Polytope of Type {16,46}

Play with this polytope as a twisty puzzle

s0 := ( 47, 70)( 48, 71)( 49, 72)( 50, 73)( 51, 74)( 52, 75)( 53, 76)( 54, 77)( 55, 78)( 56, 79)( 57, 80)( 58, 81)( 59, 82)( 60, 83)( 61, 84)( 62, 85)( 63, 86)( 64, 87)( 65, 88)( 66, 89)( 67, 90)( 68, 91)( 69, 92)( 93,139)( 94,140)( 95,141)( 96,142)( 97,143)( 98,144)( 99,145)(100,146)(101,147)(102,148)(103,149)(104,150)(105,151)(106,152)(107,153)(108,154)(109,155)(110,156)(111,157)(112,158)(113,159)(114,160)(115,161)(116,162)(117,163)(118,164)(119,165)(120,166)(121,167)(122,168)(123,169)(124,170)(125,171)(126,172)(127,173)(128,174)(129,175)(130,176)(131,177)(132,178)(133,179)(134,180)(135,181)(136,182)(137,183)(138,184)(231,254)(232,255)(233,256)(234,257)(235,258)(236,259)(237,260)(238,261)(239,262)(240,263)(241,264)(242,265)(243,266)(244,267)(245,268)(246,269)(247,270)(248,271)(249,272)(250,273)(251,274)(252,275)(253,276)(277,323)(278,324)(279,325)(280,326)(281,327)(282,328)(283,329)(284,330)(285,331)(286,332)(287,333)(288,334)(289,335)(290,336)(291,337)(292,338)(293,339)(294,340)(295,341)(296,342)(297,343)(298,344)(299,345)(300,346)(301,347)(302,348)(303,349)(304,350)(305,351)(306,352)(307,353)(308,354)(309,355)(310,356)(311,357)(312,358)(313,359)(314,360)(315,361)(316,362)(317,363)(318,364)(319,365)(320,366)(321,367)(322,368)(369,461)(370,462)(371,463)(372,464)(373,465)(374,466)(375,467)(376,468)(377,469)(378,470)(379,471)(380,472)(381,473)(382,474)(383,475)(384,476)(385,477)(386,478)(387,479)(388,480)(389,481)(390,482)(391,483)(392,484)(393,485)(394,486)(395,487)(396,488)(397,489)(398,490)(399,491)(400,492)(401,493)(402,494)(403,495)(404,496)(405,497)(406,498)(407,499)(408,500)(409,501)(410,502)(411,503)(412,504)(413,505)(414,506)(415,530)(416,531)(417,532)(418,533)(419,534)(420,535)(421,536)(422,537)(423,538)(424,539)(425,540)(426,541)(427,542)(428,543)(429,544)(430,545)(431,546)(432,547)(433,548)(434,549)(435,550)(436,551)(437,552)(438,507)(439,508)(440,509)(441,510)(442,511)(443,512)(444,513)(445,514)(446,515)(447,516)(448,517)(449,518)(450,519)(451,520)(452,521)(453,522)(454,523)(455,524)(456,525)(457,526)(458,527)(459,528)(460,529)(553,645)(554,646)(555,647)(556,648)(557,649)(558,650)(559,651)(560,652)(561,653)(562,654)(563,655)(564,656)(565,657)(566,658)(567,659)(568,660)(569,661)(570,662)(571,663)(572,664)(573,665)(574,666)(575,667)(576,668)(577,669)(578,670)(579,671)(580,672)(581,673)(582,674)(583,675)(584,676)(585,677)(586,678)(587,679)(588,680)(589,681)(590,682)(591,683)(592,684)(593,685)(594,686)(595,687)(596,688)(597,689)(598,690)(599,714)(600,715)(601,716)(602,717)(603,718)(604,719)(605,720)(606,721)(607,722)(608,723)(609,724)(610,725)(611,726)(612,727)(613,728)(614,729)(615,730)(616,731)(617,732)(618,733)(619,734)(620,735)(621,736)(622,691)(623,692)(624,693)(625,694)(626,695)(627,696)(628,697)(629,698)(630,699)(631,700)(632,701)(633,702)(634,703)(635,704)(636,705)(637,706)(638,707)(639,708)(640,709)(641,710)(642,711)(643,712)(644,713);;
s1 := (  1,553)(  2,575)(  3,574)(  4,573)(  5,572)(  6,571)(  7,570)(  8,569)(  9,568)( 10,567)( 11,566)( 12,565)( 13,564)( 14,563)( 15,562)( 16,561)( 17,560)( 18,559)( 19,558)( 20,557)( 21,556)( 22,555)( 23,554)( 24,576)( 25,598)( 26,597)( 27,596)( 28,595)( 29,594)( 30,593)( 31,592)( 32,591)( 33,590)( 34,589)( 35,588)( 36,587)( 37,586)( 38,585)( 39,584)( 40,583)( 41,582)( 42,581)( 43,580)( 44,579)( 45,578)( 46,577)( 47,622)( 48,644)( 49,643)( 50,642)( 51,641)( 52,640)( 53,639)( 54,638)( 55,637)( 56,636)( 57,635)( 58,634)( 59,633)( 60,632)( 61,631)( 62,630)( 63,629)( 64,628)( 65,627)( 66,626)( 67,625)( 68,624)( 69,623)( 70,599)( 71,621)( 72,620)( 73,619)( 74,618)( 75,617)( 76,616)( 77,615)( 78,614)( 79,613)( 80,612)( 81,611)( 82,610)( 83,609)( 84,608)( 85,607)( 86,606)( 87,605)( 88,604)( 89,603)( 90,602)( 91,601)( 92,600)( 93,691)( 94,713)( 95,712)( 96,711)( 97,710)( 98,709)( 99,708)(100,707)(101,706)(102,705)(103,704)(104,703)(105,702)(106,701)(107,700)(108,699)(109,698)(110,697)(111,696)(112,695)(113,694)(114,693)(115,692)(116,714)(117,736)(118,735)(119,734)(120,733)(121,732)(122,731)(123,730)(124,729)(125,728)(126,727)(127,726)(128,725)(129,724)(130,723)(131,722)(132,721)(133,720)(134,719)(135,718)(136,717)(137,716)(138,715)(139,645)(140,667)(141,666)(142,665)(143,664)(144,663)(145,662)(146,661)(147,660)(148,659)(149,658)(150,657)(151,656)(152,655)(153,654)(154,653)(155,652)(156,651)(157,650)(158,649)(159,648)(160,647)(161,646)(162,668)(163,690)(164,689)(165,688)(166,687)(167,686)(168,685)(169,684)(170,683)(171,682)(172,681)(173,680)(174,679)(175,678)(176,677)(177,676)(178,675)(179,674)(180,673)(181,672)(182,671)(183,670)(184,669)(185,369)(186,391)(187,390)(188,389)(189,388)(190,387)(191,386)(192,385)(193,384)(194,383)(195,382)(196,381)(197,380)(198,379)(199,378)(200,377)(201,376)(202,375)(203,374)(204,373)(205,372)(206,371)(207,370)(208,392)(209,414)(210,413)(211,412)(212,411)(213,410)(214,409)(215,408)(216,407)(217,406)(218,405)(219,404)(220,403)(221,402)(222,401)(223,400)(224,399)(225,398)(226,397)(227,396)(228,395)(229,394)(230,393)(231,438)(232,460)(233,459)(234,458)(235,457)(236,456)(237,455)(238,454)(239,453)(240,452)(241,451)(242,450)(243,449)(244,448)(245,447)(246,446)(247,445)(248,444)(249,443)(250,442)(251,441)(252,440)(253,439)(254,415)(255,437)(256,436)(257,435)(258,434)(259,433)(260,432)(261,431)(262,430)(263,429)(264,428)(265,427)(266,426)(267,425)(268,424)(269,423)(270,422)(271,421)(272,420)(273,419)(274,418)(275,417)(276,416)(277,507)(278,529)(279,528)(280,527)(281,526)(282,525)(283,524)(284,523)(285,522)(286,521)(287,520)(288,519)(289,518)(290,517)(291,516)(292,515)(293,514)(294,513)(295,512)(296,511)(297,510)(298,509)(299,508)(300,530)(301,552)(302,551)(303,550)(304,549)(305,548)(306,547)(307,546)(308,545)(309,544)(310,543)(311,542)(312,541)(313,540)(314,539)(315,538)(316,537)(317,536)(318,535)(319,534)(320,533)(321,532)(322,531)(323,461)(324,483)(325,482)(326,481)(327,480)(328,479)(329,478)(330,477)(331,476)(332,475)(333,474)(334,473)(335,472)(336,471)(337,470)(338,469)(339,468)(340,467)(341,466)(342,465)(343,464)(344,463)(345,462)(346,484)(347,506)(348,505)(349,504)(350,503)(351,502)(352,501)(353,500)(354,499)(355,498)(356,497)(357,496)(358,495)(359,494)(360,493)(361,492)(362,491)(363,490)(364,489)(365,488)(366,487)(367,486)(368,485);;
s2 := (  1,186)(  2,185)(  3,207)(  4,206)(  5,205)(  6,204)(  7,203)(  8,202)(  9,201)( 10,200)( 11,199)( 12,198)( 13,197)( 14,196)( 15,195)( 16,194)( 17,193)( 18,192)( 19,191)( 20,190)( 21,189)( 22,188)( 23,187)( 24,209)( 25,208)( 26,230)( 27,229)( 28,228)( 29,227)( 30,226)( 31,225)( 32,224)( 33,223)( 34,222)( 35,221)( 36,220)( 37,219)( 38,218)( 39,217)( 40,216)( 41,215)( 42,214)( 43,213)( 44,212)( 45,211)( 46,210)( 47,232)( 48,231)( 49,253)( 50,252)( 51,251)( 52,250)( 53,249)( 54,248)( 55,247)( 56,246)( 57,245)( 58,244)( 59,243)( 60,242)( 61,241)( 62,240)( 63,239)( 64,238)( 65,237)( 66,236)( 67,235)( 68,234)( 69,233)( 70,255)( 71,254)( 72,276)( 73,275)( 74,274)( 75,273)( 76,272)( 77,271)( 78,270)( 79,269)( 80,268)( 81,267)( 82,266)( 83,265)( 84,264)( 85,263)( 86,262)( 87,261)( 88,260)( 89,259)( 90,258)( 91,257)( 92,256)( 93,278)( 94,277)( 95,299)( 96,298)( 97,297)( 98,296)( 99,295)(100,294)(101,293)(102,292)(103,291)(104,290)(105,289)(106,288)(107,287)(108,286)(109,285)(110,284)(111,283)(112,282)(113,281)(114,280)(115,279)(116,301)(117,300)(118,322)(119,321)(120,320)(121,319)(122,318)(123,317)(124,316)(125,315)(126,314)(127,313)(128,312)(129,311)(130,310)(131,309)(132,308)(133,307)(134,306)(135,305)(136,304)(137,303)(138,302)(139,324)(140,323)(141,345)(142,344)(143,343)(144,342)(145,341)(146,340)(147,339)(148,338)(149,337)(150,336)(151,335)(152,334)(153,333)(154,332)(155,331)(156,330)(157,329)(158,328)(159,327)(160,326)(161,325)(162,347)(163,346)(164,368)(165,367)(166,366)(167,365)(168,364)(169,363)(170,362)(171,361)(172,360)(173,359)(174,358)(175,357)(176,356)(177,355)(178,354)(179,353)(180,352)(181,351)(182,350)(183,349)(184,348)(369,554)(370,553)(371,575)(372,574)(373,573)(374,572)(375,571)(376,570)(377,569)(378,568)(379,567)(380,566)(381,565)(382,564)(383,563)(384,562)(385,561)(386,560)(387,559)(388,558)(389,557)(390,556)(391,555)(392,577)(393,576)(394,598)(395,597)(396,596)(397,595)(398,594)(399,593)(400,592)(401,591)(402,590)(403,589)(404,588)(405,587)(406,586)(407,585)(408,584)(409,583)(410,582)(411,581)(412,580)(413,579)(414,578)(415,600)(416,599)(417,621)(418,620)(419,619)(420,618)(421,617)(422,616)(423,615)(424,614)(425,613)(426,612)(427,611)(428,610)(429,609)(430,608)(431,607)(432,606)(433,605)(434,604)(435,603)(436,602)(437,601)(438,623)(439,622)(440,644)(441,643)(442,642)(443,641)(444,640)(445,639)(446,638)(447,637)(448,636)(449,635)(450,634)(451,633)(452,632)(453,631)(454,630)(455,629)(456,628)(457,627)(458,626)(459,625)(460,624)(461,646)(462,645)(463,667)(464,666)(465,665)(466,664)(467,663)(468,662)(469,661)(470,660)(471,659)(472,658)(473,657)(474,656)(475,655)(476,654)(477,653)(478,652)(479,651)(480,650)(481,649)(482,648)(483,647)(484,669)(485,668)(486,690)(487,689)(488,688)(489,687)(490,686)(491,685)(492,684)(493,683)(494,682)(495,681)(496,680)(497,679)(498,678)(499,677)(500,676)(501,675)(502,674)(503,673)(504,672)(505,671)(506,670)(507,692)(508,691)(509,713)(510,712)(511,711)(512,710)(513,709)(514,708)(515,707)(516,706)(517,705)(518,704)(519,703)(520,702)(521,701)(522,700)(523,699)(524,698)(525,697)(526,696)(527,695)(528,694)(529,693)(530,715)(531,714)(532,736)(533,735)(534,734)(535,733)(536,732)(537,731)(538,730)(539,729)(540,728)(541,727)(542,726)(543,725)(544,724)(545,723)(546,722)(547,721)(548,720)(549,719)(550,718)(551,717)(552,716);;
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, 
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, 
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*s1*s2*s1*s2 ];;
poly := F / rels;;
 

s0 := Sym(736)!( 47, 70)( 48, 71)( 49, 72)( 50, 73)( 51, 74)( 52, 75)( 53, 76)( 54, 77)( 55, 78)( 56, 79)( 57, 80)( 58, 81)( 59, 82)( 60, 83)( 61, 84)( 62, 85)( 63, 86)( 64, 87)( 65, 88)( 66, 89)( 67, 90)( 68, 91)( 69, 92)( 93,139)( 94,140)( 95,141)( 96,142)( 97,143)( 98,144)( 99,145)(100,146)(101,147)(102,148)(103,149)(104,150)(105,151)(106,152)(107,153)(108,154)(109,155)(110,156)(111,157)(112,158)(113,159)(114,160)(115,161)(116,162)(117,163)(118,164)(119,165)(120,166)(121,167)(122,168)(123,169)(124,170)(125,171)(126,172)(127,173)(128,174)(129,175)(130,176)(131,177)(132,178)(133,179)(134,180)(135,181)(136,182)(137,183)(138,184)(231,254)(232,255)(233,256)(234,257)(235,258)(236,259)(237,260)(238,261)(239,262)(240,263)(241,264)(242,265)(243,266)(244,267)(245,268)(246,269)(247,270)(248,271)(249,272)(250,273)(251,274)(252,275)(253,276)(277,323)(278,324)(279,325)(280,326)(281,327)(282,328)(283,329)(284,330)(285,331)(286,332)(287,333)(288,334)(289,335)(290,336)(291,337)(292,338)(293,339)(294,340)(295,341)(296,342)(297,343)(298,344)(299,345)(300,346)(301,347)(302,348)(303,349)(304,350)(305,351)(306,352)(307,353)(308,354)(309,355)(310,356)(311,357)(312,358)(313,359)(314,360)(315,361)(316,362)(317,363)(318,364)(319,365)(320,366)(321,367)(322,368)(369,461)(370,462)(371,463)(372,464)(373,465)(374,466)(375,467)(376,468)(377,469)(378,470)(379,471)(380,472)(381,473)(382,474)(383,475)(384,476)(385,477)(386,478)(387,479)(388,480)(389,481)(390,482)(391,483)(392,484)(393,485)(394,486)(395,487)(396,488)(397,489)(398,490)(399,491)(400,492)(401,493)(402,494)(403,495)(404,496)(405,497)(406,498)(407,499)(408,500)(409,501)(410,502)(411,503)(412,504)(413,505)(414,506)(415,530)(416,531)(417,532)(418,533)(419,534)(420,535)(421,536)(422,537)(423,538)(424,539)(425,540)(426,541)(427,542)(428,543)(429,544)(430,545)(431,546)(432,547)(433,548)(434,549)(435,550)(436,551)(437,552)(438,507)(439,508)(440,509)(441,510)(442,511)(443,512)(444,513)(445,514)(446,515)(447,516)(448,517)(449,518)(450,519)(451,520)(452,521)(453,522)(454,523)(455,524)(456,525)(457,526)(458,527)(459,528)(460,529)(553,645)(554,646)(555,647)(556,648)(557,649)(558,650)(559,651)(560,652)(561,653)(562,654)(563,655)(564,656)(565,657)(566,658)(567,659)(568,660)(569,661)(570,662)(571,663)(572,664)(573,665)(574,666)(575,667)(576,668)(577,669)(578,670)(579,671)(580,672)(581,673)(582,674)(583,675)(584,676)(585,677)(586,678)(587,679)(588,680)(589,681)(590,682)(591,683)(592,684)(593,685)(594,686)(595,687)(596,688)(597,689)(598,690)(599,714)(600,715)(601,716)(602,717)(603,718)(604,719)(605,720)(606,721)(607,722)(608,723)(609,724)(610,725)(611,726)(612,727)(613,728)(614,729)(615,730)(616,731)(617,732)(618,733)(619,734)(620,735)(621,736)(622,691)(623,692)(624,693)(625,694)(626,695)(627,696)(628,697)(629,698)(630,699)(631,700)(632,701)(633,702)(634,703)(635,704)(636,705)(637,706)(638,707)(639,708)(640,709)(641,710)(642,711)(643,712)(644,713);
s1 := Sym(736)!(  1,553)(  2,575)(  3,574)(  4,573)(  5,572)(  6,571)(  7,570)(  8,569)(  9,568)( 10,567)( 11,566)( 12,565)( 13,564)( 14,563)( 15,562)( 16,561)( 17,560)( 18,559)( 19,558)( 20,557)( 21,556)( 22,555)( 23,554)( 24,576)( 25,598)( 26,597)( 27,596)( 28,595)( 29,594)( 30,593)( 31,592)( 32,591)( 33,590)( 34,589)( 35,588)( 36,587)( 37,586)( 38,585)( 39,584)( 40,583)( 41,582)( 42,581)( 43,580)( 44,579)( 45,578)( 46,577)( 47,622)( 48,644)( 49,643)( 50,642)( 51,641)( 52,640)( 53,639)( 54,638)( 55,637)( 56,636)( 57,635)( 58,634)( 59,633)( 60,632)( 61,631)( 62,630)( 63,629)( 64,628)( 65,627)( 66,626)( 67,625)( 68,624)( 69,623)( 70,599)( 71,621)( 72,620)( 73,619)( 74,618)( 75,617)( 76,616)( 77,615)( 78,614)( 79,613)( 80,612)( 81,611)( 82,610)( 83,609)( 84,608)( 85,607)( 86,606)( 87,605)( 88,604)( 89,603)( 90,602)( 91,601)( 92,600)( 93,691)( 94,713)( 95,712)( 96,711)( 97,710)( 98,709)( 99,708)(100,707)(101,706)(102,705)(103,704)(104,703)(105,702)(106,701)(107,700)(108,699)(109,698)(110,697)(111,696)(112,695)(113,694)(114,693)(115,692)(116,714)(117,736)(118,735)(119,734)(120,733)(121,732)(122,731)(123,730)(124,729)(125,728)(126,727)(127,726)(128,725)(129,724)(130,723)(131,722)(132,721)(133,720)(134,719)(135,718)(136,717)(137,716)(138,715)(139,645)(140,667)(141,666)(142,665)(143,664)(144,663)(145,662)(146,661)(147,660)(148,659)(149,658)(150,657)(151,656)(152,655)(153,654)(154,653)(155,652)(156,651)(157,650)(158,649)(159,648)(160,647)(161,646)(162,668)(163,690)(164,689)(165,688)(166,687)(167,686)(168,685)(169,684)(170,683)(171,682)(172,681)(173,680)(174,679)(175,678)(176,677)(177,676)(178,675)(179,674)(180,673)(181,672)(182,671)(183,670)(184,669)(185,369)(186,391)(187,390)(188,389)(189,388)(190,387)(191,386)(192,385)(193,384)(194,383)(195,382)(196,381)(197,380)(198,379)(199,378)(200,377)(201,376)(202,375)(203,374)(204,373)(205,372)(206,371)(207,370)(208,392)(209,414)(210,413)(211,412)(212,411)(213,410)(214,409)(215,408)(216,407)(217,406)(218,405)(219,404)(220,403)(221,402)(222,401)(223,400)(224,399)(225,398)(226,397)(227,396)(228,395)(229,394)(230,393)(231,438)(232,460)(233,459)(234,458)(235,457)(236,456)(237,455)(238,454)(239,453)(240,452)(241,451)(242,450)(243,449)(244,448)(245,447)(246,446)(247,445)(248,444)(249,443)(250,442)(251,441)(252,440)(253,439)(254,415)(255,437)(256,436)(257,435)(258,434)(259,433)(260,432)(261,431)(262,430)(263,429)(264,428)(265,427)(266,426)(267,425)(268,424)(269,423)(270,422)(271,421)(272,420)(273,419)(274,418)(275,417)(276,416)(277,507)(278,529)(279,528)(280,527)(281,526)(282,525)(283,524)(284,523)(285,522)(286,521)(287,520)(288,519)(289,518)(290,517)(291,516)(292,515)(293,514)(294,513)(295,512)(296,511)(297,510)(298,509)(299,508)(300,530)(301,552)(302,551)(303,550)(304,549)(305,548)(306,547)(307,546)(308,545)(309,544)(310,543)(311,542)(312,541)(313,540)(314,539)(315,538)(316,537)(317,536)(318,535)(319,534)(320,533)(321,532)(322,531)(323,461)(324,483)(325,482)(326,481)(327,480)(328,479)(329,478)(330,477)(331,476)(332,475)(333,474)(334,473)(335,472)(336,471)(337,470)(338,469)(339,468)(340,467)(341,466)(342,465)(343,464)(344,463)(345,462)(346,484)(347,506)(348,505)(349,504)(350,503)(351,502)(352,501)(353,500)(354,499)(355,498)(356,497)(357,496)(358,495)(359,494)(360,493)(361,492)(362,491)(363,490)(364,489)(365,488)(366,487)(367,486)(368,485);
s2 := Sym(736)!(  1,186)(  2,185)(  3,207)(  4,206)(  5,205)(  6,204)(  7,203)(  8,202)(  9,201)( 10,200)( 11,199)( 12,198)( 13,197)( 14,196)( 15,195)( 16,194)( 17,193)( 18,192)( 19,191)( 20,190)( 21,189)( 22,188)( 23,187)( 24,209)( 25,208)( 26,230)( 27,229)( 28,228)( 29,227)( 30,226)( 31,225)( 32,224)( 33,223)( 34,222)( 35,221)( 36,220)( 37,219)( 38,218)( 39,217)( 40,216)( 41,215)( 42,214)( 43,213)( 44,212)( 45,211)( 46,210)( 47,232)( 48,231)( 49,253)( 50,252)( 51,251)( 52,250)( 53,249)( 54,248)( 55,247)( 56,246)( 57,245)( 58,244)( 59,243)( 60,242)( 61,241)( 62,240)( 63,239)( 64,238)( 65,237)( 66,236)( 67,235)( 68,234)( 69,233)( 70,255)( 71,254)( 72,276)( 73,275)( 74,274)( 75,273)( 76,272)( 77,271)( 78,270)( 79,269)( 80,268)( 81,267)( 82,266)( 83,265)( 84,264)( 85,263)( 86,262)( 87,261)( 88,260)( 89,259)( 90,258)( 91,257)( 92,256)( 93,278)( 94,277)( 95,299)( 96,298)( 97,297)( 98,296)( 99,295)(100,294)(101,293)(102,292)(103,291)(104,290)(105,289)(106,288)(107,287)(108,286)(109,285)(110,284)(111,283)(112,282)(113,281)(114,280)(115,279)(116,301)(117,300)(118,322)(119,321)(120,320)(121,319)(122,318)(123,317)(124,316)(125,315)(126,314)(127,313)(128,312)(129,311)(130,310)(131,309)(132,308)(133,307)(134,306)(135,305)(136,304)(137,303)(138,302)(139,324)(140,323)(141,345)(142,344)(143,343)(144,342)(145,341)(146,340)(147,339)(148,338)(149,337)(150,336)(151,335)(152,334)(153,333)(154,332)(155,331)(156,330)(157,329)(158,328)(159,327)(160,326)(161,325)(162,347)(163,346)(164,368)(165,367)(166,366)(167,365)(168,364)(169,363)(170,362)(171,361)(172,360)(173,359)(174,358)(175,357)(176,356)(177,355)(178,354)(179,353)(180,352)(181,351)(182,350)(183,349)(184,348)(369,554)(370,553)(371,575)(372,574)(373,573)(374,572)(375,571)(376,570)(377,569)(378,568)(379,567)(380,566)(381,565)(382,564)(383,563)(384,562)(385,561)(386,560)(387,559)(388,558)(389,557)(390,556)(391,555)(392,577)(393,576)(394,598)(395,597)(396,596)(397,595)(398,594)(399,593)(400,592)(401,591)(402,590)(403,589)(404,588)(405,587)(406,586)(407,585)(408,584)(409,583)(410,582)(411,581)(412,580)(413,579)(414,578)(415,600)(416,599)(417,621)(418,620)(419,619)(420,618)(421,617)(422,616)(423,615)(424,614)(425,613)(426,612)(427,611)(428,610)(429,609)(430,608)(431,607)(432,606)(433,605)(434,604)(435,603)(436,602)(437,601)(438,623)(439,622)(440,644)(441,643)(442,642)(443,641)(444,640)(445,639)(446,638)(447,637)(448,636)(449,635)(450,634)(451,633)(452,632)(453,631)(454,630)(455,629)(456,628)(457,627)(458,626)(459,625)(460,624)(461,646)(462,645)(463,667)(464,666)(465,665)(466,664)(467,663)(468,662)(469,661)(470,660)(471,659)(472,658)(473,657)(474,656)(475,655)(476,654)(477,653)(478,652)(479,651)(480,650)(481,649)(482,648)(483,647)(484,669)(485,668)(486,690)(487,689)(488,688)(489,687)(490,686)(491,685)(492,684)(493,683)(494,682)(495,681)(496,680)(497,679)(498,678)(499,677)(500,676)(501,675)(502,674)(503,673)(504,672)(505,671)(506,670)(507,692)(508,691)(509,713)(510,712)(511,711)(512,710)(513,709)(514,708)(515,707)(516,706)(517,705)(518,704)(519,703)(520,702)(521,701)(522,700)(523,699)(524,698)(525,697)(526,696)(527,695)(528,694)(529,693)(530,715)(531,714)(532,736)(533,735)(534,734)(535,733)(536,732)(537,731)(538,730)(539,729)(540,728)(541,727)(542,726)(543,725)(544,724)(545,723)(546,722)(547,721)(548,720)(549,719)(550,718)(551,717)(552,716);
poly := sub<Sym(736)|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, 
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, 
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*s1*s2*s1*s2 >; 
 

Twisty Puzzle