Polytope of Type {6,4,16}

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

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