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Polytope of Type {9,24,2}

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

to this polytope