Polytope of Type {4,144}

Play with this polytope as a twisty puzzle

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