Polytope of Type {4,66}

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

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