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Polytope of Type {2,24,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24,9}*1728
if this polytope has a name.
Group : SmallGroup(1728,30249)
Rank : 4
Schlafli Type : {2,24,9}
Number of vertices, edges, etc : 2, 48, 216, 18
Order of s0s1s2s3 : 36
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,12,9}*864
   3-fold quotients : {2,8,9}*576, {2,24,3}*576
   6-fold quotients : {2,4,9}*288, {2,12,3}*288
   8-fold quotients : {2,6,9}*216
   9-fold quotients : {2,8,3}*192
   12-fold quotients : {2,4,9}*144
   18-fold quotients : {2,4,3}*96
   24-fold quotients : {2,2,9}*72, {2,6,3}*72
   36-fold quotients : {2,4,3}*48
   72-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  3,439)(  4,440)(  5,442)(  6,441)(  7,436)(  8,435)(  9,437)( 10,438)
( 11,447)( 12,448)( 13,450)( 14,449)( 15,444)( 16,443)( 17,445)( 18,446)
( 19,455)( 20,456)( 21,458)( 22,457)( 23,452)( 24,451)( 25,453)( 26,454)
( 27,487)( 28,488)( 29,490)( 30,489)( 31,484)( 32,483)( 33,485)( 34,486)
( 35,495)( 36,496)( 37,498)( 38,497)( 39,492)( 40,491)( 41,493)( 42,494)
( 43,503)( 44,504)( 45,506)( 46,505)( 47,500)( 48,499)( 49,501)( 50,502)
( 51,463)( 52,464)( 53,466)( 54,465)( 55,460)( 56,459)( 57,461)( 58,462)
( 59,471)( 60,472)( 61,474)( 62,473)( 63,468)( 64,467)( 65,469)( 66,470)
( 67,479)( 68,480)( 69,482)( 70,481)( 71,476)( 72,475)( 73,477)( 74,478)
( 75,511)( 76,512)( 77,514)( 78,513)( 79,508)( 80,507)( 81,509)( 82,510)
( 83,519)( 84,520)( 85,522)( 86,521)( 87,516)( 88,515)( 89,517)( 90,518)
( 91,527)( 92,528)( 93,530)( 94,529)( 95,524)( 96,523)( 97,525)( 98,526)
( 99,559)(100,560)(101,562)(102,561)(103,556)(104,555)(105,557)(106,558)
(107,567)(108,568)(109,570)(110,569)(111,564)(112,563)(113,565)(114,566)
(115,575)(116,576)(117,578)(118,577)(119,572)(120,571)(121,573)(122,574)
(123,535)(124,536)(125,538)(126,537)(127,532)(128,531)(129,533)(130,534)
(131,543)(132,544)(133,546)(134,545)(135,540)(136,539)(137,541)(138,542)
(139,551)(140,552)(141,554)(142,553)(143,548)(144,547)(145,549)(146,550)
(147,583)(148,584)(149,586)(150,585)(151,580)(152,579)(153,581)(154,582)
(155,591)(156,592)(157,594)(158,593)(159,588)(160,587)(161,589)(162,590)
(163,599)(164,600)(165,602)(166,601)(167,596)(168,595)(169,597)(170,598)
(171,631)(172,632)(173,634)(174,633)(175,628)(176,627)(177,629)(178,630)
(179,639)(180,640)(181,642)(182,641)(183,636)(184,635)(185,637)(186,638)
(187,647)(188,648)(189,650)(190,649)(191,644)(192,643)(193,645)(194,646)
(195,607)(196,608)(197,610)(198,609)(199,604)(200,603)(201,605)(202,606)
(203,615)(204,616)(205,618)(206,617)(207,612)(208,611)(209,613)(210,614)
(211,623)(212,624)(213,626)(214,625)(215,620)(216,619)(217,621)(218,622)
(219,656)(220,655)(221,657)(222,658)(223,651)(224,652)(225,654)(226,653)
(227,664)(228,663)(229,665)(230,666)(231,659)(232,660)(233,662)(234,661)
(235,672)(236,671)(237,673)(238,674)(239,667)(240,668)(241,670)(242,669)
(243,704)(244,703)(245,705)(246,706)(247,699)(248,700)(249,702)(250,701)
(251,712)(252,711)(253,713)(254,714)(255,707)(256,708)(257,710)(258,709)
(259,720)(260,719)(261,721)(262,722)(263,715)(264,716)(265,718)(266,717)
(267,680)(268,679)(269,681)(270,682)(271,675)(272,676)(273,678)(274,677)
(275,688)(276,687)(277,689)(278,690)(279,683)(280,684)(281,686)(282,685)
(283,696)(284,695)(285,697)(286,698)(287,691)(288,692)(289,694)(290,693)
(291,728)(292,727)(293,729)(294,730)(295,723)(296,724)(297,726)(298,725)
(299,736)(300,735)(301,737)(302,738)(303,731)(304,732)(305,734)(306,733)
(307,744)(308,743)(309,745)(310,746)(311,739)(312,740)(313,742)(314,741)
(315,776)(316,775)(317,777)(318,778)(319,771)(320,772)(321,774)(322,773)
(323,784)(324,783)(325,785)(326,786)(327,779)(328,780)(329,782)(330,781)
(331,792)(332,791)(333,793)(334,794)(335,787)(336,788)(337,790)(338,789)
(339,752)(340,751)(341,753)(342,754)(343,747)(344,748)(345,750)(346,749)
(347,760)(348,759)(349,761)(350,762)(351,755)(352,756)(353,758)(354,757)
(355,768)(356,767)(357,769)(358,770)(359,763)(360,764)(361,766)(362,765)
(363,800)(364,799)(365,801)(366,802)(367,795)(368,796)(369,798)(370,797)
(371,808)(372,807)(373,809)(374,810)(375,803)(376,804)(377,806)(378,805)
(379,816)(380,815)(381,817)(382,818)(383,811)(384,812)(385,814)(386,813)
(387,848)(388,847)(389,849)(390,850)(391,843)(392,844)(393,846)(394,845)
(395,856)(396,855)(397,857)(398,858)(399,851)(400,852)(401,854)(402,853)
(403,864)(404,863)(405,865)(406,866)(407,859)(408,860)(409,862)(410,861)
(411,824)(412,823)(413,825)(414,826)(415,819)(416,820)(417,822)(418,821)
(419,832)(420,831)(421,833)(422,834)(423,827)(424,828)(425,830)(426,829)
(427,840)(428,839)(429,841)(430,842)(431,835)(432,836)(433,838)(434,837);;
s2 := (  3,675)(  4,676)(  5,680)(  6,679)(  7,678)(  8,677)(  9,682)( 10,681)
( 11,691)( 12,692)( 13,696)( 14,695)( 15,694)( 16,693)( 17,698)( 18,697)
( 19,683)( 20,684)( 21,688)( 22,687)( 23,686)( 24,685)( 25,690)( 26,689)
( 27,651)( 28,652)( 29,656)( 30,655)( 31,654)( 32,653)( 33,658)( 34,657)
( 35,667)( 36,668)( 37,672)( 38,671)( 39,670)( 40,669)( 41,674)( 42,673)
( 43,659)( 44,660)( 45,664)( 46,663)( 47,662)( 48,661)( 49,666)( 50,665)
( 51,699)( 52,700)( 53,704)( 54,703)( 55,702)( 56,701)( 57,706)( 58,705)
( 59,715)( 60,716)( 61,720)( 62,719)( 63,718)( 64,717)( 65,722)( 66,721)
( 67,707)( 68,708)( 69,712)( 70,711)( 71,710)( 72,709)( 73,714)( 74,713)
( 75,835)( 76,836)( 77,840)( 78,839)( 79,838)( 80,837)( 81,842)( 82,841)
( 83,827)( 84,828)( 85,832)( 86,831)( 87,830)( 88,829)( 89,834)( 90,833)
( 91,819)( 92,820)( 93,824)( 94,823)( 95,822)( 96,821)( 97,826)( 98,825)
( 99,811)(100,812)(101,816)(102,815)(103,814)(104,813)(105,818)(106,817)
(107,803)(108,804)(109,808)(110,807)(111,806)(112,805)(113,810)(114,809)
(115,795)(116,796)(117,800)(118,799)(119,798)(120,797)(121,802)(122,801)
(123,859)(124,860)(125,864)(126,863)(127,862)(128,861)(129,866)(130,865)
(131,851)(132,852)(133,856)(134,855)(135,854)(136,853)(137,858)(138,857)
(139,843)(140,844)(141,848)(142,847)(143,846)(144,845)(145,850)(146,849)
(147,763)(148,764)(149,768)(150,767)(151,766)(152,765)(153,770)(154,769)
(155,755)(156,756)(157,760)(158,759)(159,758)(160,757)(161,762)(162,761)
(163,747)(164,748)(165,752)(166,751)(167,750)(168,749)(169,754)(170,753)
(171,739)(172,740)(173,744)(174,743)(175,742)(176,741)(177,746)(178,745)
(179,731)(180,732)(181,736)(182,735)(183,734)(184,733)(185,738)(186,737)
(187,723)(188,724)(189,728)(190,727)(191,726)(192,725)(193,730)(194,729)
(195,787)(196,788)(197,792)(198,791)(199,790)(200,789)(201,794)(202,793)
(203,779)(204,780)(205,784)(206,783)(207,782)(208,781)(209,786)(210,785)
(211,771)(212,772)(213,776)(214,775)(215,774)(216,773)(217,778)(218,777)
(219,460)(220,459)(221,463)(222,464)(223,461)(224,462)(225,465)(226,466)
(227,476)(228,475)(229,479)(230,480)(231,477)(232,478)(233,481)(234,482)
(235,468)(236,467)(237,471)(238,472)(239,469)(240,470)(241,473)(242,474)
(243,436)(244,435)(245,439)(246,440)(247,437)(248,438)(249,441)(250,442)
(251,452)(252,451)(253,455)(254,456)(255,453)(256,454)(257,457)(258,458)
(259,444)(260,443)(261,447)(262,448)(263,445)(264,446)(265,449)(266,450)
(267,484)(268,483)(269,487)(270,488)(271,485)(272,486)(273,489)(274,490)
(275,500)(276,499)(277,503)(278,504)(279,501)(280,502)(281,505)(282,506)
(283,492)(284,491)(285,495)(286,496)(287,493)(288,494)(289,497)(290,498)
(291,620)(292,619)(293,623)(294,624)(295,621)(296,622)(297,625)(298,626)
(299,612)(300,611)(301,615)(302,616)(303,613)(304,614)(305,617)(306,618)
(307,604)(308,603)(309,607)(310,608)(311,605)(312,606)(313,609)(314,610)
(315,596)(316,595)(317,599)(318,600)(319,597)(320,598)(321,601)(322,602)
(323,588)(324,587)(325,591)(326,592)(327,589)(328,590)(329,593)(330,594)
(331,580)(332,579)(333,583)(334,584)(335,581)(336,582)(337,585)(338,586)
(339,644)(340,643)(341,647)(342,648)(343,645)(344,646)(345,649)(346,650)
(347,636)(348,635)(349,639)(350,640)(351,637)(352,638)(353,641)(354,642)
(355,628)(356,627)(357,631)(358,632)(359,629)(360,630)(361,633)(362,634)
(363,548)(364,547)(365,551)(366,552)(367,549)(368,550)(369,553)(370,554)
(371,540)(372,539)(373,543)(374,544)(375,541)(376,542)(377,545)(378,546)
(379,532)(380,531)(381,535)(382,536)(383,533)(384,534)(385,537)(386,538)
(387,524)(388,523)(389,527)(390,528)(391,525)(392,526)(393,529)(394,530)
(395,516)(396,515)(397,519)(398,520)(399,517)(400,518)(401,521)(402,522)
(403,508)(404,507)(405,511)(406,512)(407,509)(408,510)(409,513)(410,514)
(411,572)(412,571)(413,575)(414,576)(415,573)(416,574)(417,577)(418,578)
(419,564)(420,563)(421,567)(422,568)(423,565)(424,566)(425,569)(426,570)
(427,556)(428,555)(429,559)(430,560)(431,557)(432,558)(433,561)(434,562);;
s3 := (  3,795)(  4,796)(  5,801)(  6,802)(  7,800)(  8,799)(  9,797)( 10,798)
( 11,811)( 12,812)( 13,817)( 14,818)( 15,816)( 16,815)( 17,813)( 18,814)
( 19,803)( 20,804)( 21,809)( 22,810)( 23,808)( 24,807)( 25,805)( 26,806)
( 27,843)( 28,844)( 29,849)( 30,850)( 31,848)( 32,847)( 33,845)( 34,846)
( 35,859)( 36,860)( 37,865)( 38,866)( 39,864)( 40,863)( 41,861)( 42,862)
( 43,851)( 44,852)( 45,857)( 46,858)( 47,856)( 48,855)( 49,853)( 50,854)
( 51,819)( 52,820)( 53,825)( 54,826)( 55,824)( 56,823)( 57,821)( 58,822)
( 59,835)( 60,836)( 61,841)( 62,842)( 63,840)( 64,839)( 65,837)( 66,838)
( 67,827)( 68,828)( 69,833)( 70,834)( 71,832)( 72,831)( 73,829)( 74,830)
( 75,723)( 76,724)( 77,729)( 78,730)( 79,728)( 80,727)( 81,725)( 82,726)
( 83,739)( 84,740)( 85,745)( 86,746)( 87,744)( 88,743)( 89,741)( 90,742)
( 91,731)( 92,732)( 93,737)( 94,738)( 95,736)( 96,735)( 97,733)( 98,734)
( 99,771)(100,772)(101,777)(102,778)(103,776)(104,775)(105,773)(106,774)
(107,787)(108,788)(109,793)(110,794)(111,792)(112,791)(113,789)(114,790)
(115,779)(116,780)(117,785)(118,786)(119,784)(120,783)(121,781)(122,782)
(123,747)(124,748)(125,753)(126,754)(127,752)(128,751)(129,749)(130,750)
(131,763)(132,764)(133,769)(134,770)(135,768)(136,767)(137,765)(138,766)
(139,755)(140,756)(141,761)(142,762)(143,760)(144,759)(145,757)(146,758)
(147,651)(148,652)(149,657)(150,658)(151,656)(152,655)(153,653)(154,654)
(155,667)(156,668)(157,673)(158,674)(159,672)(160,671)(161,669)(162,670)
(163,659)(164,660)(165,665)(166,666)(167,664)(168,663)(169,661)(170,662)
(171,699)(172,700)(173,705)(174,706)(175,704)(176,703)(177,701)(178,702)
(179,715)(180,716)(181,721)(182,722)(183,720)(184,719)(185,717)(186,718)
(187,707)(188,708)(189,713)(190,714)(191,712)(192,711)(193,709)(194,710)
(195,675)(196,676)(197,681)(198,682)(199,680)(200,679)(201,677)(202,678)
(203,691)(204,692)(205,697)(206,698)(207,696)(208,695)(209,693)(210,694)
(211,683)(212,684)(213,689)(214,690)(215,688)(216,687)(217,685)(218,686)
(219,580)(220,579)(221,586)(222,585)(223,583)(224,584)(225,582)(226,581)
(227,596)(228,595)(229,602)(230,601)(231,599)(232,600)(233,598)(234,597)
(235,588)(236,587)(237,594)(238,593)(239,591)(240,592)(241,590)(242,589)
(243,628)(244,627)(245,634)(246,633)(247,631)(248,632)(249,630)(250,629)
(251,644)(252,643)(253,650)(254,649)(255,647)(256,648)(257,646)(258,645)
(259,636)(260,635)(261,642)(262,641)(263,639)(264,640)(265,638)(266,637)
(267,604)(268,603)(269,610)(270,609)(271,607)(272,608)(273,606)(274,605)
(275,620)(276,619)(277,626)(278,625)(279,623)(280,624)(281,622)(282,621)
(283,612)(284,611)(285,618)(286,617)(287,615)(288,616)(289,614)(290,613)
(291,508)(292,507)(293,514)(294,513)(295,511)(296,512)(297,510)(298,509)
(299,524)(300,523)(301,530)(302,529)(303,527)(304,528)(305,526)(306,525)
(307,516)(308,515)(309,522)(310,521)(311,519)(312,520)(313,518)(314,517)
(315,556)(316,555)(317,562)(318,561)(319,559)(320,560)(321,558)(322,557)
(323,572)(324,571)(325,578)(326,577)(327,575)(328,576)(329,574)(330,573)
(331,564)(332,563)(333,570)(334,569)(335,567)(336,568)(337,566)(338,565)
(339,532)(340,531)(341,538)(342,537)(343,535)(344,536)(345,534)(346,533)
(347,548)(348,547)(349,554)(350,553)(351,551)(352,552)(353,550)(354,549)
(355,540)(356,539)(357,546)(358,545)(359,543)(360,544)(361,542)(362,541)
(363,436)(364,435)(365,442)(366,441)(367,439)(368,440)(369,438)(370,437)
(371,452)(372,451)(373,458)(374,457)(375,455)(376,456)(377,454)(378,453)
(379,444)(380,443)(381,450)(382,449)(383,447)(384,448)(385,446)(386,445)
(387,484)(388,483)(389,490)(390,489)(391,487)(392,488)(393,486)(394,485)
(395,500)(396,499)(397,506)(398,505)(399,503)(400,504)(401,502)(402,501)
(403,492)(404,491)(405,498)(406,497)(407,495)(408,496)(409,494)(410,493)
(411,460)(412,459)(413,466)(414,465)(415,463)(416,464)(417,462)(418,461)
(419,476)(420,475)(421,482)(422,481)(423,479)(424,480)(425,478)(426,477)
(427,468)(428,467)(429,474)(430,473)(431,471)(432,472)(433,470)(434,469);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
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*s2*s1*s2*s3*s2*s3*s2, 
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(866)!(1,2);
s1 := Sym(866)!(  3,439)(  4,440)(  5,442)(  6,441)(  7,436)(  8,435)(  9,437)
( 10,438)( 11,447)( 12,448)( 13,450)( 14,449)( 15,444)( 16,443)( 17,445)
( 18,446)( 19,455)( 20,456)( 21,458)( 22,457)( 23,452)( 24,451)( 25,453)
( 26,454)( 27,487)( 28,488)( 29,490)( 30,489)( 31,484)( 32,483)( 33,485)
( 34,486)( 35,495)( 36,496)( 37,498)( 38,497)( 39,492)( 40,491)( 41,493)
( 42,494)( 43,503)( 44,504)( 45,506)( 46,505)( 47,500)( 48,499)( 49,501)
( 50,502)( 51,463)( 52,464)( 53,466)( 54,465)( 55,460)( 56,459)( 57,461)
( 58,462)( 59,471)( 60,472)( 61,474)( 62,473)( 63,468)( 64,467)( 65,469)
( 66,470)( 67,479)( 68,480)( 69,482)( 70,481)( 71,476)( 72,475)( 73,477)
( 74,478)( 75,511)( 76,512)( 77,514)( 78,513)( 79,508)( 80,507)( 81,509)
( 82,510)( 83,519)( 84,520)( 85,522)( 86,521)( 87,516)( 88,515)( 89,517)
( 90,518)( 91,527)( 92,528)( 93,530)( 94,529)( 95,524)( 96,523)( 97,525)
( 98,526)( 99,559)(100,560)(101,562)(102,561)(103,556)(104,555)(105,557)
(106,558)(107,567)(108,568)(109,570)(110,569)(111,564)(112,563)(113,565)
(114,566)(115,575)(116,576)(117,578)(118,577)(119,572)(120,571)(121,573)
(122,574)(123,535)(124,536)(125,538)(126,537)(127,532)(128,531)(129,533)
(130,534)(131,543)(132,544)(133,546)(134,545)(135,540)(136,539)(137,541)
(138,542)(139,551)(140,552)(141,554)(142,553)(143,548)(144,547)(145,549)
(146,550)(147,583)(148,584)(149,586)(150,585)(151,580)(152,579)(153,581)
(154,582)(155,591)(156,592)(157,594)(158,593)(159,588)(160,587)(161,589)
(162,590)(163,599)(164,600)(165,602)(166,601)(167,596)(168,595)(169,597)
(170,598)(171,631)(172,632)(173,634)(174,633)(175,628)(176,627)(177,629)
(178,630)(179,639)(180,640)(181,642)(182,641)(183,636)(184,635)(185,637)
(186,638)(187,647)(188,648)(189,650)(190,649)(191,644)(192,643)(193,645)
(194,646)(195,607)(196,608)(197,610)(198,609)(199,604)(200,603)(201,605)
(202,606)(203,615)(204,616)(205,618)(206,617)(207,612)(208,611)(209,613)
(210,614)(211,623)(212,624)(213,626)(214,625)(215,620)(216,619)(217,621)
(218,622)(219,656)(220,655)(221,657)(222,658)(223,651)(224,652)(225,654)
(226,653)(227,664)(228,663)(229,665)(230,666)(231,659)(232,660)(233,662)
(234,661)(235,672)(236,671)(237,673)(238,674)(239,667)(240,668)(241,670)
(242,669)(243,704)(244,703)(245,705)(246,706)(247,699)(248,700)(249,702)
(250,701)(251,712)(252,711)(253,713)(254,714)(255,707)(256,708)(257,710)
(258,709)(259,720)(260,719)(261,721)(262,722)(263,715)(264,716)(265,718)
(266,717)(267,680)(268,679)(269,681)(270,682)(271,675)(272,676)(273,678)
(274,677)(275,688)(276,687)(277,689)(278,690)(279,683)(280,684)(281,686)
(282,685)(283,696)(284,695)(285,697)(286,698)(287,691)(288,692)(289,694)
(290,693)(291,728)(292,727)(293,729)(294,730)(295,723)(296,724)(297,726)
(298,725)(299,736)(300,735)(301,737)(302,738)(303,731)(304,732)(305,734)
(306,733)(307,744)(308,743)(309,745)(310,746)(311,739)(312,740)(313,742)
(314,741)(315,776)(316,775)(317,777)(318,778)(319,771)(320,772)(321,774)
(322,773)(323,784)(324,783)(325,785)(326,786)(327,779)(328,780)(329,782)
(330,781)(331,792)(332,791)(333,793)(334,794)(335,787)(336,788)(337,790)
(338,789)(339,752)(340,751)(341,753)(342,754)(343,747)(344,748)(345,750)
(346,749)(347,760)(348,759)(349,761)(350,762)(351,755)(352,756)(353,758)
(354,757)(355,768)(356,767)(357,769)(358,770)(359,763)(360,764)(361,766)
(362,765)(363,800)(364,799)(365,801)(366,802)(367,795)(368,796)(369,798)
(370,797)(371,808)(372,807)(373,809)(374,810)(375,803)(376,804)(377,806)
(378,805)(379,816)(380,815)(381,817)(382,818)(383,811)(384,812)(385,814)
(386,813)(387,848)(388,847)(389,849)(390,850)(391,843)(392,844)(393,846)
(394,845)(395,856)(396,855)(397,857)(398,858)(399,851)(400,852)(401,854)
(402,853)(403,864)(404,863)(405,865)(406,866)(407,859)(408,860)(409,862)
(410,861)(411,824)(412,823)(413,825)(414,826)(415,819)(416,820)(417,822)
(418,821)(419,832)(420,831)(421,833)(422,834)(423,827)(424,828)(425,830)
(426,829)(427,840)(428,839)(429,841)(430,842)(431,835)(432,836)(433,838)
(434,837);
s2 := Sym(866)!(  3,675)(  4,676)(  5,680)(  6,679)(  7,678)(  8,677)(  9,682)
( 10,681)( 11,691)( 12,692)( 13,696)( 14,695)( 15,694)( 16,693)( 17,698)
( 18,697)( 19,683)( 20,684)( 21,688)( 22,687)( 23,686)( 24,685)( 25,690)
( 26,689)( 27,651)( 28,652)( 29,656)( 30,655)( 31,654)( 32,653)( 33,658)
( 34,657)( 35,667)( 36,668)( 37,672)( 38,671)( 39,670)( 40,669)( 41,674)
( 42,673)( 43,659)( 44,660)( 45,664)( 46,663)( 47,662)( 48,661)( 49,666)
( 50,665)( 51,699)( 52,700)( 53,704)( 54,703)( 55,702)( 56,701)( 57,706)
( 58,705)( 59,715)( 60,716)( 61,720)( 62,719)( 63,718)( 64,717)( 65,722)
( 66,721)( 67,707)( 68,708)( 69,712)( 70,711)( 71,710)( 72,709)( 73,714)
( 74,713)( 75,835)( 76,836)( 77,840)( 78,839)( 79,838)( 80,837)( 81,842)
( 82,841)( 83,827)( 84,828)( 85,832)( 86,831)( 87,830)( 88,829)( 89,834)
( 90,833)( 91,819)( 92,820)( 93,824)( 94,823)( 95,822)( 96,821)( 97,826)
( 98,825)( 99,811)(100,812)(101,816)(102,815)(103,814)(104,813)(105,818)
(106,817)(107,803)(108,804)(109,808)(110,807)(111,806)(112,805)(113,810)
(114,809)(115,795)(116,796)(117,800)(118,799)(119,798)(120,797)(121,802)
(122,801)(123,859)(124,860)(125,864)(126,863)(127,862)(128,861)(129,866)
(130,865)(131,851)(132,852)(133,856)(134,855)(135,854)(136,853)(137,858)
(138,857)(139,843)(140,844)(141,848)(142,847)(143,846)(144,845)(145,850)
(146,849)(147,763)(148,764)(149,768)(150,767)(151,766)(152,765)(153,770)
(154,769)(155,755)(156,756)(157,760)(158,759)(159,758)(160,757)(161,762)
(162,761)(163,747)(164,748)(165,752)(166,751)(167,750)(168,749)(169,754)
(170,753)(171,739)(172,740)(173,744)(174,743)(175,742)(176,741)(177,746)
(178,745)(179,731)(180,732)(181,736)(182,735)(183,734)(184,733)(185,738)
(186,737)(187,723)(188,724)(189,728)(190,727)(191,726)(192,725)(193,730)
(194,729)(195,787)(196,788)(197,792)(198,791)(199,790)(200,789)(201,794)
(202,793)(203,779)(204,780)(205,784)(206,783)(207,782)(208,781)(209,786)
(210,785)(211,771)(212,772)(213,776)(214,775)(215,774)(216,773)(217,778)
(218,777)(219,460)(220,459)(221,463)(222,464)(223,461)(224,462)(225,465)
(226,466)(227,476)(228,475)(229,479)(230,480)(231,477)(232,478)(233,481)
(234,482)(235,468)(236,467)(237,471)(238,472)(239,469)(240,470)(241,473)
(242,474)(243,436)(244,435)(245,439)(246,440)(247,437)(248,438)(249,441)
(250,442)(251,452)(252,451)(253,455)(254,456)(255,453)(256,454)(257,457)
(258,458)(259,444)(260,443)(261,447)(262,448)(263,445)(264,446)(265,449)
(266,450)(267,484)(268,483)(269,487)(270,488)(271,485)(272,486)(273,489)
(274,490)(275,500)(276,499)(277,503)(278,504)(279,501)(280,502)(281,505)
(282,506)(283,492)(284,491)(285,495)(286,496)(287,493)(288,494)(289,497)
(290,498)(291,620)(292,619)(293,623)(294,624)(295,621)(296,622)(297,625)
(298,626)(299,612)(300,611)(301,615)(302,616)(303,613)(304,614)(305,617)
(306,618)(307,604)(308,603)(309,607)(310,608)(311,605)(312,606)(313,609)
(314,610)(315,596)(316,595)(317,599)(318,600)(319,597)(320,598)(321,601)
(322,602)(323,588)(324,587)(325,591)(326,592)(327,589)(328,590)(329,593)
(330,594)(331,580)(332,579)(333,583)(334,584)(335,581)(336,582)(337,585)
(338,586)(339,644)(340,643)(341,647)(342,648)(343,645)(344,646)(345,649)
(346,650)(347,636)(348,635)(349,639)(350,640)(351,637)(352,638)(353,641)
(354,642)(355,628)(356,627)(357,631)(358,632)(359,629)(360,630)(361,633)
(362,634)(363,548)(364,547)(365,551)(366,552)(367,549)(368,550)(369,553)
(370,554)(371,540)(372,539)(373,543)(374,544)(375,541)(376,542)(377,545)
(378,546)(379,532)(380,531)(381,535)(382,536)(383,533)(384,534)(385,537)
(386,538)(387,524)(388,523)(389,527)(390,528)(391,525)(392,526)(393,529)
(394,530)(395,516)(396,515)(397,519)(398,520)(399,517)(400,518)(401,521)
(402,522)(403,508)(404,507)(405,511)(406,512)(407,509)(408,510)(409,513)
(410,514)(411,572)(412,571)(413,575)(414,576)(415,573)(416,574)(417,577)
(418,578)(419,564)(420,563)(421,567)(422,568)(423,565)(424,566)(425,569)
(426,570)(427,556)(428,555)(429,559)(430,560)(431,557)(432,558)(433,561)
(434,562);
s3 := Sym(866)!(  3,795)(  4,796)(  5,801)(  6,802)(  7,800)(  8,799)(  9,797)
( 10,798)( 11,811)( 12,812)( 13,817)( 14,818)( 15,816)( 16,815)( 17,813)
( 18,814)( 19,803)( 20,804)( 21,809)( 22,810)( 23,808)( 24,807)( 25,805)
( 26,806)( 27,843)( 28,844)( 29,849)( 30,850)( 31,848)( 32,847)( 33,845)
( 34,846)( 35,859)( 36,860)( 37,865)( 38,866)( 39,864)( 40,863)( 41,861)
( 42,862)( 43,851)( 44,852)( 45,857)( 46,858)( 47,856)( 48,855)( 49,853)
( 50,854)( 51,819)( 52,820)( 53,825)( 54,826)( 55,824)( 56,823)( 57,821)
( 58,822)( 59,835)( 60,836)( 61,841)( 62,842)( 63,840)( 64,839)( 65,837)
( 66,838)( 67,827)( 68,828)( 69,833)( 70,834)( 71,832)( 72,831)( 73,829)
( 74,830)( 75,723)( 76,724)( 77,729)( 78,730)( 79,728)( 80,727)( 81,725)
( 82,726)( 83,739)( 84,740)( 85,745)( 86,746)( 87,744)( 88,743)( 89,741)
( 90,742)( 91,731)( 92,732)( 93,737)( 94,738)( 95,736)( 96,735)( 97,733)
( 98,734)( 99,771)(100,772)(101,777)(102,778)(103,776)(104,775)(105,773)
(106,774)(107,787)(108,788)(109,793)(110,794)(111,792)(112,791)(113,789)
(114,790)(115,779)(116,780)(117,785)(118,786)(119,784)(120,783)(121,781)
(122,782)(123,747)(124,748)(125,753)(126,754)(127,752)(128,751)(129,749)
(130,750)(131,763)(132,764)(133,769)(134,770)(135,768)(136,767)(137,765)
(138,766)(139,755)(140,756)(141,761)(142,762)(143,760)(144,759)(145,757)
(146,758)(147,651)(148,652)(149,657)(150,658)(151,656)(152,655)(153,653)
(154,654)(155,667)(156,668)(157,673)(158,674)(159,672)(160,671)(161,669)
(162,670)(163,659)(164,660)(165,665)(166,666)(167,664)(168,663)(169,661)
(170,662)(171,699)(172,700)(173,705)(174,706)(175,704)(176,703)(177,701)
(178,702)(179,715)(180,716)(181,721)(182,722)(183,720)(184,719)(185,717)
(186,718)(187,707)(188,708)(189,713)(190,714)(191,712)(192,711)(193,709)
(194,710)(195,675)(196,676)(197,681)(198,682)(199,680)(200,679)(201,677)
(202,678)(203,691)(204,692)(205,697)(206,698)(207,696)(208,695)(209,693)
(210,694)(211,683)(212,684)(213,689)(214,690)(215,688)(216,687)(217,685)
(218,686)(219,580)(220,579)(221,586)(222,585)(223,583)(224,584)(225,582)
(226,581)(227,596)(228,595)(229,602)(230,601)(231,599)(232,600)(233,598)
(234,597)(235,588)(236,587)(237,594)(238,593)(239,591)(240,592)(241,590)
(242,589)(243,628)(244,627)(245,634)(246,633)(247,631)(248,632)(249,630)
(250,629)(251,644)(252,643)(253,650)(254,649)(255,647)(256,648)(257,646)
(258,645)(259,636)(260,635)(261,642)(262,641)(263,639)(264,640)(265,638)
(266,637)(267,604)(268,603)(269,610)(270,609)(271,607)(272,608)(273,606)
(274,605)(275,620)(276,619)(277,626)(278,625)(279,623)(280,624)(281,622)
(282,621)(283,612)(284,611)(285,618)(286,617)(287,615)(288,616)(289,614)
(290,613)(291,508)(292,507)(293,514)(294,513)(295,511)(296,512)(297,510)
(298,509)(299,524)(300,523)(301,530)(302,529)(303,527)(304,528)(305,526)
(306,525)(307,516)(308,515)(309,522)(310,521)(311,519)(312,520)(313,518)
(314,517)(315,556)(316,555)(317,562)(318,561)(319,559)(320,560)(321,558)
(322,557)(323,572)(324,571)(325,578)(326,577)(327,575)(328,576)(329,574)
(330,573)(331,564)(332,563)(333,570)(334,569)(335,567)(336,568)(337,566)
(338,565)(339,532)(340,531)(341,538)(342,537)(343,535)(344,536)(345,534)
(346,533)(347,548)(348,547)(349,554)(350,553)(351,551)(352,552)(353,550)
(354,549)(355,540)(356,539)(357,546)(358,545)(359,543)(360,544)(361,542)
(362,541)(363,436)(364,435)(365,442)(366,441)(367,439)(368,440)(369,438)
(370,437)(371,452)(372,451)(373,458)(374,457)(375,455)(376,456)(377,454)
(378,453)(379,444)(380,443)(381,450)(382,449)(383,447)(384,448)(385,446)
(386,445)(387,484)(388,483)(389,490)(390,489)(391,487)(392,488)(393,486)
(394,485)(395,500)(396,499)(397,506)(398,505)(399,503)(400,504)(401,502)
(402,501)(403,492)(404,491)(405,498)(406,497)(407,495)(408,496)(409,494)
(410,493)(411,460)(412,459)(413,466)(414,465)(415,463)(416,464)(417,462)
(418,461)(419,476)(420,475)(421,482)(422,481)(423,479)(424,480)(425,478)
(426,477)(427,468)(428,467)(429,474)(430,473)(431,471)(432,472)(433,470)
(434,469);
poly := sub<Sym(866)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
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*s2*s1*s2*s3*s2*s3*s2, 
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

to this polytope