Polytope of Type {144,4}

Play with this polytope as a twisty puzzle

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