Polytope of Type {24,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,6}*1728f
if this polytope has a name.
Group : SmallGroup(1728,46303)
Rank : 3
Schlafli Type : {24,6}
Number of vertices, edges, etc : 144, 432, 36
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 24
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,6}*864c
   3-fold quotients : {24,6}*576b, {24,6}*576e
   6-fold quotients : {24,3}*288, {12,6}*288a, {12,6}*288b
   8-fold quotients : {6,6}*216d
   9-fold quotients : {8,6}*192b
   12-fold quotients : {12,3}*144, {12,6}*144d
   18-fold quotients : {8,3}*96, {4,6}*96
   24-fold quotients : {6,6}*72a, {6,6}*72b, {6,6}*72c
   36-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   48-fold quotients : {3,6}*36, {6,3}*36
   72-fold quotients : {4,3}*24, {2,6}*24, {6,2}*24
   144-fold quotients : {2,3}*12, {3,2}*12
   216-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope