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Polytope of Type {2,9,24}

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

to this polytope