Polytope of Type {42,8}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle