Polytope of Type {2,12,12}

s0 := (1,2);;
s1 := (  3,651)(  4,653)(  5,652)(  6,657)(  7,659)(  8,658)(  9,654)( 10,656)( 11,655)( 12,660)( 13,662)( 14,661)( 15,666)( 16,668)( 17,667)( 18,663)( 19,665)( 20,664)( 21,669)( 22,671)( 23,670)( 24,675)( 25,677)( 26,676)( 27,672)( 28,674)( 29,673)( 30,678)( 31,680)( 32,679)( 33,684)( 34,686)( 35,685)( 36,681)( 37,683)( 38,682)( 39,687)( 40,689)( 41,688)( 42,693)( 43,695)( 44,694)( 45,690)( 46,692)( 47,691)( 48,696)( 49,698)( 50,697)( 51,702)( 52,704)( 53,703)( 54,699)( 55,701)( 56,700)( 57,705)( 58,707)( 59,706)( 60,711)( 61,713)( 62,712)( 63,708)( 64,710)( 65,709)( 66,714)( 67,716)( 68,715)( 69,720)( 70,722)( 71,721)( 72,717)( 73,719)( 74,718)( 75,723)( 76,725)( 77,724)( 78,729)( 79,731)( 80,730)( 81,726)( 82,728)( 83,727)( 84,732)( 85,734)( 86,733)( 87,738)( 88,740)( 89,739)( 90,735)( 91,737)( 92,736)( 93,741)( 94,743)( 95,742)( 96,747)( 97,749)( 98,748)( 99,744)(100,746)(101,745)(102,750)(103,752)(104,751)(105,756)(106,758)(107,757)(108,753)(109,755)(110,754)(111,813)(112,815)(113,814)(114,819)(115,821)(116,820)(117,816)(118,818)(119,817)(120,822)(121,824)(122,823)(123,828)(124,830)(125,829)(126,825)(127,827)(128,826)(129,831)(130,833)(131,832)(132,837)(133,839)(134,838)(135,834)(136,836)(137,835)(138,840)(139,842)(140,841)(141,846)(142,848)(143,847)(144,843)(145,845)(146,844)(147,849)(148,851)(149,850)(150,855)(151,857)(152,856)(153,852)(154,854)(155,853)(156,858)(157,860)(158,859)(159,864)(160,866)(161,865)(162,861)(163,863)(164,862)(165,759)(166,761)(167,760)(168,765)(169,767)(170,766)(171,762)(172,764)(173,763)(174,768)(175,770)(176,769)(177,774)(178,776)(179,775)(180,771)(181,773)(182,772)(183,777)(184,779)(185,778)(186,783)(187,785)(188,784)(189,780)(190,782)(191,781)(192,786)(193,788)(194,787)(195,792)(196,794)(197,793)(198,789)(199,791)(200,790)(201,795)(202,797)(203,796)(204,801)(205,803)(206,802)(207,798)(208,800)(209,799)(210,804)(211,806)(212,805)(213,810)(214,812)(215,811)(216,807)(217,809)(218,808)(219,462)(220,464)(221,463)(222,468)(223,470)(224,469)(225,465)(226,467)(227,466)(228,471)(229,473)(230,472)(231,477)(232,479)(233,478)(234,474)(235,476)(236,475)(237,480)(238,482)(239,481)(240,486)(241,488)(242,487)(243,483)(244,485)(245,484)(246,435)(247,437)(248,436)(249,441)(250,443)(251,442)(252,438)(253,440)(254,439)(255,444)(256,446)(257,445)(258,450)(259,452)(260,451)(261,447)(262,449)(263,448)(264,453)(265,455)(266,454)(267,459)(268,461)(269,460)(270,456)(271,458)(272,457)(273,516)(274,518)(275,517)(276,522)(277,524)(278,523)(279,519)(280,521)(281,520)(282,525)(283,527)(284,526)(285,531)(286,533)(287,532)(288,528)(289,530)(290,529)(291,534)(292,536)(293,535)(294,540)(295,542)(296,541)(297,537)(298,539)(299,538)(300,489)(301,491)(302,490)(303,495)(304,497)(305,496)(306,492)(307,494)(308,493)(309,498)(310,500)(311,499)(312,504)(313,506)(314,505)(315,501)(316,503)(317,502)(318,507)(319,509)(320,508)(321,513)(322,515)(323,514)(324,510)(325,512)(326,511)(327,624)(328,626)(329,625)(330,630)(331,632)(332,631)(333,627)(334,629)(335,628)(336,633)(337,635)(338,634)(339,639)(340,641)(341,640)(342,636)(343,638)(344,637)(345,642)(346,644)(347,643)(348,648)(349,650)(350,649)(351,645)(352,647)(353,646)(354,597)(355,599)(356,598)(357,603)(358,605)(359,604)(360,600)(361,602)(362,601)(363,606)(364,608)(365,607)(366,612)(367,614)(368,613)(369,609)(370,611)(371,610)(372,615)(373,617)(374,616)(375,621)(376,623)(377,622)(378,618)(379,620)(380,619)(381,570)(382,572)(383,571)(384,576)(385,578)(386,577)(387,573)(388,575)(389,574)(390,579)(391,581)(392,580)(393,585)(394,587)(395,586)(396,582)(397,584)(398,583)(399,588)(400,590)(401,589)(402,594)(403,596)(404,595)(405,591)(406,593)(407,592)(408,543)(409,545)(410,544)(411,549)(412,551)(413,550)(414,546)(415,548)(416,547)(417,552)(418,554)(419,553)(420,558)(421,560)(422,559)(423,555)(424,557)(425,556)(426,561)(427,563)(428,562)(429,567)(430,569)(431,568)(432,564)(433,566)(434,565);;
s2 := (  3,763)(  4,762)(  5,764)(  6,760)(  7,759)(  8,761)(  9,766)( 10,765)( 11,767)( 12,781)( 13,780)( 14,782)( 15,778)( 16,777)( 17,779)( 18,784)( 19,783)( 20,785)( 21,772)( 22,771)( 23,773)( 24,769)( 25,768)( 26,770)( 27,775)( 28,774)( 29,776)( 30,790)( 31,789)( 32,791)( 33,787)( 34,786)( 35,788)( 36,793)( 37,792)( 38,794)( 39,808)( 40,807)( 41,809)( 42,805)( 43,804)( 44,806)( 45,811)( 46,810)( 47,812)( 48,799)( 49,798)( 50,800)( 51,796)( 52,795)( 53,797)( 54,802)( 55,801)( 56,803)( 57,817)( 58,816)( 59,818)( 60,814)( 61,813)( 62,815)( 63,820)( 64,819)( 65,821)( 66,835)( 67,834)( 68,836)( 69,832)( 70,831)( 71,833)( 72,838)( 73,837)( 74,839)( 75,826)( 76,825)( 77,827)( 78,823)( 79,822)( 80,824)( 81,829)( 82,828)( 83,830)( 84,844)( 85,843)( 86,845)( 87,841)( 88,840)( 89,842)( 90,847)( 91,846)( 92,848)( 93,862)( 94,861)( 95,863)( 96,859)( 97,858)( 98,860)( 99,865)(100,864)(101,866)(102,853)(103,852)(104,854)(105,850)(106,849)(107,851)(108,856)(109,855)(110,857)(111,655)(112,654)(113,656)(114,652)(115,651)(116,653)(117,658)(118,657)(119,659)(120,673)(121,672)(122,674)(123,670)(124,669)(125,671)(126,676)(127,675)(128,677)(129,664)(130,663)(131,665)(132,661)(133,660)(134,662)(135,667)(136,666)(137,668)(138,682)(139,681)(140,683)(141,679)(142,678)(143,680)(144,685)(145,684)(146,686)(147,700)(148,699)(149,701)(150,697)(151,696)(152,698)(153,703)(154,702)(155,704)(156,691)(157,690)(158,692)(159,688)(160,687)(161,689)(162,694)(163,693)(164,695)(165,709)(166,708)(167,710)(168,706)(169,705)(170,707)(171,712)(172,711)(173,713)(174,727)(175,726)(176,728)(177,724)(178,723)(179,725)(180,730)(181,729)(182,731)(183,718)(184,717)(185,719)(186,715)(187,714)(188,716)(189,721)(190,720)(191,722)(192,736)(193,735)(194,737)(195,733)(196,732)(197,734)(198,739)(199,738)(200,740)(201,754)(202,753)(203,755)(204,751)(205,750)(206,752)(207,757)(208,756)(209,758)(210,745)(211,744)(212,746)(213,742)(214,741)(215,743)(216,748)(217,747)(218,749)(219,574)(220,573)(221,575)(222,571)(223,570)(224,572)(225,577)(226,576)(227,578)(228,592)(229,591)(230,593)(231,589)(232,588)(233,590)(234,595)(235,594)(236,596)(237,583)(238,582)(239,584)(240,580)(241,579)(242,581)(243,586)(244,585)(245,587)(246,547)(247,546)(248,548)(249,544)(250,543)(251,545)(252,550)(253,549)(254,551)(255,565)(256,564)(257,566)(258,562)(259,561)(260,563)(261,568)(262,567)(263,569)(264,556)(265,555)(266,557)(267,553)(268,552)(269,554)(270,559)(271,558)(272,560)(273,628)(274,627)(275,629)(276,625)(277,624)(278,626)(279,631)(280,630)(281,632)(282,646)(283,645)(284,647)(285,643)(286,642)(287,644)(288,649)(289,648)(290,650)(291,637)(292,636)(293,638)(294,634)(295,633)(296,635)(297,640)(298,639)(299,641)(300,601)(301,600)(302,602)(303,598)(304,597)(305,599)(306,604)(307,603)(308,605)(309,619)(310,618)(311,620)(312,616)(313,615)(314,617)(315,622)(316,621)(317,623)(318,610)(319,609)(320,611)(321,607)(322,606)(323,608)(324,613)(325,612)(326,614)(327,466)(328,465)(329,467)(330,463)(331,462)(332,464)(333,469)(334,468)(335,470)(336,484)(337,483)(338,485)(339,481)(340,480)(341,482)(342,487)(343,486)(344,488)(345,475)(346,474)(347,476)(348,472)(349,471)(350,473)(351,478)(352,477)(353,479)(354,439)(355,438)(356,440)(357,436)(358,435)(359,437)(360,442)(361,441)(362,443)(363,457)(364,456)(365,458)(366,454)(367,453)(368,455)(369,460)(370,459)(371,461)(372,448)(373,447)(374,449)(375,445)(376,444)(377,446)(378,451)(379,450)(380,452)(381,520)(382,519)(383,521)(384,517)(385,516)(386,518)(387,523)(388,522)(389,524)(390,538)(391,537)(392,539)(393,535)(394,534)(395,536)(396,541)(397,540)(398,542)(399,529)(400,528)(401,530)(402,526)(403,525)(404,527)(405,532)(406,531)(407,533)(408,493)(409,492)(410,494)(411,490)(412,489)(413,491)(414,496)(415,495)(416,497)(417,511)(418,510)(419,512)(420,508)(421,507)(422,509)(423,514)(424,513)(425,515)(426,502)(427,501)(428,503)(429,499)(430,498)(431,500)(432,505)(433,504)(434,506);;
s3 := (  3,552)(  4,554)(  5,553)(  6,555)(  7,557)(  8,556)(  9,558)( 10,560)( 11,559)( 12,543)( 13,545)( 14,544)( 15,546)( 16,548)( 17,547)( 18,549)( 19,551)( 20,550)( 21,561)( 22,563)( 23,562)( 24,564)( 25,566)( 26,565)( 27,567)( 28,569)( 29,568)( 30,579)( 31,581)( 32,580)( 33,582)( 34,584)( 35,583)( 36,585)( 37,587)( 38,586)( 39,570)( 40,572)( 41,571)( 42,573)( 43,575)( 44,574)( 45,576)( 46,578)( 47,577)( 48,588)( 49,590)( 50,589)( 51,591)( 52,593)( 53,592)( 54,594)( 55,596)( 56,595)( 57,606)( 58,608)( 59,607)( 60,609)( 61,611)( 62,610)( 63,612)( 64,614)( 65,613)( 66,597)( 67,599)( 68,598)( 69,600)( 70,602)( 71,601)( 72,603)( 73,605)( 74,604)( 75,615)( 76,617)( 77,616)( 78,618)( 79,620)( 80,619)( 81,621)( 82,623)( 83,622)( 84,633)( 85,635)( 86,634)( 87,636)( 88,638)( 89,637)( 90,639)( 91,641)( 92,640)( 93,624)( 94,626)( 95,625)( 96,627)( 97,629)( 98,628)( 99,630)(100,632)(101,631)(102,642)(103,644)(104,643)(105,645)(106,647)(107,646)(108,648)(109,650)(110,649)(111,471)(112,473)(113,472)(114,474)(115,476)(116,475)(117,477)(118,479)(119,478)(120,462)(121,464)(122,463)(123,465)(124,467)(125,466)(126,468)(127,470)(128,469)(129,480)(130,482)(131,481)(132,483)(133,485)(134,484)(135,486)(136,488)(137,487)(138,444)(139,446)(140,445)(141,447)(142,449)(143,448)(144,450)(145,452)(146,451)(147,435)(148,437)(149,436)(150,438)(151,440)(152,439)(153,441)(154,443)(155,442)(156,453)(157,455)(158,454)(159,456)(160,458)(161,457)(162,459)(163,461)(164,460)(165,525)(166,527)(167,526)(168,528)(169,530)(170,529)(171,531)(172,533)(173,532)(174,516)(175,518)(176,517)(177,519)(178,521)(179,520)(180,522)(181,524)(182,523)(183,534)(184,536)(185,535)(186,537)(187,539)(188,538)(189,540)(190,542)(191,541)(192,498)(193,500)(194,499)(195,501)(196,503)(197,502)(198,504)(199,506)(200,505)(201,489)(202,491)(203,490)(204,492)(205,494)(206,493)(207,495)(208,497)(209,496)(210,507)(211,509)(212,508)(213,510)(214,512)(215,511)(216,513)(217,515)(218,514)(219,822)(220,824)(221,823)(222,825)(223,827)(224,826)(225,828)(226,830)(227,829)(228,813)(229,815)(230,814)(231,816)(232,818)(233,817)(234,819)(235,821)(236,820)(237,831)(238,833)(239,832)(240,834)(241,836)(242,835)(243,837)(244,839)(245,838)(246,849)(247,851)(248,850)(249,852)(250,854)(251,853)(252,855)(253,857)(254,856)(255,840)(256,842)(257,841)(258,843)(259,845)(260,844)(261,846)(262,848)(263,847)(264,858)(265,860)(266,859)(267,861)(268,863)(269,862)(270,864)(271,866)(272,865)(273,768)(274,770)(275,769)(276,771)(277,773)(278,772)(279,774)(280,776)(281,775)(282,759)(283,761)(284,760)(285,762)(286,764)(287,763)(288,765)(289,767)(290,766)(291,777)(292,779)(293,778)(294,780)(295,782)(296,781)(297,783)(298,785)(299,784)(300,795)(301,797)(302,796)(303,798)(304,800)(305,799)(306,801)(307,803)(308,802)(309,786)(310,788)(311,787)(312,789)(313,791)(314,790)(315,792)(316,794)(317,793)(318,804)(319,806)(320,805)(321,807)(322,809)(323,808)(324,810)(325,812)(326,811)(327,741)(328,743)(329,742)(330,744)(331,746)(332,745)(333,747)(334,749)(335,748)(336,732)(337,734)(338,733)(339,735)(340,737)(341,736)(342,738)(343,740)(344,739)(345,750)(346,752)(347,751)(348,753)(349,755)(350,754)(351,756)(352,758)(353,757)(354,714)(355,716)(356,715)(357,717)(358,719)(359,718)(360,720)(361,722)(362,721)(363,705)(364,707)(365,706)(366,708)(367,710)(368,709)(369,711)(370,713)(371,712)(372,723)(373,725)(374,724)(375,726)(376,728)(377,727)(378,729)(379,731)(380,730)(381,687)(382,689)(383,688)(384,690)(385,692)(386,691)(387,693)(388,695)(389,694)(390,678)(391,680)(392,679)(393,681)(394,683)(395,682)(396,684)(397,686)(398,685)(399,696)(400,698)(401,697)(402,699)(403,701)(404,700)(405,702)(406,704)(407,703)(408,660)(409,662)(410,661)(411,663)(412,665)(413,664)(414,666)(415,668)(416,667)(417,651)(418,653)(419,652)(420,654)(421,656)(422,655)(423,657)(424,659)(425,658)(426,669)(427,671)(428,670)(429,672)(430,674)(431,673)(432,675)(433,677)(434,676);;
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, 
s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2, 
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(866)!(1,2);
s1 := Sym(866)!(  3,651)(  4,653)(  5,652)(  6,657)(  7,659)(  8,658)(  9,654)( 10,656)( 11,655)( 12,660)( 13,662)( 14,661)( 15,666)( 16,668)( 17,667)( 18,663)( 19,665)( 20,664)( 21,669)( 22,671)( 23,670)( 24,675)( 25,677)( 26,676)( 27,672)( 28,674)( 29,673)( 30,678)( 31,680)( 32,679)( 33,684)( 34,686)( 35,685)( 36,681)( 37,683)( 38,682)( 39,687)( 40,689)( 41,688)( 42,693)( 43,695)( 44,694)( 45,690)( 46,692)( 47,691)( 48,696)( 49,698)( 50,697)( 51,702)( 52,704)( 53,703)( 54,699)( 55,701)( 56,700)( 57,705)( 58,707)( 59,706)( 60,711)( 61,713)( 62,712)( 63,708)( 64,710)( 65,709)( 66,714)( 67,716)( 68,715)( 69,720)( 70,722)( 71,721)( 72,717)( 73,719)( 74,718)( 75,723)( 76,725)( 77,724)( 78,729)( 79,731)( 80,730)( 81,726)( 82,728)( 83,727)( 84,732)( 85,734)( 86,733)( 87,738)( 88,740)( 89,739)( 90,735)( 91,737)( 92,736)( 93,741)( 94,743)( 95,742)( 96,747)( 97,749)( 98,748)( 99,744)(100,746)(101,745)(102,750)(103,752)(104,751)(105,756)(106,758)(107,757)(108,753)(109,755)(110,754)(111,813)(112,815)(113,814)(114,819)(115,821)(116,820)(117,816)(118,818)(119,817)(120,822)(121,824)(122,823)(123,828)(124,830)(125,829)(126,825)(127,827)(128,826)(129,831)(130,833)(131,832)(132,837)(133,839)(134,838)(135,834)(136,836)(137,835)(138,840)(139,842)(140,841)(141,846)(142,848)(143,847)(144,843)(145,845)(146,844)(147,849)(148,851)(149,850)(150,855)(151,857)(152,856)(153,852)(154,854)(155,853)(156,858)(157,860)(158,859)(159,864)(160,866)(161,865)(162,861)(163,863)(164,862)(165,759)(166,761)(167,760)(168,765)(169,767)(170,766)(171,762)(172,764)(173,763)(174,768)(175,770)(176,769)(177,774)(178,776)(179,775)(180,771)(181,773)(182,772)(183,777)(184,779)(185,778)(186,783)(187,785)(188,784)(189,780)(190,782)(191,781)(192,786)(193,788)(194,787)(195,792)(196,794)(197,793)(198,789)(199,791)(200,790)(201,795)(202,797)(203,796)(204,801)(205,803)(206,802)(207,798)(208,800)(209,799)(210,804)(211,806)(212,805)(213,810)(214,812)(215,811)(216,807)(217,809)(218,808)(219,462)(220,464)(221,463)(222,468)(223,470)(224,469)(225,465)(226,467)(227,466)(228,471)(229,473)(230,472)(231,477)(232,479)(233,478)(234,474)(235,476)(236,475)(237,480)(238,482)(239,481)(240,486)(241,488)(242,487)(243,483)(244,485)(245,484)(246,435)(247,437)(248,436)(249,441)(250,443)(251,442)(252,438)(253,440)(254,439)(255,444)(256,446)(257,445)(258,450)(259,452)(260,451)(261,447)(262,449)(263,448)(264,453)(265,455)(266,454)(267,459)(268,461)(269,460)(270,456)(271,458)(272,457)(273,516)(274,518)(275,517)(276,522)(277,524)(278,523)(279,519)(280,521)(281,520)(282,525)(283,527)(284,526)(285,531)(286,533)(287,532)(288,528)(289,530)(290,529)(291,534)(292,536)(293,535)(294,540)(295,542)(296,541)(297,537)(298,539)(299,538)(300,489)(301,491)(302,490)(303,495)(304,497)(305,496)(306,492)(307,494)(308,493)(309,498)(310,500)(311,499)(312,504)(313,506)(314,505)(315,501)(316,503)(317,502)(318,507)(319,509)(320,508)(321,513)(322,515)(323,514)(324,510)(325,512)(326,511)(327,624)(328,626)(329,625)(330,630)(331,632)(332,631)(333,627)(334,629)(335,628)(336,633)(337,635)(338,634)(339,639)(340,641)(341,640)(342,636)(343,638)(344,637)(345,642)(346,644)(347,643)(348,648)(349,650)(350,649)(351,645)(352,647)(353,646)(354,597)(355,599)(356,598)(357,603)(358,605)(359,604)(360,600)(361,602)(362,601)(363,606)(364,608)(365,607)(366,612)(367,614)(368,613)(369,609)(370,611)(371,610)(372,615)(373,617)(374,616)(375,621)(376,623)(377,622)(378,618)(379,620)(380,619)(381,570)(382,572)(383,571)(384,576)(385,578)(386,577)(387,573)(388,575)(389,574)(390,579)(391,581)(392,580)(393,585)(394,587)(395,586)(396,582)(397,584)(398,583)(399,588)(400,590)(401,589)(402,594)(403,596)(404,595)(405,591)(406,593)(407,592)(408,543)(409,545)(410,544)(411,549)(412,551)(413,550)(414,546)(415,548)(416,547)(417,552)(418,554)(419,553)(420,558)(421,560)(422,559)(423,555)(424,557)(425,556)(426,561)(427,563)(428,562)(429,567)(430,569)(431,568)(432,564)(433,566)(434,565);
s2 := Sym(866)!(  3,763)(  4,762)(  5,764)(  6,760)(  7,759)(  8,761)(  9,766)( 10,765)( 11,767)( 12,781)( 13,780)( 14,782)( 15,778)( 16,777)( 17,779)( 18,784)( 19,783)( 20,785)( 21,772)( 22,771)( 23,773)( 24,769)( 25,768)( 26,770)( 27,775)( 28,774)( 29,776)( 30,790)( 31,789)( 32,791)( 33,787)( 34,786)( 35,788)( 36,793)( 37,792)( 38,794)( 39,808)( 40,807)( 41,809)( 42,805)( 43,804)( 44,806)( 45,811)( 46,810)( 47,812)( 48,799)( 49,798)( 50,800)( 51,796)( 52,795)( 53,797)( 54,802)( 55,801)( 56,803)( 57,817)( 58,816)( 59,818)( 60,814)( 61,813)( 62,815)( 63,820)( 64,819)( 65,821)( 66,835)( 67,834)( 68,836)( 69,832)( 70,831)( 71,833)( 72,838)( 73,837)( 74,839)( 75,826)( 76,825)( 77,827)( 78,823)( 79,822)( 80,824)( 81,829)( 82,828)( 83,830)( 84,844)( 85,843)( 86,845)( 87,841)( 88,840)( 89,842)( 90,847)( 91,846)( 92,848)( 93,862)( 94,861)( 95,863)( 96,859)( 97,858)( 98,860)( 99,865)(100,864)(101,866)(102,853)(103,852)(104,854)(105,850)(106,849)(107,851)(108,856)(109,855)(110,857)(111,655)(112,654)(113,656)(114,652)(115,651)(116,653)(117,658)(118,657)(119,659)(120,673)(121,672)(122,674)(123,670)(124,669)(125,671)(126,676)(127,675)(128,677)(129,664)(130,663)(131,665)(132,661)(133,660)(134,662)(135,667)(136,666)(137,668)(138,682)(139,681)(140,683)(141,679)(142,678)(143,680)(144,685)(145,684)(146,686)(147,700)(148,699)(149,701)(150,697)(151,696)(152,698)(153,703)(154,702)(155,704)(156,691)(157,690)(158,692)(159,688)(160,687)(161,689)(162,694)(163,693)(164,695)(165,709)(166,708)(167,710)(168,706)(169,705)(170,707)(171,712)(172,711)(173,713)(174,727)(175,726)(176,728)(177,724)(178,723)(179,725)(180,730)(181,729)(182,731)(183,718)(184,717)(185,719)(186,715)(187,714)(188,716)(189,721)(190,720)(191,722)(192,736)(193,735)(194,737)(195,733)(196,732)(197,734)(198,739)(199,738)(200,740)(201,754)(202,753)(203,755)(204,751)(205,750)(206,752)(207,757)(208,756)(209,758)(210,745)(211,744)(212,746)(213,742)(214,741)(215,743)(216,748)(217,747)(218,749)(219,574)(220,573)(221,575)(222,571)(223,570)(224,572)(225,577)(226,576)(227,578)(228,592)(229,591)(230,593)(231,589)(232,588)(233,590)(234,595)(235,594)(236,596)(237,583)(238,582)(239,584)(240,580)(241,579)(242,581)(243,586)(244,585)(245,587)(246,547)(247,546)(248,548)(249,544)(250,543)(251,545)(252,550)(253,549)(254,551)(255,565)(256,564)(257,566)(258,562)(259,561)(260,563)(261,568)(262,567)(263,569)(264,556)(265,555)(266,557)(267,553)(268,552)(269,554)(270,559)(271,558)(272,560)(273,628)(274,627)(275,629)(276,625)(277,624)(278,626)(279,631)(280,630)(281,632)(282,646)(283,645)(284,647)(285,643)(286,642)(287,644)(288,649)(289,648)(290,650)(291,637)(292,636)(293,638)(294,634)(295,633)(296,635)(297,640)(298,639)(299,641)(300,601)(301,600)(302,602)(303,598)(304,597)(305,599)(306,604)(307,603)(308,605)(309,619)(310,618)(311,620)(312,616)(313,615)(314,617)(315,622)(316,621)(317,623)(318,610)(319,609)(320,611)(321,607)(322,606)(323,608)(324,613)(325,612)(326,614)(327,466)(328,465)(329,467)(330,463)(331,462)(332,464)(333,469)(334,468)(335,470)(336,484)(337,483)(338,485)(339,481)(340,480)(341,482)(342,487)(343,486)(344,488)(345,475)(346,474)(347,476)(348,472)(349,471)(350,473)(351,478)(352,477)(353,479)(354,439)(355,438)(356,440)(357,436)(358,435)(359,437)(360,442)(361,441)(362,443)(363,457)(364,456)(365,458)(366,454)(367,453)(368,455)(369,460)(370,459)(371,461)(372,448)(373,447)(374,449)(375,445)(376,444)(377,446)(378,451)(379,450)(380,452)(381,520)(382,519)(383,521)(384,517)(385,516)(386,518)(387,523)(388,522)(389,524)(390,538)(391,537)(392,539)(393,535)(394,534)(395,536)(396,541)(397,540)(398,542)(399,529)(400,528)(401,530)(402,526)(403,525)(404,527)(405,532)(406,531)(407,533)(408,493)(409,492)(410,494)(411,490)(412,489)(413,491)(414,496)(415,495)(416,497)(417,511)(418,510)(419,512)(420,508)(421,507)(422,509)(423,514)(424,513)(425,515)(426,502)(427,501)(428,503)(429,499)(430,498)(431,500)(432,505)(433,504)(434,506);
s3 := Sym(866)!(  3,552)(  4,554)(  5,553)(  6,555)(  7,557)(  8,556)(  9,558)( 10,560)( 11,559)( 12,543)( 13,545)( 14,544)( 15,546)( 16,548)( 17,547)( 18,549)( 19,551)( 20,550)( 21,561)( 22,563)( 23,562)( 24,564)( 25,566)( 26,565)( 27,567)( 28,569)( 29,568)( 30,579)( 31,581)( 32,580)( 33,582)( 34,584)( 35,583)( 36,585)( 37,587)( 38,586)( 39,570)( 40,572)( 41,571)( 42,573)( 43,575)( 44,574)( 45,576)( 46,578)( 47,577)( 48,588)( 49,590)( 50,589)( 51,591)( 52,593)( 53,592)( 54,594)( 55,596)( 56,595)( 57,606)( 58,608)( 59,607)( 60,609)( 61,611)( 62,610)( 63,612)( 64,614)( 65,613)( 66,597)( 67,599)( 68,598)( 69,600)( 70,602)( 71,601)( 72,603)( 73,605)( 74,604)( 75,615)( 76,617)( 77,616)( 78,618)( 79,620)( 80,619)( 81,621)( 82,623)( 83,622)( 84,633)( 85,635)( 86,634)( 87,636)( 88,638)( 89,637)( 90,639)( 91,641)( 92,640)( 93,624)( 94,626)( 95,625)( 96,627)( 97,629)( 98,628)( 99,630)(100,632)(101,631)(102,642)(103,644)(104,643)(105,645)(106,647)(107,646)(108,648)(109,650)(110,649)(111,471)(112,473)(113,472)(114,474)(115,476)(116,475)(117,477)(118,479)(119,478)(120,462)(121,464)(122,463)(123,465)(124,467)(125,466)(126,468)(127,470)(128,469)(129,480)(130,482)(131,481)(132,483)(133,485)(134,484)(135,486)(136,488)(137,487)(138,444)(139,446)(140,445)(141,447)(142,449)(143,448)(144,450)(145,452)(146,451)(147,435)(148,437)(149,436)(150,438)(151,440)(152,439)(153,441)(154,443)(155,442)(156,453)(157,455)(158,454)(159,456)(160,458)(161,457)(162,459)(163,461)(164,460)(165,525)(166,527)(167,526)(168,528)(169,530)(170,529)(171,531)(172,533)(173,532)(174,516)(175,518)(176,517)(177,519)(178,521)(179,520)(180,522)(181,524)(182,523)(183,534)(184,536)(185,535)(186,537)(187,539)(188,538)(189,540)(190,542)(191,541)(192,498)(193,500)(194,499)(195,501)(196,503)(197,502)(198,504)(199,506)(200,505)(201,489)(202,491)(203,490)(204,492)(205,494)(206,493)(207,495)(208,497)(209,496)(210,507)(211,509)(212,508)(213,510)(214,512)(215,511)(216,513)(217,515)(218,514)(219,822)(220,824)(221,823)(222,825)(223,827)(224,826)(225,828)(226,830)(227,829)(228,813)(229,815)(230,814)(231,816)(232,818)(233,817)(234,819)(235,821)(236,820)(237,831)(238,833)(239,832)(240,834)(241,836)(242,835)(243,837)(244,839)(245,838)(246,849)(247,851)(248,850)(249,852)(250,854)(251,853)(252,855)(253,857)(254,856)(255,840)(256,842)(257,841)(258,843)(259,845)(260,844)(261,846)(262,848)(263,847)(264,858)(265,860)(266,859)(267,861)(268,863)(269,862)(270,864)(271,866)(272,865)(273,768)(274,770)(275,769)(276,771)(277,773)(278,772)(279,774)(280,776)(281,775)(282,759)(283,761)(284,760)(285,762)(286,764)(287,763)(288,765)(289,767)(290,766)(291,777)(292,779)(293,778)(294,780)(295,782)(296,781)(297,783)(298,785)(299,784)(300,795)(301,797)(302,796)(303,798)(304,800)(305,799)(306,801)(307,803)(308,802)(309,786)(310,788)(311,787)(312,789)(313,791)(314,790)(315,792)(316,794)(317,793)(318,804)(319,806)(320,805)(321,807)(322,809)(323,808)(324,810)(325,812)(326,811)(327,741)(328,743)(329,742)(330,744)(331,746)(332,745)(333,747)(334,749)(335,748)(336,732)(337,734)(338,733)(339,735)(340,737)(341,736)(342,738)(343,740)(344,739)(345,750)(346,752)(347,751)(348,753)(349,755)(350,754)(351,756)(352,758)(353,757)(354,714)(355,716)(356,715)(357,717)(358,719)(359,718)(360,720)(361,722)(362,721)(363,705)(364,707)(365,706)(366,708)(367,710)(368,709)(369,711)(370,713)(371,712)(372,723)(373,725)(374,724)(375,726)(376,728)(377,727)(378,729)(379,731)(380,730)(381,687)(382,689)(383,688)(384,690)(385,692)(386,691)(387,693)(388,695)(389,694)(390,678)(391,680)(392,679)(393,681)(394,683)(395,682)(396,684)(397,686)(398,685)(399,696)(400,698)(401,697)(402,699)(403,701)(404,700)(405,702)(406,704)(407,703)(408,660)(409,662)(410,661)(411,663)(412,665)(413,664)(414,666)(415,668)(416,667)(417,651)(418,653)(419,652)(420,654)(421,656)(422,655)(423,657)(424,659)(425,658)(426,669)(427,671)(428,670)(429,672)(430,674)(431,673)(432,675)(433,677)(434,676);
poly := sub<Sym(866)|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, s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;