Polytope of Type {32,22}

Play with this polytope as a twisty puzzle

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