Polytope of Type {2,60,4}

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

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