Polytope of Type {16,44}

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)( 23,386)( 24,387)( 25,388)( 26,389)( 27,390)( 28,391)( 29,392)( 30,393)( 31,394)( 32,395)( 33,396)( 34,375)( 35,376)( 36,377)( 37,378)( 38,379)( 39,380)( 40,381)( 41,382)( 42,383)( 43,384)( 44,385)( 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)( 67,419)( 68,420)( 69,421)( 70,422)( 71,423)( 72,424)( 73,425)( 74,426)( 75,427)( 76,428)( 77,429)( 78,430)( 79,431)( 80,432)( 81,433)( 82,434)( 83,435)( 84,436)( 85,437)( 86,438)( 87,439)( 88,440)( 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)(199,562)(200,563)(201,564)(202,565)(203,566)(204,567)(205,568)(206,569)(207,570)(208,571)(209,572)(210,551)(211,552)(212,553)(213,554)(214,555)(215,556)(216,557)(217,558)(218,559)(219,560)(220,561)(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)(243,595)(244,596)(245,597)(246,598)(247,599)(248,600)(249,601)(250,602)(251,603)(252,604)(253,605)(254,606)(255,607)(256,608)(257,609)(258,610)(259,611)(260,612)(261,613)(262,614)(263,615)(264,616)(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)( 23, 34)( 24, 44)( 25, 43)( 26, 42)( 27, 41)( 28, 40)( 29, 39)( 30, 38)( 31, 37)( 32, 36)( 33, 35)( 46, 55)( 47, 54)( 48, 53)( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 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)(133,155)(134,165)(135,164)(136,163)(137,162)(138,161)(139,160)(140,159)(141,158)(142,157)(143,156)(144,166)(145,176)(146,175)(147,174)(148,173)(149,172)(150,171)(151,170)(152,169)(153,168)(154,167)(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)(199,254)(200,264)(201,263)(202,262)(203,261)(204,260)(205,259)(206,258)(207,257)(208,256)(209,255)(210,243)(211,253)(212,252)(213,251)(214,250)(215,249)(216,248)(217,247)(218,246)(219,245)(220,244)(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)(375,474)(376,484)(377,483)(378,482)(379,481)(380,480)(381,479)(382,478)(383,477)(384,476)(385,475)(386,463)(387,473)(388,472)(389,471)(390,470)(391,469)(392,468)(393,467)(394,466)(395,465)(396,464)(397,485)(398,495)(399,494)(400,493)(401,492)(402,491)(403,490)(404,489)(405,488)(406,487)(407,486)(408,496)(409,506)(410,505)(411,504)(412,503)(413,502)(414,501)(415,500)(416,499)(417,498)(418,497)(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)(551,683)(552,693)(553,692)(554,691)(555,690)(556,689)(557,688)(558,687)(559,686)(560,685)(561,684)(562,694)(563,704)(564,703)(565,702)(566,701)(567,700)(568,699)(569,698)(570,697)(571,696)(572,695)(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)(595,639)(596,649)(597,648)(598,647)(599,646)(600,645)(601,644)(602,643)(603,642)(604,641)(605,640)(606,650)(607,660)(608,659)(609,658)(610,657)(611,656)(612,655)(613,654)(614,653)(615,652)(616,651);;
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)( 45,222)( 46,221)( 47,231)( 48,230)( 49,229)( 50,228)( 51,227)( 52,226)( 53,225)( 54,224)( 55,223)( 56,233)( 57,232)( 58,242)( 59,241)( 60,240)( 61,239)( 62,238)( 63,237)( 64,236)( 65,235)( 66,234)( 67,244)( 68,243)( 69,253)( 70,252)( 71,251)( 72,250)( 73,249)( 74,248)( 75,247)( 76,246)( 77,245)( 78,255)( 79,254)( 80,264)( 81,263)( 82,262)( 83,261)( 84,260)( 85,259)( 86,258)( 87,257)( 88,256)( 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)(133,321)(134,320)(135,330)(136,329)(137,328)(138,327)(139,326)(140,325)(141,324)(142,323)(143,322)(144,310)(145,309)(146,319)(147,318)(148,317)(149,316)(150,315)(151,314)(152,313)(153,312)(154,311)(155,343)(156,342)(157,352)(158,351)(159,350)(160,349)(161,348)(162,347)(163,346)(164,345)(165,344)(166,332)(167,331)(168,341)(169,340)(170,339)(171,338)(172,337)(173,336)(174,335)(175,334)(176,333)(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)(397,574)(398,573)(399,583)(400,582)(401,581)(402,580)(403,579)(404,578)(405,577)(406,576)(407,575)(408,585)(409,584)(410,594)(411,593)(412,592)(413,591)(414,590)(415,589)(416,588)(417,587)(418,586)(419,596)(420,595)(421,605)(422,604)(423,603)(424,602)(425,601)(426,600)(427,599)(428,598)(429,597)(430,607)(431,606)(432,616)(433,615)(434,614)(435,613)(436,612)(437,611)(438,610)(439,609)(440,608)(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)(485,673)(486,672)(487,682)(488,681)(489,680)(490,679)(491,678)(492,677)(493,676)(494,675)(495,674)(496,662)(497,661)(498,671)(499,670)(500,669)(501,668)(502,667)(503,666)(504,665)(505,664)(506,663)(507,695)(508,694)(509,704)(510,703)(511,702)(512,701)(513,700)(514,699)(515,698)(516,697)(517,696)(518,684)(519,683)(520,693)(521,692)(522,691)(523,690)(524,689)(525,688)(526,687)(527,686)(528,685);;
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s2*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 ];;
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)( 23,386)( 24,387)( 25,388)( 26,389)( 27,390)( 28,391)( 29,392)( 30,393)( 31,394)( 32,395)( 33,396)( 34,375)( 35,376)( 36,377)( 37,378)( 38,379)( 39,380)( 40,381)( 41,382)( 42,383)( 43,384)( 44,385)( 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)( 67,419)( 68,420)( 69,421)( 70,422)( 71,423)( 72,424)( 73,425)( 74,426)( 75,427)( 76,428)( 77,429)( 78,430)( 79,431)( 80,432)( 81,433)( 82,434)( 83,435)( 84,436)( 85,437)( 86,438)( 87,439)( 88,440)( 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)(199,562)(200,563)(201,564)(202,565)(203,566)(204,567)(205,568)(206,569)(207,570)(208,571)(209,572)(210,551)(211,552)(212,553)(213,554)(214,555)(215,556)(216,557)(217,558)(218,559)(219,560)(220,561)(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)(243,595)(244,596)(245,597)(246,598)(247,599)(248,600)(249,601)(250,602)(251,603)(252,604)(253,605)(254,606)(255,607)(256,608)(257,609)(258,610)(259,611)(260,612)(261,613)(262,614)(263,615)(264,616)(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)( 23, 34)( 24, 44)( 25, 43)( 26, 42)( 27, 41)( 28, 40)( 29, 39)( 30, 38)( 31, 37)( 32, 36)( 33, 35)( 46, 55)( 47, 54)( 48, 53)( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 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)(133,155)(134,165)(135,164)(136,163)(137,162)(138,161)(139,160)(140,159)(141,158)(142,157)(143,156)(144,166)(145,176)(146,175)(147,174)(148,173)(149,172)(150,171)(151,170)(152,169)(153,168)(154,167)(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)(199,254)(200,264)(201,263)(202,262)(203,261)(204,260)(205,259)(206,258)(207,257)(208,256)(209,255)(210,243)(211,253)(212,252)(213,251)(214,250)(215,249)(216,248)(217,247)(218,246)(219,245)(220,244)(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)(375,474)(376,484)(377,483)(378,482)(379,481)(380,480)(381,479)(382,478)(383,477)(384,476)(385,475)(386,463)(387,473)(388,472)(389,471)(390,470)(391,469)(392,468)(393,467)(394,466)(395,465)(396,464)(397,485)(398,495)(399,494)(400,493)(401,492)(402,491)(403,490)(404,489)(405,488)(406,487)(407,486)(408,496)(409,506)(410,505)(411,504)(412,503)(413,502)(414,501)(415,500)(416,499)(417,498)(418,497)(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)(551,683)(552,693)(553,692)(554,691)(555,690)(556,689)(557,688)(558,687)(559,686)(560,685)(561,684)(562,694)(563,704)(564,703)(565,702)(566,701)(567,700)(568,699)(569,698)(570,697)(571,696)(572,695)(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)(595,639)(596,649)(597,648)(598,647)(599,646)(600,645)(601,644)(602,643)(603,642)(604,641)(605,640)(606,650)(607,660)(608,659)(609,658)(610,657)(611,656)(612,655)(613,654)(614,653)(615,652)(616,651);
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)( 45,222)( 46,221)( 47,231)( 48,230)( 49,229)( 50,228)( 51,227)( 52,226)( 53,225)( 54,224)( 55,223)( 56,233)( 57,232)( 58,242)( 59,241)( 60,240)( 61,239)( 62,238)( 63,237)( 64,236)( 65,235)( 66,234)( 67,244)( 68,243)( 69,253)( 70,252)( 71,251)( 72,250)( 73,249)( 74,248)( 75,247)( 76,246)( 77,245)( 78,255)( 79,254)( 80,264)( 81,263)( 82,262)( 83,261)( 84,260)( 85,259)( 86,258)( 87,257)( 88,256)( 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)(133,321)(134,320)(135,330)(136,329)(137,328)(138,327)(139,326)(140,325)(141,324)(142,323)(143,322)(144,310)(145,309)(146,319)(147,318)(148,317)(149,316)(150,315)(151,314)(152,313)(153,312)(154,311)(155,343)(156,342)(157,352)(158,351)(159,350)(160,349)(161,348)(162,347)(163,346)(164,345)(165,344)(166,332)(167,331)(168,341)(169,340)(170,339)(171,338)(172,337)(173,336)(174,335)(175,334)(176,333)(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)(397,574)(398,573)(399,583)(400,582)(401,581)(402,580)(403,579)(404,578)(405,577)(406,576)(407,575)(408,585)(409,584)(410,594)(411,593)(412,592)(413,591)(414,590)(415,589)(416,588)(417,587)(418,586)(419,596)(420,595)(421,605)(422,604)(423,603)(424,602)(425,601)(426,600)(427,599)(428,598)(429,597)(430,607)(431,606)(432,616)(433,615)(434,614)(435,613)(436,612)(437,611)(438,610)(439,609)(440,608)(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)(485,673)(486,672)(487,682)(488,681)(489,680)(490,679)(491,678)(492,677)(493,676)(494,675)(495,674)(496,662)(497,661)(498,671)(499,670)(500,669)(501,668)(502,667)(503,666)(504,665)(505,664)(506,663)(507,695)(508,694)(509,704)(510,703)(511,702)(512,701)(513,700)(514,699)(515,698)(516,697)(517,696)(518,684)(519,683)(520,693)(521,692)(522,691)(523,690)(524,689)(525,688)(526,687)(527,686)(528,685);
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s2*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 >; 
 

Twisty Puzzle