Polytope of Type {4,93}

Play with this polytope as a twisty puzzle

s0 := (  1,375)(  2,376)(  3,373)(  4,374)(  5,379)(  6,380)(  7,377)(  8,378)(  9,383)( 10,384)( 11,381)( 12,382)( 13,387)( 14,388)( 15,385)( 16,386)( 17,391)( 18,392)( 19,389)( 20,390)( 21,395)( 22,396)( 23,393)( 24,394)( 25,399)( 26,400)( 27,397)( 28,398)( 29,403)( 30,404)( 31,401)( 32,402)( 33,407)( 34,408)( 35,405)( 36,406)( 37,411)( 38,412)( 39,409)( 40,410)( 41,415)( 42,416)( 43,413)( 44,414)( 45,419)( 46,420)( 47,417)( 48,418)( 49,423)( 50,424)( 51,421)( 52,422)( 53,427)( 54,428)( 55,425)( 56,426)( 57,431)( 58,432)( 59,429)( 60,430)( 61,435)( 62,436)( 63,433)( 64,434)( 65,439)( 66,440)( 67,437)( 68,438)( 69,443)( 70,444)( 71,441)( 72,442)( 73,447)( 74,448)( 75,445)( 76,446)( 77,451)( 78,452)( 79,449)( 80,450)( 81,455)( 82,456)( 83,453)( 84,454)( 85,459)( 86,460)( 87,457)( 88,458)( 89,463)( 90,464)( 91,461)( 92,462)( 93,467)( 94,468)( 95,465)( 96,466)( 97,471)( 98,472)( 99,469)(100,470)(101,475)(102,476)(103,473)(104,474)(105,479)(106,480)(107,477)(108,478)(109,483)(110,484)(111,481)(112,482)(113,487)(114,488)(115,485)(116,486)(117,491)(118,492)(119,489)(120,490)(121,495)(122,496)(123,493)(124,494)(125,499)(126,500)(127,497)(128,498)(129,503)(130,504)(131,501)(132,502)(133,507)(134,508)(135,505)(136,506)(137,511)(138,512)(139,509)(140,510)(141,515)(142,516)(143,513)(144,514)(145,519)(146,520)(147,517)(148,518)(149,523)(150,524)(151,521)(152,522)(153,527)(154,528)(155,525)(156,526)(157,531)(158,532)(159,529)(160,530)(161,535)(162,536)(163,533)(164,534)(165,539)(166,540)(167,537)(168,538)(169,543)(170,544)(171,541)(172,542)(173,547)(174,548)(175,545)(176,546)(177,551)(178,552)(179,549)(180,550)(181,555)(182,556)(183,553)(184,554)(185,559)(186,560)(187,557)(188,558)(189,563)(190,564)(191,561)(192,562)(193,567)(194,568)(195,565)(196,566)(197,571)(198,572)(199,569)(200,570)(201,575)(202,576)(203,573)(204,574)(205,579)(206,580)(207,577)(208,578)(209,583)(210,584)(211,581)(212,582)(213,587)(214,588)(215,585)(216,586)(217,591)(218,592)(219,589)(220,590)(221,595)(222,596)(223,593)(224,594)(225,599)(226,600)(227,597)(228,598)(229,603)(230,604)(231,601)(232,602)(233,607)(234,608)(235,605)(236,606)(237,611)(238,612)(239,609)(240,610)(241,615)(242,616)(243,613)(244,614)(245,619)(246,620)(247,617)(248,618)(249,623)(250,624)(251,621)(252,622)(253,627)(254,628)(255,625)(256,626)(257,631)(258,632)(259,629)(260,630)(261,635)(262,636)(263,633)(264,634)(265,639)(266,640)(267,637)(268,638)(269,643)(270,644)(271,641)(272,642)(273,647)(274,648)(275,645)(276,646)(277,651)(278,652)(279,649)(280,650)(281,655)(282,656)(283,653)(284,654)(285,659)(286,660)(287,657)(288,658)(289,663)(290,664)(291,661)(292,662)(293,667)(294,668)(295,665)(296,666)(297,671)(298,672)(299,669)(300,670)(301,675)(302,676)(303,673)(304,674)(305,679)(306,680)(307,677)(308,678)(309,683)(310,684)(311,681)(312,682)(313,687)(314,688)(315,685)(316,686)(317,691)(318,692)(319,689)(320,690)(321,695)(322,696)(323,693)(324,694)(325,699)(326,700)(327,697)(328,698)(329,703)(330,704)(331,701)(332,702)(333,707)(334,708)(335,705)(336,706)(337,711)(338,712)(339,709)(340,710)(341,715)(342,716)(343,713)(344,714)(345,719)(346,720)(347,717)(348,718)(349,723)(350,724)(351,721)(352,722)(353,727)(354,728)(355,725)(356,726)(357,731)(358,732)(359,729)(360,730)(361,735)(362,736)(363,733)(364,734)(365,739)(366,740)(367,737)(368,738)(369,743)(370,744)(371,741)(372,742);;
s1 := (  3,  4)(  5,121)(  6,122)(  7,124)(  8,123)(  9,117)( 10,118)( 11,120)( 12,119)( 13,113)( 14,114)( 15,116)( 16,115)( 17,109)( 18,110)( 19,112)( 20,111)( 21,105)( 22,106)( 23,108)( 24,107)( 25,101)( 26,102)( 27,104)( 28,103)( 29, 97)( 30, 98)( 31,100)( 32, 99)( 33, 93)( 34, 94)( 35, 96)( 36, 95)( 37, 89)( 38, 90)( 39, 92)( 40, 91)( 41, 85)( 42, 86)( 43, 88)( 44, 87)( 45, 81)( 46, 82)( 47, 84)( 48, 83)( 49, 77)( 50, 78)( 51, 80)( 52, 79)( 53, 73)( 54, 74)( 55, 76)( 56, 75)( 57, 69)( 58, 70)( 59, 72)( 60, 71)( 61, 65)( 62, 66)( 63, 68)( 64, 67)(125,249)(126,250)(127,252)(128,251)(129,369)(130,370)(131,372)(132,371)(133,365)(134,366)(135,368)(136,367)(137,361)(138,362)(139,364)(140,363)(141,357)(142,358)(143,360)(144,359)(145,353)(146,354)(147,356)(148,355)(149,349)(150,350)(151,352)(152,351)(153,345)(154,346)(155,348)(156,347)(157,341)(158,342)(159,344)(160,343)(161,337)(162,338)(163,340)(164,339)(165,333)(166,334)(167,336)(168,335)(169,329)(170,330)(171,332)(172,331)(173,325)(174,326)(175,328)(176,327)(177,321)(178,322)(179,324)(180,323)(181,317)(182,318)(183,320)(184,319)(185,313)(186,314)(187,316)(188,315)(189,309)(190,310)(191,312)(192,311)(193,305)(194,306)(195,308)(196,307)(197,301)(198,302)(199,304)(200,303)(201,297)(202,298)(203,300)(204,299)(205,293)(206,294)(207,296)(208,295)(209,289)(210,290)(211,292)(212,291)(213,285)(214,286)(215,288)(216,287)(217,281)(218,282)(219,284)(220,283)(221,277)(222,278)(223,280)(224,279)(225,273)(226,274)(227,276)(228,275)(229,269)(230,270)(231,272)(232,271)(233,265)(234,266)(235,268)(236,267)(237,261)(238,262)(239,264)(240,263)(241,257)(242,258)(243,260)(244,259)(245,253)(246,254)(247,256)(248,255)(375,376)(377,493)(378,494)(379,496)(380,495)(381,489)(382,490)(383,492)(384,491)(385,485)(386,486)(387,488)(388,487)(389,481)(390,482)(391,484)(392,483)(393,477)(394,478)(395,480)(396,479)(397,473)(398,474)(399,476)(400,475)(401,469)(402,470)(403,472)(404,471)(405,465)(406,466)(407,468)(408,467)(409,461)(410,462)(411,464)(412,463)(413,457)(414,458)(415,460)(416,459)(417,453)(418,454)(419,456)(420,455)(421,449)(422,450)(423,452)(424,451)(425,445)(426,446)(427,448)(428,447)(429,441)(430,442)(431,444)(432,443)(433,437)(434,438)(435,440)(436,439)(497,621)(498,622)(499,624)(500,623)(501,741)(502,742)(503,744)(504,743)(505,737)(506,738)(507,740)(508,739)(509,733)(510,734)(511,736)(512,735)(513,729)(514,730)(515,732)(516,731)(517,725)(518,726)(519,728)(520,727)(521,721)(522,722)(523,724)(524,723)(525,717)(526,718)(527,720)(528,719)(529,713)(530,714)(531,716)(532,715)(533,709)(534,710)(535,712)(536,711)(537,705)(538,706)(539,708)(540,707)(541,701)(542,702)(543,704)(544,703)(545,697)(546,698)(547,700)(548,699)(549,693)(550,694)(551,696)(552,695)(553,689)(554,690)(555,692)(556,691)(557,685)(558,686)(559,688)(560,687)(561,681)(562,682)(563,684)(564,683)(565,677)(566,678)(567,680)(568,679)(569,673)(570,674)(571,676)(572,675)(573,669)(574,670)(575,672)(576,671)(577,665)(578,666)(579,668)(580,667)(581,661)(582,662)(583,664)(584,663)(585,657)(586,658)(587,660)(588,659)(589,653)(590,654)(591,656)(592,655)(593,649)(594,650)(595,652)(596,651)(597,645)(598,646)(599,648)(600,647)(601,641)(602,642)(603,644)(604,643)(605,637)(606,638)(607,640)(608,639)(609,633)(610,634)(611,636)(612,635)(613,629)(614,630)(615,632)(616,631)(617,625)(618,626)(619,628)(620,627);;
s2 := (  1,129)(  2,132)(  3,131)(  4,130)(  5,125)(  6,128)(  7,127)(  8,126)(  9,245)( 10,248)( 11,247)( 12,246)( 13,241)( 14,244)( 15,243)( 16,242)( 17,237)( 18,240)( 19,239)( 20,238)( 21,233)( 22,236)( 23,235)( 24,234)( 25,229)( 26,232)( 27,231)( 28,230)( 29,225)( 30,228)( 31,227)( 32,226)( 33,221)( 34,224)( 35,223)( 36,222)( 37,217)( 38,220)( 39,219)( 40,218)( 41,213)( 42,216)( 43,215)( 44,214)( 45,209)( 46,212)( 47,211)( 48,210)( 49,205)( 50,208)( 51,207)( 52,206)( 53,201)( 54,204)( 55,203)( 56,202)( 57,197)( 58,200)( 59,199)( 60,198)( 61,193)( 62,196)( 63,195)( 64,194)( 65,189)( 66,192)( 67,191)( 68,190)( 69,185)( 70,188)( 71,187)( 72,186)( 73,181)( 74,184)( 75,183)( 76,182)( 77,177)( 78,180)( 79,179)( 80,178)( 81,173)( 82,176)( 83,175)( 84,174)( 85,169)( 86,172)( 87,171)( 88,170)( 89,165)( 90,168)( 91,167)( 92,166)( 93,161)( 94,164)( 95,163)( 96,162)( 97,157)( 98,160)( 99,159)(100,158)(101,153)(102,156)(103,155)(104,154)(105,149)(106,152)(107,151)(108,150)(109,145)(110,148)(111,147)(112,146)(113,141)(114,144)(115,143)(116,142)(117,137)(118,140)(119,139)(120,138)(121,133)(122,136)(123,135)(124,134)(249,253)(250,256)(251,255)(252,254)(257,369)(258,372)(259,371)(260,370)(261,365)(262,368)(263,367)(264,366)(265,361)(266,364)(267,363)(268,362)(269,357)(270,360)(271,359)(272,358)(273,353)(274,356)(275,355)(276,354)(277,349)(278,352)(279,351)(280,350)(281,345)(282,348)(283,347)(284,346)(285,341)(286,344)(287,343)(288,342)(289,337)(290,340)(291,339)(292,338)(293,333)(294,336)(295,335)(296,334)(297,329)(298,332)(299,331)(300,330)(301,325)(302,328)(303,327)(304,326)(305,321)(306,324)(307,323)(308,322)(309,317)(310,320)(311,319)(312,318)(314,316)(373,501)(374,504)(375,503)(376,502)(377,497)(378,500)(379,499)(380,498)(381,617)(382,620)(383,619)(384,618)(385,613)(386,616)(387,615)(388,614)(389,609)(390,612)(391,611)(392,610)(393,605)(394,608)(395,607)(396,606)(397,601)(398,604)(399,603)(400,602)(401,597)(402,600)(403,599)(404,598)(405,593)(406,596)(407,595)(408,594)(409,589)(410,592)(411,591)(412,590)(413,585)(414,588)(415,587)(416,586)(417,581)(418,584)(419,583)(420,582)(421,577)(422,580)(423,579)(424,578)(425,573)(426,576)(427,575)(428,574)(429,569)(430,572)(431,571)(432,570)(433,565)(434,568)(435,567)(436,566)(437,561)(438,564)(439,563)(440,562)(441,557)(442,560)(443,559)(444,558)(445,553)(446,556)(447,555)(448,554)(449,549)(450,552)(451,551)(452,550)(453,545)(454,548)(455,547)(456,546)(457,541)(458,544)(459,543)(460,542)(461,537)(462,540)(463,539)(464,538)(465,533)(466,536)(467,535)(468,534)(469,529)(470,532)(471,531)(472,530)(473,525)(474,528)(475,527)(476,526)(477,521)(478,524)(479,523)(480,522)(481,517)(482,520)(483,519)(484,518)(485,513)(486,516)(487,515)(488,514)(489,509)(490,512)(491,511)(492,510)(493,505)(494,508)(495,507)(496,506)(621,625)(622,628)(623,627)(624,626)(629,741)(630,744)(631,743)(632,742)(633,737)(634,740)(635,739)(636,738)(637,733)(638,736)(639,735)(640,734)(641,729)(642,732)(643,731)(644,730)(645,725)(646,728)(647,727)(648,726)(649,721)(650,724)(651,723)(652,722)(653,717)(654,720)(655,719)(656,718)(657,713)(658,716)(659,715)(660,714)(661,709)(662,712)(663,711)(664,710)(665,705)(666,708)(667,707)(668,706)(669,701)(670,704)(671,703)(672,702)(673,697)(674,700)(675,699)(676,698)(677,693)(678,696)(679,695)(680,694)(681,689)(682,692)(683,691)(684,690)(686,688);;
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*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*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*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*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(744)!(  1,375)(  2,376)(  3,373)(  4,374)(  5,379)(  6,380)(  7,377)(  8,378)(  9,383)( 10,384)( 11,381)( 12,382)( 13,387)( 14,388)( 15,385)( 16,386)( 17,391)( 18,392)( 19,389)( 20,390)( 21,395)( 22,396)( 23,393)( 24,394)( 25,399)( 26,400)( 27,397)( 28,398)( 29,403)( 30,404)( 31,401)( 32,402)( 33,407)( 34,408)( 35,405)( 36,406)( 37,411)( 38,412)( 39,409)( 40,410)( 41,415)( 42,416)( 43,413)( 44,414)( 45,419)( 46,420)( 47,417)( 48,418)( 49,423)( 50,424)( 51,421)( 52,422)( 53,427)( 54,428)( 55,425)( 56,426)( 57,431)( 58,432)( 59,429)( 60,430)( 61,435)( 62,436)( 63,433)( 64,434)( 65,439)( 66,440)( 67,437)( 68,438)( 69,443)( 70,444)( 71,441)( 72,442)( 73,447)( 74,448)( 75,445)( 76,446)( 77,451)( 78,452)( 79,449)( 80,450)( 81,455)( 82,456)( 83,453)( 84,454)( 85,459)( 86,460)( 87,457)( 88,458)( 89,463)( 90,464)( 91,461)( 92,462)( 93,467)( 94,468)( 95,465)( 96,466)( 97,471)( 98,472)( 99,469)(100,470)(101,475)(102,476)(103,473)(104,474)(105,479)(106,480)(107,477)(108,478)(109,483)(110,484)(111,481)(112,482)(113,487)(114,488)(115,485)(116,486)(117,491)(118,492)(119,489)(120,490)(121,495)(122,496)(123,493)(124,494)(125,499)(126,500)(127,497)(128,498)(129,503)(130,504)(131,501)(132,502)(133,507)(134,508)(135,505)(136,506)(137,511)(138,512)(139,509)(140,510)(141,515)(142,516)(143,513)(144,514)(145,519)(146,520)(147,517)(148,518)(149,523)(150,524)(151,521)(152,522)(153,527)(154,528)(155,525)(156,526)(157,531)(158,532)(159,529)(160,530)(161,535)(162,536)(163,533)(164,534)(165,539)(166,540)(167,537)(168,538)(169,543)(170,544)(171,541)(172,542)(173,547)(174,548)(175,545)(176,546)(177,551)(178,552)(179,549)(180,550)(181,555)(182,556)(183,553)(184,554)(185,559)(186,560)(187,557)(188,558)(189,563)(190,564)(191,561)(192,562)(193,567)(194,568)(195,565)(196,566)(197,571)(198,572)(199,569)(200,570)(201,575)(202,576)(203,573)(204,574)(205,579)(206,580)(207,577)(208,578)(209,583)(210,584)(211,581)(212,582)(213,587)(214,588)(215,585)(216,586)(217,591)(218,592)(219,589)(220,590)(221,595)(222,596)(223,593)(224,594)(225,599)(226,600)(227,597)(228,598)(229,603)(230,604)(231,601)(232,602)(233,607)(234,608)(235,605)(236,606)(237,611)(238,612)(239,609)(240,610)(241,615)(242,616)(243,613)(244,614)(245,619)(246,620)(247,617)(248,618)(249,623)(250,624)(251,621)(252,622)(253,627)(254,628)(255,625)(256,626)(257,631)(258,632)(259,629)(260,630)(261,635)(262,636)(263,633)(264,634)(265,639)(266,640)(267,637)(268,638)(269,643)(270,644)(271,641)(272,642)(273,647)(274,648)(275,645)(276,646)(277,651)(278,652)(279,649)(280,650)(281,655)(282,656)(283,653)(284,654)(285,659)(286,660)(287,657)(288,658)(289,663)(290,664)(291,661)(292,662)(293,667)(294,668)(295,665)(296,666)(297,671)(298,672)(299,669)(300,670)(301,675)(302,676)(303,673)(304,674)(305,679)(306,680)(307,677)(308,678)(309,683)(310,684)(311,681)(312,682)(313,687)(314,688)(315,685)(316,686)(317,691)(318,692)(319,689)(320,690)(321,695)(322,696)(323,693)(324,694)(325,699)(326,700)(327,697)(328,698)(329,703)(330,704)(331,701)(332,702)(333,707)(334,708)(335,705)(336,706)(337,711)(338,712)(339,709)(340,710)(341,715)(342,716)(343,713)(344,714)(345,719)(346,720)(347,717)(348,718)(349,723)(350,724)(351,721)(352,722)(353,727)(354,728)(355,725)(356,726)(357,731)(358,732)(359,729)(360,730)(361,735)(362,736)(363,733)(364,734)(365,739)(366,740)(367,737)(368,738)(369,743)(370,744)(371,741)(372,742);
s1 := Sym(744)!(  3,  4)(  5,121)(  6,122)(  7,124)(  8,123)(  9,117)( 10,118)( 11,120)( 12,119)( 13,113)( 14,114)( 15,116)( 16,115)( 17,109)( 18,110)( 19,112)( 20,111)( 21,105)( 22,106)( 23,108)( 24,107)( 25,101)( 26,102)( 27,104)( 28,103)( 29, 97)( 30, 98)( 31,100)( 32, 99)( 33, 93)( 34, 94)( 35, 96)( 36, 95)( 37, 89)( 38, 90)( 39, 92)( 40, 91)( 41, 85)( 42, 86)( 43, 88)( 44, 87)( 45, 81)( 46, 82)( 47, 84)( 48, 83)( 49, 77)( 50, 78)( 51, 80)( 52, 79)( 53, 73)( 54, 74)( 55, 76)( 56, 75)( 57, 69)( 58, 70)( 59, 72)( 60, 71)( 61, 65)( 62, 66)( 63, 68)( 64, 67)(125,249)(126,250)(127,252)(128,251)(129,369)(130,370)(131,372)(132,371)(133,365)(134,366)(135,368)(136,367)(137,361)(138,362)(139,364)(140,363)(141,357)(142,358)(143,360)(144,359)(145,353)(146,354)(147,356)(148,355)(149,349)(150,350)(151,352)(152,351)(153,345)(154,346)(155,348)(156,347)(157,341)(158,342)(159,344)(160,343)(161,337)(162,338)(163,340)(164,339)(165,333)(166,334)(167,336)(168,335)(169,329)(170,330)(171,332)(172,331)(173,325)(174,326)(175,328)(176,327)(177,321)(178,322)(179,324)(180,323)(181,317)(182,318)(183,320)(184,319)(185,313)(186,314)(187,316)(188,315)(189,309)(190,310)(191,312)(192,311)(193,305)(194,306)(195,308)(196,307)(197,301)(198,302)(199,304)(200,303)(201,297)(202,298)(203,300)(204,299)(205,293)(206,294)(207,296)(208,295)(209,289)(210,290)(211,292)(212,291)(213,285)(214,286)(215,288)(216,287)(217,281)(218,282)(219,284)(220,283)(221,277)(222,278)(223,280)(224,279)(225,273)(226,274)(227,276)(228,275)(229,269)(230,270)(231,272)(232,271)(233,265)(234,266)(235,268)(236,267)(237,261)(238,262)(239,264)(240,263)(241,257)(242,258)(243,260)(244,259)(245,253)(246,254)(247,256)(248,255)(375,376)(377,493)(378,494)(379,496)(380,495)(381,489)(382,490)(383,492)(384,491)(385,485)(386,486)(387,488)(388,487)(389,481)(390,482)(391,484)(392,483)(393,477)(394,478)(395,480)(396,479)(397,473)(398,474)(399,476)(400,475)(401,469)(402,470)(403,472)(404,471)(405,465)(406,466)(407,468)(408,467)(409,461)(410,462)(411,464)(412,463)(413,457)(414,458)(415,460)(416,459)(417,453)(418,454)(419,456)(420,455)(421,449)(422,450)(423,452)(424,451)(425,445)(426,446)(427,448)(428,447)(429,441)(430,442)(431,444)(432,443)(433,437)(434,438)(435,440)(436,439)(497,621)(498,622)(499,624)(500,623)(501,741)(502,742)(503,744)(504,743)(505,737)(506,738)(507,740)(508,739)(509,733)(510,734)(511,736)(512,735)(513,729)(514,730)(515,732)(516,731)(517,725)(518,726)(519,728)(520,727)(521,721)(522,722)(523,724)(524,723)(525,717)(526,718)(527,720)(528,719)(529,713)(530,714)(531,716)(532,715)(533,709)(534,710)(535,712)(536,711)(537,705)(538,706)(539,708)(540,707)(541,701)(542,702)(543,704)(544,703)(545,697)(546,698)(547,700)(548,699)(549,693)(550,694)(551,696)(552,695)(553,689)(554,690)(555,692)(556,691)(557,685)(558,686)(559,688)(560,687)(561,681)(562,682)(563,684)(564,683)(565,677)(566,678)(567,680)(568,679)(569,673)(570,674)(571,676)(572,675)(573,669)(574,670)(575,672)(576,671)(577,665)(578,666)(579,668)(580,667)(581,661)(582,662)(583,664)(584,663)(585,657)(586,658)(587,660)(588,659)(589,653)(590,654)(591,656)(592,655)(593,649)(594,650)(595,652)(596,651)(597,645)(598,646)(599,648)(600,647)(601,641)(602,642)(603,644)(604,643)(605,637)(606,638)(607,640)(608,639)(609,633)(610,634)(611,636)(612,635)(613,629)(614,630)(615,632)(616,631)(617,625)(618,626)(619,628)(620,627);
s2 := Sym(744)!(  1,129)(  2,132)(  3,131)(  4,130)(  5,125)(  6,128)(  7,127)(  8,126)(  9,245)( 10,248)( 11,247)( 12,246)( 13,241)( 14,244)( 15,243)( 16,242)( 17,237)( 18,240)( 19,239)( 20,238)( 21,233)( 22,236)( 23,235)( 24,234)( 25,229)( 26,232)( 27,231)( 28,230)( 29,225)( 30,228)( 31,227)( 32,226)( 33,221)( 34,224)( 35,223)( 36,222)( 37,217)( 38,220)( 39,219)( 40,218)( 41,213)( 42,216)( 43,215)( 44,214)( 45,209)( 46,212)( 47,211)( 48,210)( 49,205)( 50,208)( 51,207)( 52,206)( 53,201)( 54,204)( 55,203)( 56,202)( 57,197)( 58,200)( 59,199)( 60,198)( 61,193)( 62,196)( 63,195)( 64,194)( 65,189)( 66,192)( 67,191)( 68,190)( 69,185)( 70,188)( 71,187)( 72,186)( 73,181)( 74,184)( 75,183)( 76,182)( 77,177)( 78,180)( 79,179)( 80,178)( 81,173)( 82,176)( 83,175)( 84,174)( 85,169)( 86,172)( 87,171)( 88,170)( 89,165)( 90,168)( 91,167)( 92,166)( 93,161)( 94,164)( 95,163)( 96,162)( 97,157)( 98,160)( 99,159)(100,158)(101,153)(102,156)(103,155)(104,154)(105,149)(106,152)(107,151)(108,150)(109,145)(110,148)(111,147)(112,146)(113,141)(114,144)(115,143)(116,142)(117,137)(118,140)(119,139)(120,138)(121,133)(122,136)(123,135)(124,134)(249,253)(250,256)(251,255)(252,254)(257,369)(258,372)(259,371)(260,370)(261,365)(262,368)(263,367)(264,366)(265,361)(266,364)(267,363)(268,362)(269,357)(270,360)(271,359)(272,358)(273,353)(274,356)(275,355)(276,354)(277,349)(278,352)(279,351)(280,350)(281,345)(282,348)(283,347)(284,346)(285,341)(286,344)(287,343)(288,342)(289,337)(290,340)(291,339)(292,338)(293,333)(294,336)(295,335)(296,334)(297,329)(298,332)(299,331)(300,330)(301,325)(302,328)(303,327)(304,326)(305,321)(306,324)(307,323)(308,322)(309,317)(310,320)(311,319)(312,318)(314,316)(373,501)(374,504)(375,503)(376,502)(377,497)(378,500)(379,499)(380,498)(381,617)(382,620)(383,619)(384,618)(385,613)(386,616)(387,615)(388,614)(389,609)(390,612)(391,611)(392,610)(393,605)(394,608)(395,607)(396,606)(397,601)(398,604)(399,603)(400,602)(401,597)(402,600)(403,599)(404,598)(405,593)(406,596)(407,595)(408,594)(409,589)(410,592)(411,591)(412,590)(413,585)(414,588)(415,587)(416,586)(417,581)(418,584)(419,583)(420,582)(421,577)(422,580)(423,579)(424,578)(425,573)(426,576)(427,575)(428,574)(429,569)(430,572)(431,571)(432,570)(433,565)(434,568)(435,567)(436,566)(437,561)(438,564)(439,563)(440,562)(441,557)(442,560)(443,559)(444,558)(445,553)(446,556)(447,555)(448,554)(449,549)(450,552)(451,551)(452,550)(453,545)(454,548)(455,547)(456,546)(457,541)(458,544)(459,543)(460,542)(461,537)(462,540)(463,539)(464,538)(465,533)(466,536)(467,535)(468,534)(469,529)(470,532)(471,531)(472,530)(473,525)(474,528)(475,527)(476,526)(477,521)(478,524)(479,523)(480,522)(481,517)(482,520)(483,519)(484,518)(485,513)(486,516)(487,515)(488,514)(489,509)(490,512)(491,511)(492,510)(493,505)(494,508)(495,507)(496,506)(621,625)(622,628)(623,627)(624,626)(629,741)(630,744)(631,743)(632,742)(633,737)(634,740)(635,739)(636,738)(637,733)(638,736)(639,735)(640,734)(641,729)(642,732)(643,731)(644,730)(645,725)(646,728)(647,727)(648,726)(649,721)(650,724)(651,723)(652,722)(653,717)(654,720)(655,719)(656,718)(657,713)(658,716)(659,715)(660,714)(661,709)(662,712)(663,711)(664,710)(665,705)(666,708)(667,707)(668,706)(669,701)(670,704)(671,703)(672,702)(673,697)(674,700)(675,699)(676,698)(677,693)(678,696)(679,695)(680,694)(681,689)(682,692)(683,691)(684,690)(686,688);
poly := sub<Sym(744)|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*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*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*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*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