Polytope of Type {4,146}

s0 := (293,366)(294,367)(295,368)(296,369)(297,370)(298,371)(299,372)(300,373)(301,374)(302,375)(303,376)(304,377)(305,378)(306,379)(307,380)(308,381)(309,382)(310,383)(311,384)(312,385)(313,386)(314,387)(315,388)(316,389)(317,390)(318,391)(319,392)(320,393)(321,394)(322,395)(323,396)(324,397)(325,398)(326,399)(327,400)(328,401)(329,402)(330,403)(331,404)(332,405)(333,406)(334,407)(335,408)(336,409)(337,410)(338,411)(339,412)(340,413)(341,414)(342,415)(343,416)(344,417)(345,418)(346,419)(347,420)(348,421)(349,422)(350,423)(351,424)(352,425)(353,426)(354,427)(355,428)(356,429)(357,430)(358,431)(359,432)(360,433)(361,434)(362,435)(363,436)(364,437)(365,438)(439,512)(440,513)(441,514)(442,515)(443,516)(444,517)(445,518)(446,519)(447,520)(448,521)(449,522)(450,523)(451,524)(452,525)(453,526)(454,527)(455,528)(456,529)(457,530)(458,531)(459,532)(460,533)(461,534)(462,535)(463,536)(464,537)(465,538)(466,539)(467,540)(468,541)(469,542)(470,543)(471,544)(472,545)(473,546)(474,547)(475,548)(476,549)(477,550)(478,551)(479,552)(480,553)(481,554)(482,555)(483,556)(484,557)(485,558)(486,559)(487,560)(488,561)(489,562)(490,563)(491,564)(492,565)(493,566)(494,567)(495,568)(496,569)(497,570)(498,571)(499,572)(500,573)(501,574)(502,575)(503,576)(504,577)(505,578)(506,579)(507,580)(508,581)(509,582)(510,583)(511,584);;
s1 := (  1,439)(  2,511)(  3,510)(  4,509)(  5,508)(  6,507)(  7,506)(  8,505)(  9,504)( 10,503)( 11,502)( 12,501)( 13,500)( 14,499)( 15,498)( 16,497)( 17,496)( 18,495)( 19,494)( 20,493)( 21,492)( 22,491)( 23,490)( 24,489)( 25,488)( 26,487)( 27,486)( 28,485)( 29,484)( 30,483)( 31,482)( 32,481)( 33,480)( 34,479)( 35,478)( 36,477)( 37,476)( 38,475)( 39,474)( 40,473)( 41,472)( 42,471)( 43,470)( 44,469)( 45,468)( 46,467)( 47,466)( 48,465)( 49,464)( 50,463)( 51,462)( 52,461)( 53,460)( 54,459)( 55,458)( 56,457)( 57,456)( 58,455)( 59,454)( 60,453)( 61,452)( 62,451)( 63,450)( 64,449)( 65,448)( 66,447)( 67,446)( 68,445)( 69,444)( 70,443)( 71,442)( 72,441)( 73,440)( 74,512)( 75,584)( 76,583)( 77,582)( 78,581)( 79,580)( 80,579)( 81,578)( 82,577)( 83,576)( 84,575)( 85,574)( 86,573)( 87,572)( 88,571)( 89,570)( 90,569)( 91,568)( 92,567)( 93,566)( 94,565)( 95,564)( 96,563)( 97,562)( 98,561)( 99,560)(100,559)(101,558)(102,557)(103,556)(104,555)(105,554)(106,553)(107,552)(108,551)(109,550)(110,549)(111,548)(112,547)(113,546)(114,545)(115,544)(116,543)(117,542)(118,541)(119,540)(120,539)(121,538)(122,537)(123,536)(124,535)(125,534)(126,533)(127,532)(128,531)(129,530)(130,529)(131,528)(132,527)(133,526)(134,525)(135,524)(136,523)(137,522)(138,521)(139,520)(140,519)(141,518)(142,517)(143,516)(144,515)(145,514)(146,513)(147,293)(148,365)(149,364)(150,363)(151,362)(152,361)(153,360)(154,359)(155,358)(156,357)(157,356)(158,355)(159,354)(160,353)(161,352)(162,351)(163,350)(164,349)(165,348)(166,347)(167,346)(168,345)(169,344)(170,343)(171,342)(172,341)(173,340)(174,339)(175,338)(176,337)(177,336)(178,335)(179,334)(180,333)(181,332)(182,331)(183,330)(184,329)(185,328)(186,327)(187,326)(188,325)(189,324)(190,323)(191,322)(192,321)(193,320)(194,319)(195,318)(196,317)(197,316)(198,315)(199,314)(200,313)(201,312)(202,311)(203,310)(204,309)(205,308)(206,307)(207,306)(208,305)(209,304)(210,303)(211,302)(212,301)(213,300)(214,299)(215,298)(216,297)(217,296)(218,295)(219,294)(220,366)(221,438)(222,437)(223,436)(224,435)(225,434)(226,433)(227,432)(228,431)(229,430)(230,429)(231,428)(232,427)(233,426)(234,425)(235,424)(236,423)(237,422)(238,421)(239,420)(240,419)(241,418)(242,417)(243,416)(244,415)(245,414)(246,413)(247,412)(248,411)(249,410)(250,409)(251,408)(252,407)(253,406)(254,405)(255,404)(256,403)(257,402)(258,401)(259,400)(260,399)(261,398)(262,397)(263,396)(264,395)(265,394)(266,393)(267,392)(268,391)(269,390)(270,389)(271,388)(272,387)(273,386)(274,385)(275,384)(276,383)(277,382)(278,381)(279,380)(280,379)(281,378)(282,377)(283,376)(284,375)(285,374)(286,373)(287,372)(288,371)(289,370)(290,369)(291,368)(292,367);;
s2 := (  1,148)(  2,147)(  3,219)(  4,218)(  5,217)(  6,216)(  7,215)(  8,214)(  9,213)( 10,212)( 11,211)( 12,210)( 13,209)( 14,208)( 15,207)( 16,206)( 17,205)( 18,204)( 19,203)( 20,202)( 21,201)( 22,200)( 23,199)( 24,198)( 25,197)( 26,196)( 27,195)( 28,194)( 29,193)( 30,192)( 31,191)( 32,190)( 33,189)( 34,188)( 35,187)( 36,186)( 37,185)( 38,184)( 39,183)( 40,182)( 41,181)( 42,180)( 43,179)( 44,178)( 45,177)( 46,176)( 47,175)( 48,174)( 49,173)( 50,172)( 51,171)( 52,170)( 53,169)( 54,168)( 55,167)( 56,166)( 57,165)( 58,164)( 59,163)( 60,162)( 61,161)( 62,160)( 63,159)( 64,158)( 65,157)( 66,156)( 67,155)( 68,154)( 69,153)( 70,152)( 71,151)( 72,150)( 73,149)( 74,221)( 75,220)( 76,292)( 77,291)( 78,290)( 79,289)( 80,288)( 81,287)( 82,286)( 83,285)( 84,284)( 85,283)( 86,282)( 87,281)( 88,280)( 89,279)( 90,278)( 91,277)( 92,276)( 93,275)( 94,274)( 95,273)( 96,272)( 97,271)( 98,270)( 99,269)(100,268)(101,267)(102,266)(103,265)(104,264)(105,263)(106,262)(107,261)(108,260)(109,259)(110,258)(111,257)(112,256)(113,255)(114,254)(115,253)(116,252)(117,251)(118,250)(119,249)(120,248)(121,247)(122,246)(123,245)(124,244)(125,243)(126,242)(127,241)(128,240)(129,239)(130,238)(131,237)(132,236)(133,235)(134,234)(135,233)(136,232)(137,231)(138,230)(139,229)(140,228)(141,227)(142,226)(143,225)(144,224)(145,223)(146,222)(293,440)(294,439)(295,511)(296,510)(297,509)(298,508)(299,507)(300,506)(301,505)(302,504)(303,503)(304,502)(305,501)(306,500)(307,499)(308,498)(309,497)(310,496)(311,495)(312,494)(313,493)(314,492)(315,491)(316,490)(317,489)(318,488)(319,487)(320,486)(321,485)(322,484)(323,483)(324,482)(325,481)(326,480)(327,479)(328,478)(329,477)(330,476)(331,475)(332,474)(333,473)(334,472)(335,471)(336,470)(337,469)(338,468)(339,467)(340,466)(341,465)(342,464)(343,463)(344,462)(345,461)(346,460)(347,459)(348,458)(349,457)(350,456)(351,455)(352,454)(353,453)(354,452)(355,451)(356,450)(357,449)(358,448)(359,447)(360,446)(361,445)(362,444)(363,443)(364,442)(365,441)(366,513)(367,512)(368,584)(369,583)(370,582)(371,581)(372,580)(373,579)(374,578)(375,577)(376,576)(377,575)(378,574)(379,573)(380,572)(381,571)(382,570)(383,569)(384,568)(385,567)(386,566)(387,565)(388,564)(389,563)(390,562)(391,561)(392,560)(393,559)(394,558)(395,557)(396,556)(397,555)(398,554)(399,553)(400,552)(401,551)(402,550)(403,549)(404,548)(405,547)(406,546)(407,545)(408,544)(409,543)(410,542)(411,541)(412,540)(413,539)(414,538)(415,537)(416,536)(417,535)(418,534)(419,533)(420,532)(421,531)(422,530)(423,529)(424,528)(425,527)(426,526)(427,525)(428,524)(429,523)(430,522)(431,521)(432,520)(433,519)(434,518)(435,517)(436,516)(437,515)(438,514);;
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 ];;
poly := F / rels;;

s0 := Sym(584)!(293,366)(294,367)(295,368)(296,369)(297,370)(298,371)(299,372)(300,373)(301,374)(302,375)(303,376)(304,377)(305,378)(306,379)(307,380)(308,381)(309,382)(310,383)(311,384)(312,385)(313,386)(314,387)(315,388)(316,389)(317,390)(318,391)(319,392)(320,393)(321,394)(322,395)(323,396)(324,397)(325,398)(326,399)(327,400)(328,401)(329,402)(330,403)(331,404)(332,405)(333,406)(334,407)(335,408)(336,409)(337,410)(338,411)(339,412)(340,413)(341,414)(342,415)(343,416)(344,417)(345,418)(346,419)(347,420)(348,421)(349,422)(350,423)(351,424)(352,425)(353,426)(354,427)(355,428)(356,429)(357,430)(358,431)(359,432)(360,433)(361,434)(362,435)(363,436)(364,437)(365,438)(439,512)(440,513)(441,514)(442,515)(443,516)(444,517)(445,518)(446,519)(447,520)(448,521)(449,522)(450,523)(451,524)(452,525)(453,526)(454,527)(455,528)(456,529)(457,530)(458,531)(459,532)(460,533)(461,534)(462,535)(463,536)(464,537)(465,538)(466,539)(467,540)(468,541)(469,542)(470,543)(471,544)(472,545)(473,546)(474,547)(475,548)(476,549)(477,550)(478,551)(479,552)(480,553)(481,554)(482,555)(483,556)(484,557)(485,558)(486,559)(487,560)(488,561)(489,562)(490,563)(491,564)(492,565)(493,566)(494,567)(495,568)(496,569)(497,570)(498,571)(499,572)(500,573)(501,574)(502,575)(503,576)(504,577)(505,578)(506,579)(507,580)(508,581)(509,582)(510,583)(511,584);
s1 := Sym(584)!(  1,439)(  2,511)(  3,510)(  4,509)(  5,508)(  6,507)(  7,506)(  8,505)(  9,504)( 10,503)( 11,502)( 12,501)( 13,500)( 14,499)( 15,498)( 16,497)( 17,496)( 18,495)( 19,494)( 20,493)( 21,492)( 22,491)( 23,490)( 24,489)( 25,488)( 26,487)( 27,486)( 28,485)( 29,484)( 30,483)( 31,482)( 32,481)( 33,480)( 34,479)( 35,478)( 36,477)( 37,476)( 38,475)( 39,474)( 40,473)( 41,472)( 42,471)( 43,470)( 44,469)( 45,468)( 46,467)( 47,466)( 48,465)( 49,464)( 50,463)( 51,462)( 52,461)( 53,460)( 54,459)( 55,458)( 56,457)( 57,456)( 58,455)( 59,454)( 60,453)( 61,452)( 62,451)( 63,450)( 64,449)( 65,448)( 66,447)( 67,446)( 68,445)( 69,444)( 70,443)( 71,442)( 72,441)( 73,440)( 74,512)( 75,584)( 76,583)( 77,582)( 78,581)( 79,580)( 80,579)( 81,578)( 82,577)( 83,576)( 84,575)( 85,574)( 86,573)( 87,572)( 88,571)( 89,570)( 90,569)( 91,568)( 92,567)( 93,566)( 94,565)( 95,564)( 96,563)( 97,562)( 98,561)( 99,560)(100,559)(101,558)(102,557)(103,556)(104,555)(105,554)(106,553)(107,552)(108,551)(109,550)(110,549)(111,548)(112,547)(113,546)(114,545)(115,544)(116,543)(117,542)(118,541)(119,540)(120,539)(121,538)(122,537)(123,536)(124,535)(125,534)(126,533)(127,532)(128,531)(129,530)(130,529)(131,528)(132,527)(133,526)(134,525)(135,524)(136,523)(137,522)(138,521)(139,520)(140,519)(141,518)(142,517)(143,516)(144,515)(145,514)(146,513)(147,293)(148,365)(149,364)(150,363)(151,362)(152,361)(153,360)(154,359)(155,358)(156,357)(157,356)(158,355)(159,354)(160,353)(161,352)(162,351)(163,350)(164,349)(165,348)(166,347)(167,346)(168,345)(169,344)(170,343)(171,342)(172,341)(173,340)(174,339)(175,338)(176,337)(177,336)(178,335)(179,334)(180,333)(181,332)(182,331)(183,330)(184,329)(185,328)(186,327)(187,326)(188,325)(189,324)(190,323)(191,322)(192,321)(193,320)(194,319)(195,318)(196,317)(197,316)(198,315)(199,314)(200,313)(201,312)(202,311)(203,310)(204,309)(205,308)(206,307)(207,306)(208,305)(209,304)(210,303)(211,302)(212,301)(213,300)(214,299)(215,298)(216,297)(217,296)(218,295)(219,294)(220,366)(221,438)(222,437)(223,436)(224,435)(225,434)(226,433)(227,432)(228,431)(229,430)(230,429)(231,428)(232,427)(233,426)(234,425)(235,424)(236,423)(237,422)(238,421)(239,420)(240,419)(241,418)(242,417)(243,416)(244,415)(245,414)(246,413)(247,412)(248,411)(249,410)(250,409)(251,408)(252,407)(253,406)(254,405)(255,404)(256,403)(257,402)(258,401)(259,400)(260,399)(261,398)(262,397)(263,396)(264,395)(265,394)(266,393)(267,392)(268,391)(269,390)(270,389)(271,388)(272,387)(273,386)(274,385)(275,384)(276,383)(277,382)(278,381)(279,380)(280,379)(281,378)(282,377)(283,376)(284,375)(285,374)(286,373)(287,372)(288,371)(289,370)(290,369)(291,368)(292,367);
s2 := Sym(584)!(  1,148)(  2,147)(  3,219)(  4,218)(  5,217)(  6,216)(  7,215)(  8,214)(  9,213)( 10,212)( 11,211)( 12,210)( 13,209)( 14,208)( 15,207)( 16,206)( 17,205)( 18,204)( 19,203)( 20,202)( 21,201)( 22,200)( 23,199)( 24,198)( 25,197)( 26,196)( 27,195)( 28,194)( 29,193)( 30,192)( 31,191)( 32,190)( 33,189)( 34,188)( 35,187)( 36,186)( 37,185)( 38,184)( 39,183)( 40,182)( 41,181)( 42,180)( 43,179)( 44,178)( 45,177)( 46,176)( 47,175)( 48,174)( 49,173)( 50,172)( 51,171)( 52,170)( 53,169)( 54,168)( 55,167)( 56,166)( 57,165)( 58,164)( 59,163)( 60,162)( 61,161)( 62,160)( 63,159)( 64,158)( 65,157)( 66,156)( 67,155)( 68,154)( 69,153)( 70,152)( 71,151)( 72,150)( 73,149)( 74,221)( 75,220)( 76,292)( 77,291)( 78,290)( 79,289)( 80,288)( 81,287)( 82,286)( 83,285)( 84,284)( 85,283)( 86,282)( 87,281)( 88,280)( 89,279)( 90,278)( 91,277)( 92,276)( 93,275)( 94,274)( 95,273)( 96,272)( 97,271)( 98,270)( 99,269)(100,268)(101,267)(102,266)(103,265)(104,264)(105,263)(106,262)(107,261)(108,260)(109,259)(110,258)(111,257)(112,256)(113,255)(114,254)(115,253)(116,252)(117,251)(118,250)(119,249)(120,248)(121,247)(122,246)(123,245)(124,244)(125,243)(126,242)(127,241)(128,240)(129,239)(130,238)(131,237)(132,236)(133,235)(134,234)(135,233)(136,232)(137,231)(138,230)(139,229)(140,228)(141,227)(142,226)(143,225)(144,224)(145,223)(146,222)(293,440)(294,439)(295,511)(296,510)(297,509)(298,508)(299,507)(300,506)(301,505)(302,504)(303,503)(304,502)(305,501)(306,500)(307,499)(308,498)(309,497)(310,496)(311,495)(312,494)(313,493)(314,492)(315,491)(316,490)(317,489)(318,488)(319,487)(320,486)(321,485)(322,484)(323,483)(324,482)(325,481)(326,480)(327,479)(328,478)(329,477)(330,476)(331,475)(332,474)(333,473)(334,472)(335,471)(336,470)(337,469)(338,468)(339,467)(340,466)(341,465)(342,464)(343,463)(344,462)(345,461)(346,460)(347,459)(348,458)(349,457)(350,456)(351,455)(352,454)(353,453)(354,452)(355,451)(356,450)(357,449)(358,448)(359,447)(360,446)(361,445)(362,444)(363,443)(364,442)(365,441)(366,513)(367,512)(368,584)(369,583)(370,582)(371,581)(372,580)(373,579)(374,578)(375,577)(376,576)(377,575)(378,574)(379,573)(380,572)(381,571)(382,570)(383,569)(384,568)(385,567)(386,566)(387,565)(388,564)(389,563)(390,562)(391,561)(392,560)(393,559)(394,558)(395,557)(396,556)(397,555)(398,554)(399,553)(400,552)(401,551)(402,550)(403,549)(404,548)(405,547)(406,546)(407,545)(408,544)(409,543)(410,542)(411,541)(412,540)(413,539)(414,538)(415,537)(416,536)(417,535)(418,534)(419,533)(420,532)(421,531)(422,530)(423,529)(424,528)(425,527)(426,526)(427,525)(428,524)(429,523)(430,522)(431,521)(432,520)(433,519)(434,518)(435,517)(436,516)(437,515)(438,514);
poly := sub<Sym(584)|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 >;