Polytope of Type {4,242}

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