Polytope of Type {90,4}

Play with this polytope as a twisty puzzle

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

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

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s2*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 >; 
 

Twisty Puzzle