Polytope of Type {8,12,6}

s0 := (  1,289)(  2,290)(  3,291)(  4,292)(  5,293)(  6,294)(  7,295)(  8,296)(  9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)( 16,304)( 17,305)( 18,306)( 19,316)( 20,317)( 21,318)( 22,319)( 23,320)( 24,321)( 25,322)( 26,323)( 27,324)( 28,307)( 29,308)( 30,309)( 31,310)( 32,311)( 33,312)( 34,313)( 35,314)( 36,315)( 37,334)( 38,335)( 39,336)( 40,337)( 41,338)( 42,339)( 43,340)( 44,341)( 45,342)( 46,325)( 47,326)( 48,327)( 49,328)( 50,329)( 51,330)( 52,331)( 53,332)( 54,333)( 55,343)( 56,344)( 57,345)( 58,346)( 59,347)( 60,348)( 61,349)( 62,350)( 63,351)( 64,352)( 65,353)( 66,354)( 67,355)( 68,356)( 69,357)( 70,358)( 71,359)( 72,360)( 73,361)( 74,362)( 75,363)( 76,364)( 77,365)( 78,366)( 79,367)( 80,368)( 81,369)( 82,370)( 83,371)( 84,372)( 85,373)( 86,374)( 87,375)( 88,376)( 89,377)( 90,378)( 91,388)( 92,389)( 93,390)( 94,391)( 95,392)( 96,393)( 97,394)( 98,395)( 99,396)(100,379)(101,380)(102,381)(103,382)(104,383)(105,384)(106,385)(107,386)(108,387)(109,406)(110,407)(111,408)(112,409)(113,410)(114,411)(115,412)(116,413)(117,414)(118,397)(119,398)(120,399)(121,400)(122,401)(123,402)(124,403)(125,404)(126,405)(127,415)(128,416)(129,417)(130,418)(131,419)(132,420)(133,421)(134,422)(135,423)(136,424)(137,425)(138,426)(139,427)(140,428)(141,429)(142,430)(143,431)(144,432)(145,433)(146,434)(147,435)(148,436)(149,437)(150,438)(151,439)(152,440)(153,441)(154,442)(155,443)(156,444)(157,445)(158,446)(159,447)(160,448)(161,449)(162,450)(163,460)(164,461)(165,462)(166,463)(167,464)(168,465)(169,466)(170,467)(171,468)(172,451)(173,452)(174,453)(175,454)(176,455)(177,456)(178,457)(179,458)(180,459)(181,478)(182,479)(183,480)(184,481)(185,482)(186,483)(187,484)(188,485)(189,486)(190,469)(191,470)(192,471)(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(199,487)(200,488)(201,489)(202,490)(203,491)(204,492)(205,493)(206,494)(207,495)(208,496)(209,497)(210,498)(211,499)(212,500)(213,501)(214,502)(215,503)(216,504)(217,505)(218,506)(219,507)(220,508)(221,509)(222,510)(223,511)(224,512)(225,513)(226,514)(227,515)(228,516)(229,517)(230,518)(231,519)(232,520)(233,521)(234,522)(235,532)(236,533)(237,534)(238,535)(239,536)(240,537)(241,538)(242,539)(243,540)(244,523)(245,524)(246,525)(247,526)(248,527)(249,528)(250,529)(251,530)(252,531)(253,550)(254,551)(255,552)(256,553)(257,554)(258,555)(259,556)(260,557)(261,558)(262,541)(263,542)(264,543)(265,544)(266,545)(267,546)(268,547)(269,548)(270,549)(271,559)(272,560)(273,561)(274,562)(275,563)(276,564)(277,565)(278,566)(279,567)(280,568)(281,569)(282,570)(283,571)(284,572)(285,573)(286,574)(287,575)(288,576);;
s1 := (  1, 73)(  2, 80)(  3, 78)(  4, 79)(  5, 77)(  6, 75)(  7, 76)(  8, 74)(  9, 81)( 10, 82)( 11, 89)( 12, 87)( 13, 88)( 14, 86)( 15, 84)( 16, 85)( 17, 83)( 18, 90)( 19, 91)( 20, 98)( 21, 96)( 22, 97)( 23, 95)( 24, 93)( 25, 94)( 26, 92)( 27, 99)( 28,100)( 29,107)( 30,105)( 31,106)( 32,104)( 33,102)( 34,103)( 35,101)( 36,108)( 37,118)( 38,125)( 39,123)( 40,124)( 41,122)( 42,120)( 43,121)( 44,119)( 45,126)( 46,109)( 47,116)( 48,114)( 49,115)( 50,113)( 51,111)( 52,112)( 53,110)( 54,117)( 55,136)( 56,143)( 57,141)( 58,142)( 59,140)( 60,138)( 61,139)( 62,137)( 63,144)( 64,127)( 65,134)( 66,132)( 67,133)( 68,131)( 69,129)( 70,130)( 71,128)( 72,135)(145,235)(146,242)(147,240)(148,241)(149,239)(150,237)(151,238)(152,236)(153,243)(154,244)(155,251)(156,249)(157,250)(158,248)(159,246)(160,247)(161,245)(162,252)(163,217)(164,224)(165,222)(166,223)(167,221)(168,219)(169,220)(170,218)(171,225)(172,226)(173,233)(174,231)(175,232)(176,230)(177,228)(178,229)(179,227)(180,234)(181,280)(182,287)(183,285)(184,286)(185,284)(186,282)(187,283)(188,281)(189,288)(190,271)(191,278)(192,276)(193,277)(194,275)(195,273)(196,274)(197,272)(198,279)(199,262)(200,269)(201,267)(202,268)(203,266)(204,264)(205,265)(206,263)(207,270)(208,253)(209,260)(210,258)(211,259)(212,257)(213,255)(214,256)(215,254)(216,261)(289,397)(290,404)(291,402)(292,403)(293,401)(294,399)(295,400)(296,398)(297,405)(298,406)(299,413)(300,411)(301,412)(302,410)(303,408)(304,409)(305,407)(306,414)(307,415)(308,422)(309,420)(310,421)(311,419)(312,417)(313,418)(314,416)(315,423)(316,424)(317,431)(318,429)(319,430)(320,428)(321,426)(322,427)(323,425)(324,432)(325,361)(326,368)(327,366)(328,367)(329,365)(330,363)(331,364)(332,362)(333,369)(334,370)(335,377)(336,375)(337,376)(338,374)(339,372)(340,373)(341,371)(342,378)(343,379)(344,386)(345,384)(346,385)(347,383)(348,381)(349,382)(350,380)(351,387)(352,388)(353,395)(354,393)(355,394)(356,392)(357,390)(358,391)(359,389)(360,396)(433,568)(434,575)(435,573)(436,574)(437,572)(438,570)(439,571)(440,569)(441,576)(442,559)(443,566)(444,564)(445,565)(446,563)(447,561)(448,562)(449,560)(450,567)(451,550)(452,557)(453,555)(454,556)(455,554)(456,552)(457,553)(458,551)(459,558)(460,541)(461,548)(462,546)(463,547)(464,545)(465,543)(466,544)(467,542)(468,549)(469,532)(470,539)(471,537)(472,538)(473,536)(474,534)(475,535)(476,533)(477,540)(478,523)(479,530)(480,528)(481,529)(482,527)(483,525)(484,526)(485,524)(486,531)(487,514)(488,521)(489,519)(490,520)(491,518)(492,516)(493,517)(494,515)(495,522)(496,505)(497,512)(498,510)(499,511)(500,509)(501,507)(502,508)(503,506)(504,513);;
s2 := (  1,148)(  2,150)(  3,149)(  4,145)(  5,147)(  6,146)(  7,151)(  8,153)(  9,152)( 10,157)( 11,159)( 12,158)( 13,154)( 14,156)( 15,155)( 16,160)( 17,162)( 18,161)( 19,166)( 20,168)( 21,167)( 22,163)( 23,165)( 24,164)( 25,169)( 26,171)( 27,170)( 28,175)( 29,177)( 30,176)( 31,172)( 32,174)( 33,173)( 34,178)( 35,180)( 36,179)( 37,193)( 38,195)( 39,194)( 40,190)( 41,192)( 42,191)( 43,196)( 44,198)( 45,197)( 46,184)( 47,186)( 48,185)( 49,181)( 50,183)( 51,182)( 52,187)( 53,189)( 54,188)( 55,211)( 56,213)( 57,212)( 58,208)( 59,210)( 60,209)( 61,214)( 62,216)( 63,215)( 64,202)( 65,204)( 66,203)( 67,199)( 68,201)( 69,200)( 70,205)( 71,207)( 72,206)( 73,220)( 74,222)( 75,221)( 76,217)( 77,219)( 78,218)( 79,223)( 80,225)( 81,224)( 82,229)( 83,231)( 84,230)( 85,226)( 86,228)( 87,227)( 88,232)( 89,234)( 90,233)( 91,238)( 92,240)( 93,239)( 94,235)( 95,237)( 96,236)( 97,241)( 98,243)( 99,242)(100,247)(101,249)(102,248)(103,244)(104,246)(105,245)(106,250)(107,252)(108,251)(109,265)(110,267)(111,266)(112,262)(113,264)(114,263)(115,268)(116,270)(117,269)(118,256)(119,258)(120,257)(121,253)(122,255)(123,254)(124,259)(125,261)(126,260)(127,283)(128,285)(129,284)(130,280)(131,282)(132,281)(133,286)(134,288)(135,287)(136,274)(137,276)(138,275)(139,271)(140,273)(141,272)(142,277)(143,279)(144,278)(289,436)(290,438)(291,437)(292,433)(293,435)(294,434)(295,439)(296,441)(297,440)(298,445)(299,447)(300,446)(301,442)(302,444)(303,443)(304,448)(305,450)(306,449)(307,454)(308,456)(309,455)(310,451)(311,453)(312,452)(313,457)(314,459)(315,458)(316,463)(317,465)(318,464)(319,460)(320,462)(321,461)(322,466)(323,468)(324,467)(325,481)(326,483)(327,482)(328,478)(329,480)(330,479)(331,484)(332,486)(333,485)(334,472)(335,474)(336,473)(337,469)(338,471)(339,470)(340,475)(341,477)(342,476)(343,499)(344,501)(345,500)(346,496)(347,498)(348,497)(349,502)(350,504)(351,503)(352,490)(353,492)(354,491)(355,487)(356,489)(357,488)(358,493)(359,495)(360,494)(361,508)(362,510)(363,509)(364,505)(365,507)(366,506)(367,511)(368,513)(369,512)(370,517)(371,519)(372,518)(373,514)(374,516)(375,515)(376,520)(377,522)(378,521)(379,526)(380,528)(381,527)(382,523)(383,525)(384,524)(385,529)(386,531)(387,530)(388,535)(389,537)(390,536)(391,532)(392,534)(393,533)(394,538)(395,540)(396,539)(397,553)(398,555)(399,554)(400,550)(401,552)(402,551)(403,556)(404,558)(405,557)(406,544)(407,546)(408,545)(409,541)(410,543)(411,542)(412,547)(413,549)(414,548)(415,571)(416,573)(417,572)(418,568)(419,570)(420,569)(421,574)(422,576)(423,575)(424,562)(425,564)(426,563)(427,559)(428,561)(429,560)(430,565)(431,567)(432,566);;
s3 := (  1, 77)(  2, 79)(  3, 75)(  4, 80)(  5, 73)(  6, 78)(  7, 74)(  8, 76)(  9, 81)( 10, 86)( 11, 88)( 12, 84)( 13, 89)( 14, 82)( 15, 87)( 16, 83)( 17, 85)( 18, 90)( 19, 95)( 20, 97)( 21, 93)( 22, 98)( 23, 91)( 24, 96)( 25, 92)( 26, 94)( 27, 99)( 28,104)( 29,106)( 30,102)( 31,107)( 32,100)( 33,105)( 34,101)( 35,103)( 36,108)( 37,113)( 38,115)( 39,111)( 40,116)( 41,109)( 42,114)( 43,110)( 44,112)( 45,117)( 46,122)( 47,124)( 48,120)( 49,125)( 50,118)( 51,123)( 52,119)( 53,121)( 54,126)( 55,131)( 56,133)( 57,129)( 58,134)( 59,127)( 60,132)( 61,128)( 62,130)( 63,135)( 64,140)( 65,142)( 66,138)( 67,143)( 68,136)( 69,141)( 70,137)( 71,139)( 72,144)(145,221)(146,223)(147,219)(148,224)(149,217)(150,222)(151,218)(152,220)(153,225)(154,230)(155,232)(156,228)(157,233)(158,226)(159,231)(160,227)(161,229)(162,234)(163,239)(164,241)(165,237)(166,242)(167,235)(168,240)(169,236)(170,238)(171,243)(172,248)(173,250)(174,246)(175,251)(176,244)(177,249)(178,245)(179,247)(180,252)(181,257)(182,259)(183,255)(184,260)(185,253)(186,258)(187,254)(188,256)(189,261)(190,266)(191,268)(192,264)(193,269)(194,262)(195,267)(196,263)(197,265)(198,270)(199,275)(200,277)(201,273)(202,278)(203,271)(204,276)(205,272)(206,274)(207,279)(208,284)(209,286)(210,282)(211,287)(212,280)(213,285)(214,281)(215,283)(216,288)(289,365)(290,367)(291,363)(292,368)(293,361)(294,366)(295,362)(296,364)(297,369)(298,374)(299,376)(300,372)(301,377)(302,370)(303,375)(304,371)(305,373)(306,378)(307,383)(308,385)(309,381)(310,386)(311,379)(312,384)(313,380)(314,382)(315,387)(316,392)(317,394)(318,390)(319,395)(320,388)(321,393)(322,389)(323,391)(324,396)(325,401)(326,403)(327,399)(328,404)(329,397)(330,402)(331,398)(332,400)(333,405)(334,410)(335,412)(336,408)(337,413)(338,406)(339,411)(340,407)(341,409)(342,414)(343,419)(344,421)(345,417)(346,422)(347,415)(348,420)(349,416)(350,418)(351,423)(352,428)(353,430)(354,426)(355,431)(356,424)(357,429)(358,425)(359,427)(360,432)(433,509)(434,511)(435,507)(436,512)(437,505)(438,510)(439,506)(440,508)(441,513)(442,518)(443,520)(444,516)(445,521)(446,514)(447,519)(448,515)(449,517)(450,522)(451,527)(452,529)(453,525)(454,530)(455,523)(456,528)(457,524)(458,526)(459,531)(460,536)(461,538)(462,534)(463,539)(464,532)(465,537)(466,533)(467,535)(468,540)(469,545)(470,547)(471,543)(472,548)(473,541)(474,546)(475,542)(476,544)(477,549)(478,554)(479,556)(480,552)(481,557)(482,550)(483,555)(484,551)(485,553)(486,558)(487,563)(488,565)(489,561)(490,566)(491,559)(492,564)(493,560)(494,562)(495,567)(496,572)(497,574)(498,570)(499,575)(500,568)(501,573)(502,569)(503,571)(504,576);;
poly := Group([s0,s1,s2,s3]);;

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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 ];;
poly := F / rels;;

s0 := Sym(576)!(  1,289)(  2,290)(  3,291)(  4,292)(  5,293)(  6,294)(  7,295)(  8,296)(  9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)( 16,304)( 17,305)( 18,306)( 19,316)( 20,317)( 21,318)( 22,319)( 23,320)( 24,321)( 25,322)( 26,323)( 27,324)( 28,307)( 29,308)( 30,309)( 31,310)( 32,311)( 33,312)( 34,313)( 35,314)( 36,315)( 37,334)( 38,335)( 39,336)( 40,337)( 41,338)( 42,339)( 43,340)( 44,341)( 45,342)( 46,325)( 47,326)( 48,327)( 49,328)( 50,329)( 51,330)( 52,331)( 53,332)( 54,333)( 55,343)( 56,344)( 57,345)( 58,346)( 59,347)( 60,348)( 61,349)( 62,350)( 63,351)( 64,352)( 65,353)( 66,354)( 67,355)( 68,356)( 69,357)( 70,358)( 71,359)( 72,360)( 73,361)( 74,362)( 75,363)( 76,364)( 77,365)( 78,366)( 79,367)( 80,368)( 81,369)( 82,370)( 83,371)( 84,372)( 85,373)( 86,374)( 87,375)( 88,376)( 89,377)( 90,378)( 91,388)( 92,389)( 93,390)( 94,391)( 95,392)( 96,393)( 97,394)( 98,395)( 99,396)(100,379)(101,380)(102,381)(103,382)(104,383)(105,384)(106,385)(107,386)(108,387)(109,406)(110,407)(111,408)(112,409)(113,410)(114,411)(115,412)(116,413)(117,414)(118,397)(119,398)(120,399)(121,400)(122,401)(123,402)(124,403)(125,404)(126,405)(127,415)(128,416)(129,417)(130,418)(131,419)(132,420)(133,421)(134,422)(135,423)(136,424)(137,425)(138,426)(139,427)(140,428)(141,429)(142,430)(143,431)(144,432)(145,433)(146,434)(147,435)(148,436)(149,437)(150,438)(151,439)(152,440)(153,441)(154,442)(155,443)(156,444)(157,445)(158,446)(159,447)(160,448)(161,449)(162,450)(163,460)(164,461)(165,462)(166,463)(167,464)(168,465)(169,466)(170,467)(171,468)(172,451)(173,452)(174,453)(175,454)(176,455)(177,456)(178,457)(179,458)(180,459)(181,478)(182,479)(183,480)(184,481)(185,482)(186,483)(187,484)(188,485)(189,486)(190,469)(191,470)(192,471)(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(199,487)(200,488)(201,489)(202,490)(203,491)(204,492)(205,493)(206,494)(207,495)(208,496)(209,497)(210,498)(211,499)(212,500)(213,501)(214,502)(215,503)(216,504)(217,505)(218,506)(219,507)(220,508)(221,509)(222,510)(223,511)(224,512)(225,513)(226,514)(227,515)(228,516)(229,517)(230,518)(231,519)(232,520)(233,521)(234,522)(235,532)(236,533)(237,534)(238,535)(239,536)(240,537)(241,538)(242,539)(243,540)(244,523)(245,524)(246,525)(247,526)(248,527)(249,528)(250,529)(251,530)(252,531)(253,550)(254,551)(255,552)(256,553)(257,554)(258,555)(259,556)(260,557)(261,558)(262,541)(263,542)(264,543)(265,544)(266,545)(267,546)(268,547)(269,548)(270,549)(271,559)(272,560)(273,561)(274,562)(275,563)(276,564)(277,565)(278,566)(279,567)(280,568)(281,569)(282,570)(283,571)(284,572)(285,573)(286,574)(287,575)(288,576);
s1 := Sym(576)!(  1, 73)(  2, 80)(  3, 78)(  4, 79)(  5, 77)(  6, 75)(  7, 76)(  8, 74)(  9, 81)( 10, 82)( 11, 89)( 12, 87)( 13, 88)( 14, 86)( 15, 84)( 16, 85)( 17, 83)( 18, 90)( 19, 91)( 20, 98)( 21, 96)( 22, 97)( 23, 95)( 24, 93)( 25, 94)( 26, 92)( 27, 99)( 28,100)( 29,107)( 30,105)( 31,106)( 32,104)( 33,102)( 34,103)( 35,101)( 36,108)( 37,118)( 38,125)( 39,123)( 40,124)( 41,122)( 42,120)( 43,121)( 44,119)( 45,126)( 46,109)( 47,116)( 48,114)( 49,115)( 50,113)( 51,111)( 52,112)( 53,110)( 54,117)( 55,136)( 56,143)( 57,141)( 58,142)( 59,140)( 60,138)( 61,139)( 62,137)( 63,144)( 64,127)( 65,134)( 66,132)( 67,133)( 68,131)( 69,129)( 70,130)( 71,128)( 72,135)(145,235)(146,242)(147,240)(148,241)(149,239)(150,237)(151,238)(152,236)(153,243)(154,244)(155,251)(156,249)(157,250)(158,248)(159,246)(160,247)(161,245)(162,252)(163,217)(164,224)(165,222)(166,223)(167,221)(168,219)(169,220)(170,218)(171,225)(172,226)(173,233)(174,231)(175,232)(176,230)(177,228)(178,229)(179,227)(180,234)(181,280)(182,287)(183,285)(184,286)(185,284)(186,282)(187,283)(188,281)(189,288)(190,271)(191,278)(192,276)(193,277)(194,275)(195,273)(196,274)(197,272)(198,279)(199,262)(200,269)(201,267)(202,268)(203,266)(204,264)(205,265)(206,263)(207,270)(208,253)(209,260)(210,258)(211,259)(212,257)(213,255)(214,256)(215,254)(216,261)(289,397)(290,404)(291,402)(292,403)(293,401)(294,399)(295,400)(296,398)(297,405)(298,406)(299,413)(300,411)(301,412)(302,410)(303,408)(304,409)(305,407)(306,414)(307,415)(308,422)(309,420)(310,421)(311,419)(312,417)(313,418)(314,416)(315,423)(316,424)(317,431)(318,429)(319,430)(320,428)(321,426)(322,427)(323,425)(324,432)(325,361)(326,368)(327,366)(328,367)(329,365)(330,363)(331,364)(332,362)(333,369)(334,370)(335,377)(336,375)(337,376)(338,374)(339,372)(340,373)(341,371)(342,378)(343,379)(344,386)(345,384)(346,385)(347,383)(348,381)(349,382)(350,380)(351,387)(352,388)(353,395)(354,393)(355,394)(356,392)(357,390)(358,391)(359,389)(360,396)(433,568)(434,575)(435,573)(436,574)(437,572)(438,570)(439,571)(440,569)(441,576)(442,559)(443,566)(444,564)(445,565)(446,563)(447,561)(448,562)(449,560)(450,567)(451,550)(452,557)(453,555)(454,556)(455,554)(456,552)(457,553)(458,551)(459,558)(460,541)(461,548)(462,546)(463,547)(464,545)(465,543)(466,544)(467,542)(468,549)(469,532)(470,539)(471,537)(472,538)(473,536)(474,534)(475,535)(476,533)(477,540)(478,523)(479,530)(480,528)(481,529)(482,527)(483,525)(484,526)(485,524)(486,531)(487,514)(488,521)(489,519)(490,520)(491,518)(492,516)(493,517)(494,515)(495,522)(496,505)(497,512)(498,510)(499,511)(500,509)(501,507)(502,508)(503,506)(504,513);
s2 := Sym(576)!(  1,148)(  2,150)(  3,149)(  4,145)(  5,147)(  6,146)(  7,151)(  8,153)(  9,152)( 10,157)( 11,159)( 12,158)( 13,154)( 14,156)( 15,155)( 16,160)( 17,162)( 18,161)( 19,166)( 20,168)( 21,167)( 22,163)( 23,165)( 24,164)( 25,169)( 26,171)( 27,170)( 28,175)( 29,177)( 30,176)( 31,172)( 32,174)( 33,173)( 34,178)( 35,180)( 36,179)( 37,193)( 38,195)( 39,194)( 40,190)( 41,192)( 42,191)( 43,196)( 44,198)( 45,197)( 46,184)( 47,186)( 48,185)( 49,181)( 50,183)( 51,182)( 52,187)( 53,189)( 54,188)( 55,211)( 56,213)( 57,212)( 58,208)( 59,210)( 60,209)( 61,214)( 62,216)( 63,215)( 64,202)( 65,204)( 66,203)( 67,199)( 68,201)( 69,200)( 70,205)( 71,207)( 72,206)( 73,220)( 74,222)( 75,221)( 76,217)( 77,219)( 78,218)( 79,223)( 80,225)( 81,224)( 82,229)( 83,231)( 84,230)( 85,226)( 86,228)( 87,227)( 88,232)( 89,234)( 90,233)( 91,238)( 92,240)( 93,239)( 94,235)( 95,237)( 96,236)( 97,241)( 98,243)( 99,242)(100,247)(101,249)(102,248)(103,244)(104,246)(105,245)(106,250)(107,252)(108,251)(109,265)(110,267)(111,266)(112,262)(113,264)(114,263)(115,268)(116,270)(117,269)(118,256)(119,258)(120,257)(121,253)(122,255)(123,254)(124,259)(125,261)(126,260)(127,283)(128,285)(129,284)(130,280)(131,282)(132,281)(133,286)(134,288)(135,287)(136,274)(137,276)(138,275)(139,271)(140,273)(141,272)(142,277)(143,279)(144,278)(289,436)(290,438)(291,437)(292,433)(293,435)(294,434)(295,439)(296,441)(297,440)(298,445)(299,447)(300,446)(301,442)(302,444)(303,443)(304,448)(305,450)(306,449)(307,454)(308,456)(309,455)(310,451)(311,453)(312,452)(313,457)(314,459)(315,458)(316,463)(317,465)(318,464)(319,460)(320,462)(321,461)(322,466)(323,468)(324,467)(325,481)(326,483)(327,482)(328,478)(329,480)(330,479)(331,484)(332,486)(333,485)(334,472)(335,474)(336,473)(337,469)(338,471)(339,470)(340,475)(341,477)(342,476)(343,499)(344,501)(345,500)(346,496)(347,498)(348,497)(349,502)(350,504)(351,503)(352,490)(353,492)(354,491)(355,487)(356,489)(357,488)(358,493)(359,495)(360,494)(361,508)(362,510)(363,509)(364,505)(365,507)(366,506)(367,511)(368,513)(369,512)(370,517)(371,519)(372,518)(373,514)(374,516)(375,515)(376,520)(377,522)(378,521)(379,526)(380,528)(381,527)(382,523)(383,525)(384,524)(385,529)(386,531)(387,530)(388,535)(389,537)(390,536)(391,532)(392,534)(393,533)(394,538)(395,540)(396,539)(397,553)(398,555)(399,554)(400,550)(401,552)(402,551)(403,556)(404,558)(405,557)(406,544)(407,546)(408,545)(409,541)(410,543)(411,542)(412,547)(413,549)(414,548)(415,571)(416,573)(417,572)(418,568)(419,570)(420,569)(421,574)(422,576)(423,575)(424,562)(425,564)(426,563)(427,559)(428,561)(429,560)(430,565)(431,567)(432,566);
s3 := Sym(576)!(  1, 77)(  2, 79)(  3, 75)(  4, 80)(  5, 73)(  6, 78)(  7, 74)(  8, 76)(  9, 81)( 10, 86)( 11, 88)( 12, 84)( 13, 89)( 14, 82)( 15, 87)( 16, 83)( 17, 85)( 18, 90)( 19, 95)( 20, 97)( 21, 93)( 22, 98)( 23, 91)( 24, 96)( 25, 92)( 26, 94)( 27, 99)( 28,104)( 29,106)( 30,102)( 31,107)( 32,100)( 33,105)( 34,101)( 35,103)( 36,108)( 37,113)( 38,115)( 39,111)( 40,116)( 41,109)( 42,114)( 43,110)( 44,112)( 45,117)( 46,122)( 47,124)( 48,120)( 49,125)( 50,118)( 51,123)( 52,119)( 53,121)( 54,126)( 55,131)( 56,133)( 57,129)( 58,134)( 59,127)( 60,132)( 61,128)( 62,130)( 63,135)( 64,140)( 65,142)( 66,138)( 67,143)( 68,136)( 69,141)( 70,137)( 71,139)( 72,144)(145,221)(146,223)(147,219)(148,224)(149,217)(150,222)(151,218)(152,220)(153,225)(154,230)(155,232)(156,228)(157,233)(158,226)(159,231)(160,227)(161,229)(162,234)(163,239)(164,241)(165,237)(166,242)(167,235)(168,240)(169,236)(170,238)(171,243)(172,248)(173,250)(174,246)(175,251)(176,244)(177,249)(178,245)(179,247)(180,252)(181,257)(182,259)(183,255)(184,260)(185,253)(186,258)(187,254)(188,256)(189,261)(190,266)(191,268)(192,264)(193,269)(194,262)(195,267)(196,263)(197,265)(198,270)(199,275)(200,277)(201,273)(202,278)(203,271)(204,276)(205,272)(206,274)(207,279)(208,284)(209,286)(210,282)(211,287)(212,280)(213,285)(214,281)(215,283)(216,288)(289,365)(290,367)(291,363)(292,368)(293,361)(294,366)(295,362)(296,364)(297,369)(298,374)(299,376)(300,372)(301,377)(302,370)(303,375)(304,371)(305,373)(306,378)(307,383)(308,385)(309,381)(310,386)(311,379)(312,384)(313,380)(314,382)(315,387)(316,392)(317,394)(318,390)(319,395)(320,388)(321,393)(322,389)(323,391)(324,396)(325,401)(326,403)(327,399)(328,404)(329,397)(330,402)(331,398)(332,400)(333,405)(334,410)(335,412)(336,408)(337,413)(338,406)(339,411)(340,407)(341,409)(342,414)(343,419)(344,421)(345,417)(346,422)(347,415)(348,420)(349,416)(350,418)(351,423)(352,428)(353,430)(354,426)(355,431)(356,424)(357,429)(358,425)(359,427)(360,432)(433,509)(434,511)(435,507)(436,512)(437,505)(438,510)(439,506)(440,508)(441,513)(442,518)(443,520)(444,516)(445,521)(446,514)(447,519)(448,515)(449,517)(450,522)(451,527)(452,529)(453,525)(454,530)(455,523)(456,528)(457,524)(458,526)(459,531)(460,536)(461,538)(462,534)(463,539)(464,532)(465,537)(466,533)(467,535)(468,540)(469,545)(470,547)(471,543)(472,548)(473,541)(474,546)(475,542)(476,544)(477,549)(478,554)(479,556)(480,552)(481,557)(482,550)(483,555)(484,551)(485,553)(486,558)(487,563)(488,565)(489,561)(490,566)(491,559)(492,564)(493,560)(494,562)(495,567)(496,572)(497,574)(498,570)(499,575)(500,568)(501,573)(502,569)(503,571)(504,576);
poly := sub<Sym(576)|s0,s1,s2,s3>;

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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 >;