Polytope of Type {8,88}

Play with this polytope as a twisty puzzle

s0 := (  1,353)(  2,354)(  3,355)(  4,356)(  5,357)(  6,358)(  7,359)(  8,360)(  9,361)( 10,362)( 11,363)( 12,364)( 13,365)( 14,366)( 15,367)( 16,368)( 17,369)( 18,370)( 19,371)( 20,372)( 21,373)( 22,374)( 23,375)( 24,376)( 25,377)( 26,378)( 27,379)( 28,380)( 29,381)( 30,382)( 31,383)( 32,384)( 33,385)( 34,386)( 35,387)( 36,388)( 37,389)( 38,390)( 39,391)( 40,392)( 41,393)( 42,394)( 43,395)( 44,396)( 45,408)( 46,409)( 47,410)( 48,411)( 49,412)( 50,413)( 51,414)( 52,415)( 53,416)( 54,417)( 55,418)( 56,397)( 57,398)( 58,399)( 59,400)( 60,401)( 61,402)( 62,403)( 63,404)( 64,405)( 65,406)( 66,407)( 67,430)( 68,431)( 69,432)( 70,433)( 71,434)( 72,435)( 73,436)( 74,437)( 75,438)( 76,439)( 77,440)( 78,419)( 79,420)( 80,421)( 81,422)( 82,423)( 83,424)( 84,425)( 85,426)( 86,427)( 87,428)( 88,429)( 89,463)( 90,464)( 91,465)( 92,466)( 93,467)( 94,468)( 95,469)( 96,470)( 97,471)( 98,472)( 99,473)(100,474)(101,475)(102,476)(103,477)(104,478)(105,479)(106,480)(107,481)(108,482)(109,483)(110,484)(111,441)(112,442)(113,443)(114,444)(115,445)(116,446)(117,447)(118,448)(119,449)(120,450)(121,451)(122,452)(123,453)(124,454)(125,455)(126,456)(127,457)(128,458)(129,459)(130,460)(131,461)(132,462)(133,518)(134,519)(135,520)(136,521)(137,522)(138,523)(139,524)(140,525)(141,526)(142,527)(143,528)(144,507)(145,508)(146,509)(147,510)(148,511)(149,512)(150,513)(151,514)(152,515)(153,516)(154,517)(155,496)(156,497)(157,498)(158,499)(159,500)(160,501)(161,502)(162,503)(163,504)(164,505)(165,506)(166,485)(167,486)(168,487)(169,488)(170,489)(171,490)(172,491)(173,492)(174,493)(175,494)(176,495)(177,529)(178,530)(179,531)(180,532)(181,533)(182,534)(183,535)(184,536)(185,537)(186,538)(187,539)(188,540)(189,541)(190,542)(191,543)(192,544)(193,545)(194,546)(195,547)(196,548)(197,549)(198,550)(199,551)(200,552)(201,553)(202,554)(203,555)(204,556)(205,557)(206,558)(207,559)(208,560)(209,561)(210,562)(211,563)(212,564)(213,565)(214,566)(215,567)(216,568)(217,569)(218,570)(219,571)(220,572)(221,584)(222,585)(223,586)(224,587)(225,588)(226,589)(227,590)(228,591)(229,592)(230,593)(231,594)(232,573)(233,574)(234,575)(235,576)(236,577)(237,578)(238,579)(239,580)(240,581)(241,582)(242,583)(243,606)(244,607)(245,608)(246,609)(247,610)(248,611)(249,612)(250,613)(251,614)(252,615)(253,616)(254,595)(255,596)(256,597)(257,598)(258,599)(259,600)(260,601)(261,602)(262,603)(263,604)(264,605)(265,639)(266,640)(267,641)(268,642)(269,643)(270,644)(271,645)(272,646)(273,647)(274,648)(275,649)(276,650)(277,651)(278,652)(279,653)(280,654)(281,655)(282,656)(283,657)(284,658)(285,659)(286,660)(287,617)(288,618)(289,619)(290,620)(291,621)(292,622)(293,623)(294,624)(295,625)(296,626)(297,627)(298,628)(299,629)(300,630)(301,631)(302,632)(303,633)(304,634)(305,635)(306,636)(307,637)(308,638)(309,694)(310,695)(311,696)(312,697)(313,698)(314,699)(315,700)(316,701)(317,702)(318,703)(319,704)(320,683)(321,684)(322,685)(323,686)(324,687)(325,688)(326,689)(327,690)(328,691)(329,692)(330,693)(331,672)(332,673)(333,674)(334,675)(335,676)(336,677)(337,678)(338,679)(339,680)(340,681)(341,682)(342,661)(343,662)(344,663)(345,664)(346,665)(347,666)(348,667)(349,668)(350,669)(351,670)(352,671);;
s1 := (  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 13, 22)( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 45, 56)( 46, 66)( 47, 65)( 48, 64)( 49, 63)( 50, 62)( 51, 61)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 67, 78)( 68, 88)( 69, 87)( 70, 86)( 71, 85)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)( 89,111)( 90,121)( 91,120)( 92,119)( 93,118)( 94,117)( 95,116)( 96,115)( 97,114)( 98,113)( 99,112)(100,122)(101,132)(102,131)(103,130)(104,129)(105,128)(106,127)(107,126)(108,125)(109,124)(110,123)(133,166)(134,176)(135,175)(136,174)(137,173)(138,172)(139,171)(140,170)(141,169)(142,168)(143,167)(144,155)(145,165)(146,164)(147,163)(148,162)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)(177,221)(178,231)(179,230)(180,229)(181,228)(182,227)(183,226)(184,225)(185,224)(186,223)(187,222)(188,232)(189,242)(190,241)(191,240)(192,239)(193,238)(194,237)(195,236)(196,235)(197,234)(198,233)(199,243)(200,253)(201,252)(202,251)(203,250)(204,249)(205,248)(206,247)(207,246)(208,245)(209,244)(210,254)(211,264)(212,263)(213,262)(214,261)(215,260)(216,259)(217,258)(218,257)(219,256)(220,255)(265,331)(266,341)(267,340)(268,339)(269,338)(270,337)(271,336)(272,335)(273,334)(274,333)(275,332)(276,342)(277,352)(278,351)(279,350)(280,349)(281,348)(282,347)(283,346)(284,345)(285,344)(286,343)(287,309)(288,319)(289,318)(290,317)(291,316)(292,315)(293,314)(294,313)(295,312)(296,311)(297,310)(298,320)(299,330)(300,329)(301,328)(302,327)(303,326)(304,325)(305,324)(306,323)(307,322)(308,321)(353,441)(354,451)(355,450)(356,449)(357,448)(358,447)(359,446)(360,445)(361,444)(362,443)(363,442)(364,452)(365,462)(366,461)(367,460)(368,459)(369,458)(370,457)(371,456)(372,455)(373,454)(374,453)(375,463)(376,473)(377,472)(378,471)(379,470)(380,469)(381,468)(382,467)(383,466)(384,465)(385,464)(386,474)(387,484)(388,483)(389,482)(390,481)(391,480)(392,479)(393,478)(394,477)(395,476)(396,475)(397,496)(398,506)(399,505)(400,504)(401,503)(402,502)(403,501)(404,500)(405,499)(406,498)(407,497)(408,485)(409,495)(410,494)(411,493)(412,492)(413,491)(414,490)(415,489)(416,488)(417,487)(418,486)(419,518)(420,528)(421,527)(422,526)(423,525)(424,524)(425,523)(426,522)(427,521)(428,520)(429,519)(430,507)(431,517)(432,516)(433,515)(434,514)(435,513)(436,512)(437,511)(438,510)(439,509)(440,508)(529,672)(530,682)(531,681)(532,680)(533,679)(534,678)(535,677)(536,676)(537,675)(538,674)(539,673)(540,661)(541,671)(542,670)(543,669)(544,668)(545,667)(546,666)(547,665)(548,664)(549,663)(550,662)(551,694)(552,704)(553,703)(554,702)(555,701)(556,700)(557,699)(558,698)(559,697)(560,696)(561,695)(562,683)(563,693)(564,692)(565,691)(566,690)(567,689)(568,688)(569,687)(570,686)(571,685)(572,684)(573,628)(574,638)(575,637)(576,636)(577,635)(578,634)(579,633)(580,632)(581,631)(582,630)(583,629)(584,617)(585,627)(586,626)(587,625)(588,624)(589,623)(590,622)(591,621)(592,620)(593,619)(594,618)(595,650)(596,660)(597,659)(598,658)(599,657)(600,656)(601,655)(602,654)(603,653)(604,652)(605,651)(606,639)(607,649)(608,648)(609,647)(610,646)(611,645)(612,644)(613,643)(614,642)(615,641)(616,640);;
s2 := (  1,178)(  2,177)(  3,187)(  4,186)(  5,185)(  6,184)(  7,183)(  8,182)(  9,181)( 10,180)( 11,179)( 12,189)( 13,188)( 14,198)( 15,197)( 16,196)( 17,195)( 18,194)( 19,193)( 20,192)( 21,191)( 22,190)( 23,200)( 24,199)( 25,209)( 26,208)( 27,207)( 28,206)( 29,205)( 30,204)( 31,203)( 32,202)( 33,201)( 34,211)( 35,210)( 36,220)( 37,219)( 38,218)( 39,217)( 40,216)( 41,215)( 42,214)( 43,213)( 44,212)( 45,233)( 46,232)( 47,242)( 48,241)( 49,240)( 50,239)( 51,238)( 52,237)( 53,236)( 54,235)( 55,234)( 56,222)( 57,221)( 58,231)( 59,230)( 60,229)( 61,228)( 62,227)( 63,226)( 64,225)( 65,224)( 66,223)( 67,255)( 68,254)( 69,264)( 70,263)( 71,262)( 72,261)( 73,260)( 74,259)( 75,258)( 76,257)( 77,256)( 78,244)( 79,243)( 80,253)( 81,252)( 82,251)( 83,250)( 84,249)( 85,248)( 86,247)( 87,246)( 88,245)( 89,277)( 90,276)( 91,286)( 92,285)( 93,284)( 94,283)( 95,282)( 96,281)( 97,280)( 98,279)( 99,278)(100,266)(101,265)(102,275)(103,274)(104,273)(105,272)(106,271)(107,270)(108,269)(109,268)(110,267)(111,299)(112,298)(113,308)(114,307)(115,306)(116,305)(117,304)(118,303)(119,302)(120,301)(121,300)(122,288)(123,287)(124,297)(125,296)(126,295)(127,294)(128,293)(129,292)(130,291)(131,290)(132,289)(133,310)(134,309)(135,319)(136,318)(137,317)(138,316)(139,315)(140,314)(141,313)(142,312)(143,311)(144,321)(145,320)(146,330)(147,329)(148,328)(149,327)(150,326)(151,325)(152,324)(153,323)(154,322)(155,332)(156,331)(157,341)(158,340)(159,339)(160,338)(161,337)(162,336)(163,335)(164,334)(165,333)(166,343)(167,342)(168,352)(169,351)(170,350)(171,349)(172,348)(173,347)(174,346)(175,345)(176,344)(353,530)(354,529)(355,539)(356,538)(357,537)(358,536)(359,535)(360,534)(361,533)(362,532)(363,531)(364,541)(365,540)(366,550)(367,549)(368,548)(369,547)(370,546)(371,545)(372,544)(373,543)(374,542)(375,552)(376,551)(377,561)(378,560)(379,559)(380,558)(381,557)(382,556)(383,555)(384,554)(385,553)(386,563)(387,562)(388,572)(389,571)(390,570)(391,569)(392,568)(393,567)(394,566)(395,565)(396,564)(397,585)(398,584)(399,594)(400,593)(401,592)(402,591)(403,590)(404,589)(405,588)(406,587)(407,586)(408,574)(409,573)(410,583)(411,582)(412,581)(413,580)(414,579)(415,578)(416,577)(417,576)(418,575)(419,607)(420,606)(421,616)(422,615)(423,614)(424,613)(425,612)(426,611)(427,610)(428,609)(429,608)(430,596)(431,595)(432,605)(433,604)(434,603)(435,602)(436,601)(437,600)(438,599)(439,598)(440,597)(441,629)(442,628)(443,638)(444,637)(445,636)(446,635)(447,634)(448,633)(449,632)(450,631)(451,630)(452,618)(453,617)(454,627)(455,626)(456,625)(457,624)(458,623)(459,622)(460,621)(461,620)(462,619)(463,651)(464,650)(465,660)(466,659)(467,658)(468,657)(469,656)(470,655)(471,654)(472,653)(473,652)(474,640)(475,639)(476,649)(477,648)(478,647)(479,646)(480,645)(481,644)(482,643)(483,642)(484,641)(485,662)(486,661)(487,671)(488,670)(489,669)(490,668)(491,667)(492,666)(493,665)(494,664)(495,663)(496,673)(497,672)(498,682)(499,681)(500,680)(501,679)(502,678)(503,677)(504,676)(505,675)(506,674)(507,684)(508,683)(509,693)(510,692)(511,691)(512,690)(513,689)(514,688)(515,687)(516,686)(517,685)(518,695)(519,694)(520,704)(521,703)(522,702)(523,701)(524,700)(525,699)(526,698)(527,697)(528,696);;
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*s2*s0*s1*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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s2*s1*s0*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*s0*s2*s1 ];;
poly := F / rels;;
 

s0 := Sym(704)!(  1,353)(  2,354)(  3,355)(  4,356)(  5,357)(  6,358)(  7,359)(  8,360)(  9,361)( 10,362)( 11,363)( 12,364)( 13,365)( 14,366)( 15,367)( 16,368)( 17,369)( 18,370)( 19,371)( 20,372)( 21,373)( 22,374)( 23,375)( 24,376)( 25,377)( 26,378)( 27,379)( 28,380)( 29,381)( 30,382)( 31,383)( 32,384)( 33,385)( 34,386)( 35,387)( 36,388)( 37,389)( 38,390)( 39,391)( 40,392)( 41,393)( 42,394)( 43,395)( 44,396)( 45,408)( 46,409)( 47,410)( 48,411)( 49,412)( 50,413)( 51,414)( 52,415)( 53,416)( 54,417)( 55,418)( 56,397)( 57,398)( 58,399)( 59,400)( 60,401)( 61,402)( 62,403)( 63,404)( 64,405)( 65,406)( 66,407)( 67,430)( 68,431)( 69,432)( 70,433)( 71,434)( 72,435)( 73,436)( 74,437)( 75,438)( 76,439)( 77,440)( 78,419)( 79,420)( 80,421)( 81,422)( 82,423)( 83,424)( 84,425)( 85,426)( 86,427)( 87,428)( 88,429)( 89,463)( 90,464)( 91,465)( 92,466)( 93,467)( 94,468)( 95,469)( 96,470)( 97,471)( 98,472)( 99,473)(100,474)(101,475)(102,476)(103,477)(104,478)(105,479)(106,480)(107,481)(108,482)(109,483)(110,484)(111,441)(112,442)(113,443)(114,444)(115,445)(116,446)(117,447)(118,448)(119,449)(120,450)(121,451)(122,452)(123,453)(124,454)(125,455)(126,456)(127,457)(128,458)(129,459)(130,460)(131,461)(132,462)(133,518)(134,519)(135,520)(136,521)(137,522)(138,523)(139,524)(140,525)(141,526)(142,527)(143,528)(144,507)(145,508)(146,509)(147,510)(148,511)(149,512)(150,513)(151,514)(152,515)(153,516)(154,517)(155,496)(156,497)(157,498)(158,499)(159,500)(160,501)(161,502)(162,503)(163,504)(164,505)(165,506)(166,485)(167,486)(168,487)(169,488)(170,489)(171,490)(172,491)(173,492)(174,493)(175,494)(176,495)(177,529)(178,530)(179,531)(180,532)(181,533)(182,534)(183,535)(184,536)(185,537)(186,538)(187,539)(188,540)(189,541)(190,542)(191,543)(192,544)(193,545)(194,546)(195,547)(196,548)(197,549)(198,550)(199,551)(200,552)(201,553)(202,554)(203,555)(204,556)(205,557)(206,558)(207,559)(208,560)(209,561)(210,562)(211,563)(212,564)(213,565)(214,566)(215,567)(216,568)(217,569)(218,570)(219,571)(220,572)(221,584)(222,585)(223,586)(224,587)(225,588)(226,589)(227,590)(228,591)(229,592)(230,593)(231,594)(232,573)(233,574)(234,575)(235,576)(236,577)(237,578)(238,579)(239,580)(240,581)(241,582)(242,583)(243,606)(244,607)(245,608)(246,609)(247,610)(248,611)(249,612)(250,613)(251,614)(252,615)(253,616)(254,595)(255,596)(256,597)(257,598)(258,599)(259,600)(260,601)(261,602)(262,603)(263,604)(264,605)(265,639)(266,640)(267,641)(268,642)(269,643)(270,644)(271,645)(272,646)(273,647)(274,648)(275,649)(276,650)(277,651)(278,652)(279,653)(280,654)(281,655)(282,656)(283,657)(284,658)(285,659)(286,660)(287,617)(288,618)(289,619)(290,620)(291,621)(292,622)(293,623)(294,624)(295,625)(296,626)(297,627)(298,628)(299,629)(300,630)(301,631)(302,632)(303,633)(304,634)(305,635)(306,636)(307,637)(308,638)(309,694)(310,695)(311,696)(312,697)(313,698)(314,699)(315,700)(316,701)(317,702)(318,703)(319,704)(320,683)(321,684)(322,685)(323,686)(324,687)(325,688)(326,689)(327,690)(328,691)(329,692)(330,693)(331,672)(332,673)(333,674)(334,675)(335,676)(336,677)(337,678)(338,679)(339,680)(340,681)(341,682)(342,661)(343,662)(344,663)(345,664)(346,665)(347,666)(348,667)(349,668)(350,669)(351,670)(352,671);
s1 := Sym(704)!(  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 13, 22)( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 45, 56)( 46, 66)( 47, 65)( 48, 64)( 49, 63)( 50, 62)( 51, 61)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 67, 78)( 68, 88)( 69, 87)( 70, 86)( 71, 85)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)( 89,111)( 90,121)( 91,120)( 92,119)( 93,118)( 94,117)( 95,116)( 96,115)( 97,114)( 98,113)( 99,112)(100,122)(101,132)(102,131)(103,130)(104,129)(105,128)(106,127)(107,126)(108,125)(109,124)(110,123)(133,166)(134,176)(135,175)(136,174)(137,173)(138,172)(139,171)(140,170)(141,169)(142,168)(143,167)(144,155)(145,165)(146,164)(147,163)(148,162)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)(177,221)(178,231)(179,230)(180,229)(181,228)(182,227)(183,226)(184,225)(185,224)(186,223)(187,222)(188,232)(189,242)(190,241)(191,240)(192,239)(193,238)(194,237)(195,236)(196,235)(197,234)(198,233)(199,243)(200,253)(201,252)(202,251)(203,250)(204,249)(205,248)(206,247)(207,246)(208,245)(209,244)(210,254)(211,264)(212,263)(213,262)(214,261)(215,260)(216,259)(217,258)(218,257)(219,256)(220,255)(265,331)(266,341)(267,340)(268,339)(269,338)(270,337)(271,336)(272,335)(273,334)(274,333)(275,332)(276,342)(277,352)(278,351)(279,350)(280,349)(281,348)(282,347)(283,346)(284,345)(285,344)(286,343)(287,309)(288,319)(289,318)(290,317)(291,316)(292,315)(293,314)(294,313)(295,312)(296,311)(297,310)(298,320)(299,330)(300,329)(301,328)(302,327)(303,326)(304,325)(305,324)(306,323)(307,322)(308,321)(353,441)(354,451)(355,450)(356,449)(357,448)(358,447)(359,446)(360,445)(361,444)(362,443)(363,442)(364,452)(365,462)(366,461)(367,460)(368,459)(369,458)(370,457)(371,456)(372,455)(373,454)(374,453)(375,463)(376,473)(377,472)(378,471)(379,470)(380,469)(381,468)(382,467)(383,466)(384,465)(385,464)(386,474)(387,484)(388,483)(389,482)(390,481)(391,480)(392,479)(393,478)(394,477)(395,476)(396,475)(397,496)(398,506)(399,505)(400,504)(401,503)(402,502)(403,501)(404,500)(405,499)(406,498)(407,497)(408,485)(409,495)(410,494)(411,493)(412,492)(413,491)(414,490)(415,489)(416,488)(417,487)(418,486)(419,518)(420,528)(421,527)(422,526)(423,525)(424,524)(425,523)(426,522)(427,521)(428,520)(429,519)(430,507)(431,517)(432,516)(433,515)(434,514)(435,513)(436,512)(437,511)(438,510)(439,509)(440,508)(529,672)(530,682)(531,681)(532,680)(533,679)(534,678)(535,677)(536,676)(537,675)(538,674)(539,673)(540,661)(541,671)(542,670)(543,669)(544,668)(545,667)(546,666)(547,665)(548,664)(549,663)(550,662)(551,694)(552,704)(553,703)(554,702)(555,701)(556,700)(557,699)(558,698)(559,697)(560,696)(561,695)(562,683)(563,693)(564,692)(565,691)(566,690)(567,689)(568,688)(569,687)(570,686)(571,685)(572,684)(573,628)(574,638)(575,637)(576,636)(577,635)(578,634)(579,633)(580,632)(581,631)(582,630)(583,629)(584,617)(585,627)(586,626)(587,625)(588,624)(589,623)(590,622)(591,621)(592,620)(593,619)(594,618)(595,650)(596,660)(597,659)(598,658)(599,657)(600,656)(601,655)(602,654)(603,653)(604,652)(605,651)(606,639)(607,649)(608,648)(609,647)(610,646)(611,645)(612,644)(613,643)(614,642)(615,641)(616,640);
s2 := Sym(704)!(  1,178)(  2,177)(  3,187)(  4,186)(  5,185)(  6,184)(  7,183)(  8,182)(  9,181)( 10,180)( 11,179)( 12,189)( 13,188)( 14,198)( 15,197)( 16,196)( 17,195)( 18,194)( 19,193)( 20,192)( 21,191)( 22,190)( 23,200)( 24,199)( 25,209)( 26,208)( 27,207)( 28,206)( 29,205)( 30,204)( 31,203)( 32,202)( 33,201)( 34,211)( 35,210)( 36,220)( 37,219)( 38,218)( 39,217)( 40,216)( 41,215)( 42,214)( 43,213)( 44,212)( 45,233)( 46,232)( 47,242)( 48,241)( 49,240)( 50,239)( 51,238)( 52,237)( 53,236)( 54,235)( 55,234)( 56,222)( 57,221)( 58,231)( 59,230)( 60,229)( 61,228)( 62,227)( 63,226)( 64,225)( 65,224)( 66,223)( 67,255)( 68,254)( 69,264)( 70,263)( 71,262)( 72,261)( 73,260)( 74,259)( 75,258)( 76,257)( 77,256)( 78,244)( 79,243)( 80,253)( 81,252)( 82,251)( 83,250)( 84,249)( 85,248)( 86,247)( 87,246)( 88,245)( 89,277)( 90,276)( 91,286)( 92,285)( 93,284)( 94,283)( 95,282)( 96,281)( 97,280)( 98,279)( 99,278)(100,266)(101,265)(102,275)(103,274)(104,273)(105,272)(106,271)(107,270)(108,269)(109,268)(110,267)(111,299)(112,298)(113,308)(114,307)(115,306)(116,305)(117,304)(118,303)(119,302)(120,301)(121,300)(122,288)(123,287)(124,297)(125,296)(126,295)(127,294)(128,293)(129,292)(130,291)(131,290)(132,289)(133,310)(134,309)(135,319)(136,318)(137,317)(138,316)(139,315)(140,314)(141,313)(142,312)(143,311)(144,321)(145,320)(146,330)(147,329)(148,328)(149,327)(150,326)(151,325)(152,324)(153,323)(154,322)(155,332)(156,331)(157,341)(158,340)(159,339)(160,338)(161,337)(162,336)(163,335)(164,334)(165,333)(166,343)(167,342)(168,352)(169,351)(170,350)(171,349)(172,348)(173,347)(174,346)(175,345)(176,344)(353,530)(354,529)(355,539)(356,538)(357,537)(358,536)(359,535)(360,534)(361,533)(362,532)(363,531)(364,541)(365,540)(366,550)(367,549)(368,548)(369,547)(370,546)(371,545)(372,544)(373,543)(374,542)(375,552)(376,551)(377,561)(378,560)(379,559)(380,558)(381,557)(382,556)(383,555)(384,554)(385,553)(386,563)(387,562)(388,572)(389,571)(390,570)(391,569)(392,568)(393,567)(394,566)(395,565)(396,564)(397,585)(398,584)(399,594)(400,593)(401,592)(402,591)(403,590)(404,589)(405,588)(406,587)(407,586)(408,574)(409,573)(410,583)(411,582)(412,581)(413,580)(414,579)(415,578)(416,577)(417,576)(418,575)(419,607)(420,606)(421,616)(422,615)(423,614)(424,613)(425,612)(426,611)(427,610)(428,609)(429,608)(430,596)(431,595)(432,605)(433,604)(434,603)(435,602)(436,601)(437,600)(438,599)(439,598)(440,597)(441,629)(442,628)(443,638)(444,637)(445,636)(446,635)(447,634)(448,633)(449,632)(450,631)(451,630)(452,618)(453,617)(454,627)(455,626)(456,625)(457,624)(458,623)(459,622)(460,621)(461,620)(462,619)(463,651)(464,650)(465,660)(466,659)(467,658)(468,657)(469,656)(470,655)(471,654)(472,653)(473,652)(474,640)(475,639)(476,649)(477,648)(478,647)(479,646)(480,645)(481,644)(482,643)(483,642)(484,641)(485,662)(486,661)(487,671)(488,670)(489,669)(490,668)(491,667)(492,666)(493,665)(494,664)(495,663)(496,673)(497,672)(498,682)(499,681)(500,680)(501,679)(502,678)(503,677)(504,676)(505,675)(506,674)(507,684)(508,683)(509,693)(510,692)(511,691)(512,690)(513,689)(514,688)(515,687)(516,686)(517,685)(518,695)(519,694)(520,704)(521,703)(522,702)(523,701)(524,700)(525,699)(526,698)(527,697)(528,696);
poly := sub<Sym(704)|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*s2*s0*s1*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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s2*s1*s0*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*s0*s2*s1 >; 
 

Twisty Puzzle