Polytope of Type {24,15}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle