80,163)( 81,166)( 82,165)( 83,168)( 84,167)(169,254)(170,253)(171,256)(172,255)(173,258)(174,257)(175,260)(176,259)(177,262)(178,261)(179,264)(180,263)(181,266)(182,265)(183,268)(184,267)(185,270)(186,269)(187,272)(188,271)(189,274)(190,273)(191,276)(192,275)(193,278)(194,277)(195,280)(196,279)(197,282)(198,281)(199,284)(200,283)(201,286)(202,285)(203,288)(204,287)(205,290)(206,289)(207,292)(208,291)(209,294)(210,293)(211,296)(212,295)(213,298)(214,297)(215,300)(216,299)(217,302)(218,301)(219,304)(220,303)(221,306)(222,305)(223,308)(224,307)(225,310)(226,309)(227,312)(228,311)(229,314)(230,313)(231,316)(232,315)(233,318)(234,317)(235,320)(236,319)(237,322)(238,321)(239,324)(240,323)(241,326)(242,325)(243,328)(244,327)(245,330)(246,329)(247,332)(248,331)(249,334)(250,333)(251,336)(252,335)(337,422)(338,421)(339,424)(340,423)(341,426)(342,425)(343,428)(344,427)(345,430)(346,429)(347,432)(348,431)(349,434)(350,433)(351,436)(352,435)(353,438)(354,437)(355,440)(356,439)(357,442)(358,441)(359,444)(360,443)(361,446)(362,445)(363,448)(364,447)(365,450)(366,449)(367,452)(368,451)(369,454)(370,453)(371,456)(372,455)(373,458)(374,457)(375,460)(376,459)(377,462)(378,461)(379,464)(380,463)(381,466)(382,465)(383,468)(384,467)(385,470)(386,469)(387,472)(388,471)(389,474)(390,473)(391,476)(392,475)(393,478)(394,477)(395,480)(396,479)(397,482)(398,481)(399,484)(400,483)(401,486)(402,485)(403,488)(404,487)(405,490)(406,489)(407,492)(408,491)(409,494)(410,493)(411,496)(412,495)(413,498)(414,497)(415,500)(416,499)(417,502)(418,501)(419,504)(420,503)(505,590)(506,589)(507,592)(508,591)(509,594)(510,593)(511,596)(512,595)(513,598)(514,597)(515,600)(516,599)(517,602)(518,601)(519,604)(520,603)(521,606)(522,605)(523,608)(524,607)(525,610)(526,609)(527,612)(528,611)(529,614)(530,613)(531,616)(532,615)(533,618)(534,617)(535,620)(536,619)(537,622)(538,621)(539,624)(540,623)(541,626)(542,625)(543,628)(544,627)(545,630)(546,629)(547,632)(548,631)(549,634)(550,633)(551,636)(552,635)(553,638)(554,637)(555,640)(556,639)(557,642)(558,641)(559,644)(560,643)(561,646)(562,645)(563,648)(564,647)(565,650)(566,649)(567,652)(568,651)(569,654)(570,653)(571,656)(572,655)(573,658)(574,657)(575,660)(576,659)(577,662)(578,661)(579,664)(580,663)(581,666)(582,665)(583,668)(584,667)(585,670)(586,669)(587,672)(588,671);;
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*s1*s0*s1*s2*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*s2*s0*s1*s2*s0*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 ];;
poly := F / rels;;
 

s0 := Sym(672)!(  3,  4)(  5, 25)(  6, 26)(  7, 28)(  8, 27)(  9, 21)( 10, 22)( 11, 24)( 12, 23)( 13, 17)( 14, 18)( 15, 20)( 16, 19)( 29, 57)( 30, 58)( 31, 60)( 32, 59)( 33, 81)( 34, 82)( 35, 84)( 36, 83)( 37, 77)( 38, 78)( 39, 80)( 40, 79)( 41, 73)( 42, 74)( 43, 76)( 44, 75)( 45, 69)( 46, 70)( 47, 72)( 48, 71)( 49, 65)( 50, 66)( 51, 68)( 52, 67)( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 87, 88)( 89,109)( 90,110)( 91,112)( 92,111)( 93,105)( 94,106)( 95,108)( 96,107)( 97,101)( 98,102)( 99,104)(100,103)(113,141)(114,142)(115,144)(116,143)(117,165)(118,166)(119,168)(120,167)(121,161)(122,162)(123,164)(124,163)(125,157)(126,158)(127,160)(128,159)(129,153)(130,154)(131,156)(132,155)(133,149)(134,150)(135,152)(136,151)(137,145)(138,146)(139,148)(140,147)(169,253)(170,254)(171,256)(172,255)(173,277)(174,278)(175,280)(176,279)(177,273)(178,274)(179,276)(180,275)(181,269)(182,270)(183,272)(184,271)(185,265)(186,266)(187,268)(188,267)(189,261)(190,262)(191,264)(192,263)(193,257)(194,258)(195,260)(196,259)(197,309)(198,310)(199,312)(200,311)(201,333)(202,334)(203,336)(204,335)(205,329)(206,330)(207,332)(208,331)(209,325)(210,326)(211,328)(212,327)(213,321)(214,322)(215,324)(216,323)(217,317)(218,318)(219,320)(220,319)(221,313)(222,314)(223,316)(224,315)(225,281)(226,282)(227,284)(228,283)(229,305)(230,306)(231,308)(232,307)(233,301)(234,302)(235,304)(236,303)(237,297)(238,298)(239,300)(240,299)(241,293)(242,294)(243,296)(244,295)(245,289)(246,290)(247,292)(248,291)(249,285)(250,286)(251,288)(252,287)(337,505)(338,506)(339,508)(340,507)(341,529)(342,530)(343,532)(344,531)(345,525)(346,526)(347,528)(348,527)(349,521)(350,522)(351,524)(352,523)(353,517)(354,518)(355,520)(356,519)(357,513)(358,514)(359,516)(360,515)(361,509)(362,510)(363,512)(364,511)(365,561)(366,562)(367,564)(368,563)(369,585)(370,586)(371,588)(372,587)(373,581)(374,582)(375,584)(376,583)(377,577)(378,578)(379,580)(380,579)(381,573)(382,574)(383,576)(384,575)(385,569)(386,570)(387,572)(388,571)(389,565)(390,566)(391,568)(392,567)(393,533)(394,534)(395,536)(396,535)(397,557)(398,558)(399,560)(400,559)(401,553)(402,554)(403,556)(404,555)(405,549)(406,550)(407,552)(408,551)(409,545)(410,546)(411,548)(412,547)(413,541)(414,542)(415,544)(416,543)(417,537)(418,538)(419,540)(420,539)(421,589)(422,590)(423,592)(424,591)(425,613)(426,614)(427,616)(428,615)(429,609)(430,610)(431,612)(432,611)(433,605)(434,606)(435,608)(436,607)(437,601)(438,602)(439,604)(440,603)(441,597)(442,598)(443,600)(444,599)(445,593)(446,594)(447,596)(448,595)(449,645)(450,646)(451,648)(452,647)(453,669)(454,670)(455,672)(456,671)(457,665)(458,666)(459,668)(460,667)(461,661)(462,662)(463,664)(464,663)(465,657)(466,658)(467,660)(468,659)(469,653)(470,654)(471,656)(472,655)(473,649)(474,650)(475,652)(476,651)(477,617)(478,618)(479,620)(480,619)(481,641)(482,642)(483,644)(484,643)(485,637)(486,638)(487,640)(488,639)(489,633)(490,634)(491,636)(492,635)(493,629)(494,630)(495,632)(496,631)(497,625)(498,626)(499,628)(500,627)(501,621)(502,622)(503,624)(504,623);
s1 := Sym(672)!(  1,369)(  2,372)(  3,371)(  4,370)(  5,365)(  6,368)(  7,367)(  8,366)(  9,389)( 10,392)( 11,391)( 12,390)( 13,385)( 14,388)( 15,387)( 16,386)( 17,381)( 18,384)( 19,383)( 20,382)( 21,377)( 22,380)( 23,379)( 24,378)( 25,373)( 26,376)( 27,375)( 28,374)( 29,341)( 30,344)( 31,343)( 32,342)( 33,337)( 34,340)( 35,339)( 36,338)( 37,361)( 38,364)( 39,363)( 40,362)( 41,357)( 42,360)( 43,359)( 44,358)( 45,353)( 46,356)( 47,355)( 48,354)( 49,349)( 50,352)( 51,351)( 52,350)( 53,345)( 54,348)( 55,347)( 56,346)( 57,397)( 58,400)( 59,399)( 60,398)( 61,393)( 62,396)( 63,395)( 64,394)( 65,417)( 66,420)( 67,419)( 68,418)( 69,413)( 70,416)( 71,415)( 72,414)( 73,409)( 74,412)( 75,411)( 76,410)( 77,405)( 78,408)( 79,407)( 80,406)( 81,401)( 82,404)( 83,403)( 84,402)( 85,453)( 86,456)( 87,455)( 88,454)( 89,449)( 90,452)( 91,451)( 92,450)( 93,473)( 94,476)( 95,475)( 96,474)( 97,469)( 98,472)( 99,471)(100,470)(101,465)(102,468)(103,467)(104,466)(105,461)(106,464)(107,463)(108,462)(109,457)(110,460)(111,459)(112,458)(113,425)(114,428)(115,427)(116,426)(117,421)(118,424)(119,423)(120,422)(121,445)(122,448)(123,447)(124,446)(125,441)(126,444)(127,443)(128,442)(129,437)(130,440)(131,439)(132,438)(133,433)(134,436)(135,435)(136,434)(137,429)(138,432)(139,431)(140,430)(141,481)(142,484)(143,483)(144,482)(145,477)(146,480)(147,479)(148,478)(149,501)(150,504)(151,503)(152,502)(153,497)(154,500)(155,499)(156,498)(157,493)(158,496)(159,495)(160,494)(161,489)(162,492)(163,491)(164,490)(165,485)(166,488)(167,487)(168,486)(169,621)(170,624)(171,623)(172,622)(173,617)(174,620)(175,619)(176,618)(177,641)(178,644)(179,643)(180,642)(181,637)(182,640)(183,639)(184,638)(185,633)(186,636)(187,635)(188,634)(189,629)(190,632)(191,631)(192,630)(193,625)(194,628)(195,627)(196,626)(197,593)(198,596)(199,595)(200,594)(201,589)(202,592)(203,591)(204,590)(205,613)(206,616)(207,615)(208,614)(209,609)(210,612)(211,611)(212,610)(213,605)(214,608)(215,607)(216,606)(217,601)(218,604)(219,603)(220,602)(221,597)(222,600)(223,599)(224,598)(225,649)(226,652)(227,651)(228,650)(229,645)(230,648)(231,647)(232,646)(233,669)(234,672)(235,671)(236,670)(237,665)(238,668)(239,667)(240,666)(241,661)(242,664)(243,663)(244,662)(245,657)(246,660)(247,659)(248,658)(249,653)(250,656)(251,655)(252,654)(253,537)(254,540)(255,539)(256,538)(257,533)(258,536)(259,535)(260,534)(261,557)(262,560)(263,559)(264,558)(265,553)(266,556)(267,555)(268,554)(269,549)(270,552)(271,551)(272,550)(273,545)(274,548)(275,547)(276,546)(277,541)(278,544)(279,543)(280,542)(281,509)(282,512)(283,511)(284,510)(285,505)(286,508)(287,507)(288,506)(289,529)(290,532)(291,531)(292,530)(293,525)(294,528)(295,527)(296,526)(297,521)(298,524)(299,523)(300,522)(301,517)(302,520)(303,519)(304,518)(305,513)(306,516)(307,515)(308,514)(309,565)(310,568)(311,567)(312,566)(313,561)(314,564)(315,563)(316,562)(317,585)(318,588)(319,587)(320,586)(321,581)(322,584)(323,583)(324,582)(325,577)(326,580)(327,579)(328,578)(329,573)(330,576)(331,575)(332,574)(333,569)(334,572)(335,571)(336,570);
s2 := Sym(672)!(  1, 86)(  2, 85)(  3, 88)(  4, 87)(  5, 90)(  6, 89)(  7, 92)(  8, 91)(  9, 94)( 10, 93)( 11, 96)( 12, 95)( 13, 98)( 14, 97)( 15,100)( 16, 99)( 17,102)( 18,101)( 19,104)( 20,103)( 21,106)( 22,105)( 23,108)( 24,107)( 25,110)( 26,109)( 27,112)( 28,111)( 29,114)( 30,113)( 31,116)( 32,115)( 33,118)( 34,117)( 35,120)( 36,119)( 37,122)( 38,121)( 39,124)( 40,123)( 41,126)( 42,125)( 43,128)( 44,127)( 45,130)( 46,129)( 47,132)( 48,131)( 49,134)( 50,133)( 51,136)( 52,135)( 53,138)( 54,137)( 55,140)( 56,139)( 57,142)( 58,141)( 59,144)( 60,143)( 61,146)( 62,145)( 63,148)( 64,147)( 65,150)( 66,149)( 67,152)( 68,151)( 69,154)( 70,153)( 71,156)( 72,155)( 73,158)( 74,157)( 75,160)( 76,159)( 77,162)( 78,161)( 79,164)( 80,163)( 81,166)( 82,165)( 83,168)( 84,167)(169,254)(170,253)(171,256)(172,255)(173,258)(174,257)(175,260)(176,259)(177,262)(178,261)(179,264)(180,263)(181,266)(182,265)(183,268)(184,267)(185,270)(186,269)(187,272)(188,271)(189,274)(190,273)(191,276)(192,275)(193,278)(194,277)(195,280)(196,279)(197,282)(198,281)(199,284)(200,283)(201,286)(202,285)(203,288)(204,287)(205,290)(206,289)(207,292)(208,291)(209,294)(210,293)(211,296)(212,295)(213,298)(214,297)(215,300)(216,299)(217,302)(218,301)(219,304)(220,303)(221,306)(222,305)(223,308)(224,307)(225,310)(226,309)(227,312)(228,311)(229,314)(230,313)(231,316)(232,315)(233,318)(234,317)(235,320)(236,319)(237,322)(238,321)(239,324)(240,323)(241,326)(242,325)(243,328)(244,327)(245,330)(246,329)(247,332)(248,331)(249,334)(250,333)(251,336)(252,335)(337,422)(338,421)(339,424)(340,423)(341,426)(342,425)(343,428)(344,427)(345,430)(346,429)(347,432)(348,431)(349,434)(350,433)(351,436)(352,435)(353,438)(354,437)(355,440)(356,439)(357,442)(358,441)(359,444)(360,443)(361,446)(362,445)(363,448)(364,447)(365,450)(366,449)(367,452)(368,451)(369,454)(370,453)(371,456)(372,455)(373,458)(374,457)(375,460)(376,459)(377,462)(378,461)(379,464)(380,463)(381,466)(382,465)(383,468)(384,467)(385,470)(386,469)(387,472)(388,471)(389,474)(390,473)(391,476)(392,475)(393,478)(394,477)(395,480)(396,479)(397,482)(398,481)(399,484)(400,483)(401,486)(402,485)(403,488)(404,487)(405,490)(406,489)(407,492)(408,491)(409,494)(410,493)(411,496)(412,495)(413,498)(414,497)(415,500)(416,499)(417,502)(418,501)(419,504)(420,503)(505,590)(506,589)(507,592)(508,591)(509,594)(510,593)(511,596)(512,595)(513,598)(514,597)(515,600)(516,599)(517,602)(518,601)(519,604)(520,603)(521,606)(522,605)(523,608)(524,607)(525,610)(526,609)(527,612)(528,611)(529,614)(530,613)(531,616)(532,615)(533,618)(534,617)(535,620)(536,619)(537,622)(538,621)(539,624)(540,623)(541,626)(542,625)(543,628)(544,627)(545,630)(546,629)(547,632)(548,631)(549,634)(550,633)(551,636)(552,635)(553,638)(554,637)(555,640)(556,639)(557,642)(558,641)(559,644)(560,643)(561,646)(562,645)(563,648)(564,647)(565,650)(566,649)(567,652)(568,651)(569,654)(570,653)(571,656)(572,655)(573,658)(574,657)(575,660)(576,659)(577,662)(578,661)(579,664)(580,663)(581,666)(582,665)(583,668)(584,667)(585,670)(586,669)(587,672)(588,671);
poly := sub<Sym(672)|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*s1*s0*s1*s2*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*s2*s0*s1*s2*s0*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 >; 
 

Twisty Puzzle