Polytope of Type {92,8}

Play with this polytope as a twisty puzzle

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