Polytope of Type {144,4}

Play with this polytope as a twisty puzzle

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