Questions?
See the FAQ
or other info.

Polytope of Type {2,24,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24,6}*1728g
if this polytope has a name.
Group : SmallGroup(1728,46634)
Rank : 4
Schlafli Type : {2,24,6}
Number of vertices, edges, etc : 2, 72, 216, 18
Order of s0s1s2s3 : 8
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 : {2,12,6}*864h
   3-fold quotients : {2,8,6}*576
   6-fold quotients : {2,4,6}*288
   12-fold quotients : {2,4,6}*144
   27-fold quotients : {2,8,2}*64
   54-fold quotients : {2,4,2}*32
   108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  3,651)(  4,653)(  5,652)(  6,672)(  7,674)(  8,673)(  9,666)( 10,668)
( 11,667)( 12,669)( 13,671)( 14,670)( 15,663)( 16,665)( 17,664)( 18,657)
( 19,659)( 20,658)( 21,660)( 22,662)( 23,661)( 24,654)( 25,656)( 26,655)
( 27,675)( 28,677)( 29,676)( 30,678)( 31,680)( 32,679)( 33,699)( 34,701)
( 35,700)( 36,693)( 37,695)( 38,694)( 39,696)( 40,698)( 41,697)( 42,690)
( 43,692)( 44,691)( 45,684)( 46,686)( 47,685)( 48,687)( 49,689)( 50,688)
( 51,681)( 52,683)( 53,682)( 54,702)( 55,704)( 56,703)( 57,732)( 58,734)
( 59,733)( 60,753)( 61,755)( 62,754)( 63,747)( 64,749)( 65,748)( 66,750)
( 67,752)( 68,751)( 69,744)( 70,746)( 71,745)( 72,738)( 73,740)( 74,739)
( 75,741)( 76,743)( 77,742)( 78,735)( 79,737)( 80,736)( 81,756)( 82,758)
( 83,757)( 84,705)( 85,707)( 86,706)( 87,726)( 88,728)( 89,727)( 90,720)
( 91,722)( 92,721)( 93,723)( 94,725)( 95,724)( 96,717)( 97,719)( 98,718)
( 99,711)(100,713)(101,712)(102,714)(103,716)(104,715)(105,708)(106,710)
(107,709)(108,729)(109,731)(110,730)(111,840)(112,842)(113,841)(114,861)
(115,863)(116,862)(117,855)(118,857)(119,856)(120,858)(121,860)(122,859)
(123,852)(124,854)(125,853)(126,846)(127,848)(128,847)(129,849)(130,851)
(131,850)(132,843)(133,845)(134,844)(135,864)(136,866)(137,865)(138,813)
(139,815)(140,814)(141,834)(142,836)(143,835)(144,828)(145,830)(146,829)
(147,831)(148,833)(149,832)(150,825)(151,827)(152,826)(153,819)(154,821)
(155,820)(156,822)(157,824)(158,823)(159,816)(160,818)(161,817)(162,837)
(163,839)(164,838)(165,786)(166,788)(167,787)(168,807)(169,809)(170,808)
(171,801)(172,803)(173,802)(174,804)(175,806)(176,805)(177,798)(178,800)
(179,799)(180,792)(181,794)(182,793)(183,795)(184,797)(185,796)(186,789)
(187,791)(188,790)(189,810)(190,812)(191,811)(192,759)(193,761)(194,760)
(195,780)(196,782)(197,781)(198,774)(199,776)(200,775)(201,777)(202,779)
(203,778)(204,771)(205,773)(206,772)(207,765)(208,767)(209,766)(210,768)
(211,770)(212,769)(213,762)(214,764)(215,763)(216,783)(217,785)(218,784)
(219,462)(220,464)(221,463)(222,483)(223,485)(224,484)(225,477)(226,479)
(227,478)(228,480)(229,482)(230,481)(231,474)(232,476)(233,475)(234,468)
(235,470)(236,469)(237,471)(238,473)(239,472)(240,465)(241,467)(242,466)
(243,486)(244,488)(245,487)(246,435)(247,437)(248,436)(249,456)(250,458)
(251,457)(252,450)(253,452)(254,451)(255,453)(256,455)(257,454)(258,447)
(259,449)(260,448)(261,441)(262,443)(263,442)(264,444)(265,446)(266,445)
(267,438)(268,440)(269,439)(270,459)(271,461)(272,460)(273,489)(274,491)
(275,490)(276,510)(277,512)(278,511)(279,504)(280,506)(281,505)(282,507)
(283,509)(284,508)(285,501)(286,503)(287,502)(288,495)(289,497)(290,496)
(291,498)(292,500)(293,499)(294,492)(295,494)(296,493)(297,513)(298,515)
(299,514)(300,516)(301,518)(302,517)(303,537)(304,539)(305,538)(306,531)
(307,533)(308,532)(309,534)(310,536)(311,535)(312,528)(313,530)(314,529)
(315,522)(316,524)(317,523)(318,525)(319,527)(320,526)(321,519)(322,521)
(323,520)(324,540)(325,542)(326,541)(327,597)(328,599)(329,598)(330,618)
(331,620)(332,619)(333,612)(334,614)(335,613)(336,615)(337,617)(338,616)
(339,609)(340,611)(341,610)(342,603)(343,605)(344,604)(345,606)(346,608)
(347,607)(348,600)(349,602)(350,601)(351,621)(352,623)(353,622)(354,624)
(355,626)(356,625)(357,645)(358,647)(359,646)(360,639)(361,641)(362,640)
(363,642)(364,644)(365,643)(366,636)(367,638)(368,637)(369,630)(370,632)
(371,631)(372,633)(373,635)(374,634)(375,627)(376,629)(377,628)(378,648)
(379,650)(380,649)(381,543)(382,545)(383,544)(384,564)(385,566)(386,565)
(387,558)(388,560)(389,559)(390,561)(391,563)(392,562)(393,555)(394,557)
(395,556)(396,549)(397,551)(398,550)(399,552)(400,554)(401,553)(402,546)
(403,548)(404,547)(405,567)(406,569)(407,568)(408,570)(409,572)(410,571)
(411,591)(412,593)(413,592)(414,585)(415,587)(416,586)(417,588)(418,590)
(419,589)(420,582)(421,584)(422,583)(423,576)(424,578)(425,577)(426,579)
(427,581)(428,580)(429,573)(430,575)(431,574)(432,594)(433,596)(434,595);;
s2 := (  3,544)(  4,543)(  5,545)(  6,547)(  7,546)(  8,548)(  9,550)( 10,549)
( 11,551)( 12,568)( 13,567)( 14,569)( 15,562)( 16,561)( 17,563)( 18,565)
( 19,564)( 20,566)( 21,556)( 22,555)( 23,557)( 24,559)( 25,558)( 26,560)
( 27,553)( 28,552)( 29,554)( 30,571)( 31,570)( 32,572)( 33,574)( 34,573)
( 35,575)( 36,577)( 37,576)( 38,578)( 39,595)( 40,594)( 41,596)( 42,589)
( 43,588)( 44,590)( 45,592)( 46,591)( 47,593)( 48,583)( 49,582)( 50,584)
( 51,586)( 52,585)( 53,587)( 54,580)( 55,579)( 56,581)( 57,625)( 58,624)
( 59,626)( 60,628)( 61,627)( 62,629)( 63,631)( 64,630)( 65,632)( 66,649)
( 67,648)( 68,650)( 69,643)( 70,642)( 71,644)( 72,646)( 73,645)( 74,647)
( 75,637)( 76,636)( 77,638)( 78,640)( 79,639)( 80,641)( 81,634)( 82,633)
( 83,635)( 84,598)( 85,597)( 86,599)( 87,601)( 88,600)( 89,602)( 90,604)
( 91,603)( 92,605)( 93,622)( 94,621)( 95,623)( 96,616)( 97,615)( 98,617)
( 99,619)(100,618)(101,620)(102,610)(103,609)(104,611)(105,613)(106,612)
(107,614)(108,607)(109,606)(110,608)(111,463)(112,462)(113,464)(114,466)
(115,465)(116,467)(117,469)(118,468)(119,470)(120,487)(121,486)(122,488)
(123,481)(124,480)(125,482)(126,484)(127,483)(128,485)(129,475)(130,474)
(131,476)(132,478)(133,477)(134,479)(135,472)(136,471)(137,473)(138,436)
(139,435)(140,437)(141,439)(142,438)(143,440)(144,442)(145,441)(146,443)
(147,460)(148,459)(149,461)(150,454)(151,453)(152,455)(153,457)(154,456)
(155,458)(156,448)(157,447)(158,449)(159,451)(160,450)(161,452)(162,445)
(163,444)(164,446)(165,490)(166,489)(167,491)(168,493)(169,492)(170,494)
(171,496)(172,495)(173,497)(174,514)(175,513)(176,515)(177,508)(178,507)
(179,509)(180,511)(181,510)(182,512)(183,502)(184,501)(185,503)(186,505)
(187,504)(188,506)(189,499)(190,498)(191,500)(192,517)(193,516)(194,518)
(195,520)(196,519)(197,521)(198,523)(199,522)(200,524)(201,541)(202,540)
(203,542)(204,535)(205,534)(206,536)(207,538)(208,537)(209,539)(210,529)
(211,528)(212,530)(213,532)(214,531)(215,533)(216,526)(217,525)(218,527)
(219,787)(220,786)(221,788)(222,790)(223,789)(224,791)(225,793)(226,792)
(227,794)(228,811)(229,810)(230,812)(231,805)(232,804)(233,806)(234,808)
(235,807)(236,809)(237,799)(238,798)(239,800)(240,802)(241,801)(242,803)
(243,796)(244,795)(245,797)(246,760)(247,759)(248,761)(249,763)(250,762)
(251,764)(252,766)(253,765)(254,767)(255,784)(256,783)(257,785)(258,778)
(259,777)(260,779)(261,781)(262,780)(263,782)(264,772)(265,771)(266,773)
(267,775)(268,774)(269,776)(270,769)(271,768)(272,770)(273,814)(274,813)
(275,815)(276,817)(277,816)(278,818)(279,820)(280,819)(281,821)(282,838)
(283,837)(284,839)(285,832)(286,831)(287,833)(288,835)(289,834)(290,836)
(291,826)(292,825)(293,827)(294,829)(295,828)(296,830)(297,823)(298,822)
(299,824)(300,841)(301,840)(302,842)(303,844)(304,843)(305,845)(306,847)
(307,846)(308,848)(309,865)(310,864)(311,866)(312,859)(313,858)(314,860)
(315,862)(316,861)(317,863)(318,853)(319,852)(320,854)(321,856)(322,855)
(323,857)(324,850)(325,849)(326,851)(327,652)(328,651)(329,653)(330,655)
(331,654)(332,656)(333,658)(334,657)(335,659)(336,676)(337,675)(338,677)
(339,670)(340,669)(341,671)(342,673)(343,672)(344,674)(345,664)(346,663)
(347,665)(348,667)(349,666)(350,668)(351,661)(352,660)(353,662)(354,679)
(355,678)(356,680)(357,682)(358,681)(359,683)(360,685)(361,684)(362,686)
(363,703)(364,702)(365,704)(366,697)(367,696)(368,698)(369,700)(370,699)
(371,701)(372,691)(373,690)(374,692)(375,694)(376,693)(377,695)(378,688)
(379,687)(380,689)(381,733)(382,732)(383,734)(384,736)(385,735)(386,737)
(387,739)(388,738)(389,740)(390,757)(391,756)(392,758)(393,751)(394,750)
(395,752)(396,754)(397,753)(398,755)(399,745)(400,744)(401,746)(402,748)
(403,747)(404,749)(405,742)(406,741)(407,743)(408,706)(409,705)(410,707)
(411,709)(412,708)(413,710)(414,712)(415,711)(416,713)(417,730)(418,729)
(419,731)(420,724)(421,723)(422,725)(423,727)(424,726)(425,728)(426,718)
(427,717)(428,719)(429,721)(430,720)(431,722)(432,715)(433,714)(434,716);;
s3 := (  3,501)(  4,503)(  5,502)(  6,498)(  7,500)(  8,499)(  9,504)( 10,506)
( 11,505)( 12,492)( 13,494)( 14,493)( 15,489)( 16,491)( 17,490)( 18,495)
( 19,497)( 20,496)( 21,510)( 22,512)( 23,511)( 24,507)( 25,509)( 26,508)
( 27,513)( 28,515)( 29,514)( 30,528)( 31,530)( 32,529)( 33,525)( 34,527)
( 35,526)( 36,531)( 37,533)( 38,532)( 39,519)( 40,521)( 41,520)( 42,516)
( 43,518)( 44,517)( 45,522)( 46,524)( 47,523)( 48,537)( 49,539)( 50,538)
( 51,534)( 52,536)( 53,535)( 54,540)( 55,542)( 56,541)( 57,474)( 58,476)
( 59,475)( 60,471)( 61,473)( 62,472)( 63,477)( 64,479)( 65,478)( 66,465)
( 67,467)( 68,466)( 69,462)( 70,464)( 71,463)( 72,468)( 73,470)( 74,469)
( 75,483)( 76,485)( 77,484)( 78,480)( 79,482)( 80,481)( 81,486)( 82,488)
( 83,487)( 84,447)( 85,449)( 86,448)( 87,444)( 88,446)( 89,445)( 90,450)
( 91,452)( 92,451)( 93,438)( 94,440)( 95,439)( 96,435)( 97,437)( 98,436)
( 99,441)(100,443)(101,442)(102,456)(103,458)(104,457)(105,453)(106,455)
(107,454)(108,459)(109,461)(110,460)(111,636)(112,638)(113,637)(114,633)
(115,635)(116,634)(117,639)(118,641)(119,640)(120,627)(121,629)(122,628)
(123,624)(124,626)(125,625)(126,630)(127,632)(128,631)(129,645)(130,647)
(131,646)(132,642)(133,644)(134,643)(135,648)(136,650)(137,649)(138,609)
(139,611)(140,610)(141,606)(142,608)(143,607)(144,612)(145,614)(146,613)
(147,600)(148,602)(149,601)(150,597)(151,599)(152,598)(153,603)(154,605)
(155,604)(156,618)(157,620)(158,619)(159,615)(160,617)(161,616)(162,621)
(163,623)(164,622)(165,555)(166,557)(167,556)(168,552)(169,554)(170,553)
(171,558)(172,560)(173,559)(174,546)(175,548)(176,547)(177,543)(178,545)
(179,544)(180,549)(181,551)(182,550)(183,564)(184,566)(185,565)(186,561)
(187,563)(188,562)(189,567)(190,569)(191,568)(192,582)(193,584)(194,583)
(195,579)(196,581)(197,580)(198,585)(199,587)(200,586)(201,573)(202,575)
(203,574)(204,570)(205,572)(206,571)(207,576)(208,578)(209,577)(210,591)
(211,593)(212,592)(213,588)(214,590)(215,589)(216,594)(217,596)(218,595)
(219,744)(220,746)(221,745)(222,741)(223,743)(224,742)(225,747)(226,749)
(227,748)(228,735)(229,737)(230,736)(231,732)(232,734)(233,733)(234,738)
(235,740)(236,739)(237,753)(238,755)(239,754)(240,750)(241,752)(242,751)
(243,756)(244,758)(245,757)(246,717)(247,719)(248,718)(249,714)(250,716)
(251,715)(252,720)(253,722)(254,721)(255,708)(256,710)(257,709)(258,705)
(259,707)(260,706)(261,711)(262,713)(263,712)(264,726)(265,728)(266,727)
(267,723)(268,725)(269,724)(270,729)(271,731)(272,730)(273,663)(274,665)
(275,664)(276,660)(277,662)(278,661)(279,666)(280,668)(281,667)(282,654)
(283,656)(284,655)(285,651)(286,653)(287,652)(288,657)(289,659)(290,658)
(291,672)(292,674)(293,673)(294,669)(295,671)(296,670)(297,675)(298,677)
(299,676)(300,690)(301,692)(302,691)(303,687)(304,689)(305,688)(306,693)
(307,695)(308,694)(309,681)(310,683)(311,682)(312,678)(313,680)(314,679)
(315,684)(316,686)(317,685)(318,699)(319,701)(320,700)(321,696)(322,698)
(323,697)(324,702)(325,704)(326,703)(327,825)(328,827)(329,826)(330,822)
(331,824)(332,823)(333,828)(334,830)(335,829)(336,816)(337,818)(338,817)
(339,813)(340,815)(341,814)(342,819)(343,821)(344,820)(345,834)(346,836)
(347,835)(348,831)(349,833)(350,832)(351,837)(352,839)(353,838)(354,852)
(355,854)(356,853)(357,849)(358,851)(359,850)(360,855)(361,857)(362,856)
(363,843)(364,845)(365,844)(366,840)(367,842)(368,841)(369,846)(370,848)
(371,847)(372,861)(373,863)(374,862)(375,858)(376,860)(377,859)(378,864)
(379,866)(380,865)(381,798)(382,800)(383,799)(384,795)(385,797)(386,796)
(387,801)(388,803)(389,802)(390,789)(391,791)(392,790)(393,786)(394,788)
(395,787)(396,792)(397,794)(398,793)(399,807)(400,809)(401,808)(402,804)
(403,806)(404,805)(405,810)(406,812)(407,811)(408,771)(409,773)(410,772)
(411,768)(412,770)(413,769)(414,774)(415,776)(416,775)(417,762)(418,764)
(419,763)(420,759)(421,761)(422,760)(423,765)(424,767)(425,766)(426,780)
(427,782)(428,781)(429,777)(430,779)(431,778)(432,783)(433,785)(434,784);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(866)!(1,2);
s1 := Sym(866)!(  3,651)(  4,653)(  5,652)(  6,672)(  7,674)(  8,673)(  9,666)
( 10,668)( 11,667)( 12,669)( 13,671)( 14,670)( 15,663)( 16,665)( 17,664)
( 18,657)( 19,659)( 20,658)( 21,660)( 22,662)( 23,661)( 24,654)( 25,656)
( 26,655)( 27,675)( 28,677)( 29,676)( 30,678)( 31,680)( 32,679)( 33,699)
( 34,701)( 35,700)( 36,693)( 37,695)( 38,694)( 39,696)( 40,698)( 41,697)
( 42,690)( 43,692)( 44,691)( 45,684)( 46,686)( 47,685)( 48,687)( 49,689)
( 50,688)( 51,681)( 52,683)( 53,682)( 54,702)( 55,704)( 56,703)( 57,732)
( 58,734)( 59,733)( 60,753)( 61,755)( 62,754)( 63,747)( 64,749)( 65,748)
( 66,750)( 67,752)( 68,751)( 69,744)( 70,746)( 71,745)( 72,738)( 73,740)
( 74,739)( 75,741)( 76,743)( 77,742)( 78,735)( 79,737)( 80,736)( 81,756)
( 82,758)( 83,757)( 84,705)( 85,707)( 86,706)( 87,726)( 88,728)( 89,727)
( 90,720)( 91,722)( 92,721)( 93,723)( 94,725)( 95,724)( 96,717)( 97,719)
( 98,718)( 99,711)(100,713)(101,712)(102,714)(103,716)(104,715)(105,708)
(106,710)(107,709)(108,729)(109,731)(110,730)(111,840)(112,842)(113,841)
(114,861)(115,863)(116,862)(117,855)(118,857)(119,856)(120,858)(121,860)
(122,859)(123,852)(124,854)(125,853)(126,846)(127,848)(128,847)(129,849)
(130,851)(131,850)(132,843)(133,845)(134,844)(135,864)(136,866)(137,865)
(138,813)(139,815)(140,814)(141,834)(142,836)(143,835)(144,828)(145,830)
(146,829)(147,831)(148,833)(149,832)(150,825)(151,827)(152,826)(153,819)
(154,821)(155,820)(156,822)(157,824)(158,823)(159,816)(160,818)(161,817)
(162,837)(163,839)(164,838)(165,786)(166,788)(167,787)(168,807)(169,809)
(170,808)(171,801)(172,803)(173,802)(174,804)(175,806)(176,805)(177,798)
(178,800)(179,799)(180,792)(181,794)(182,793)(183,795)(184,797)(185,796)
(186,789)(187,791)(188,790)(189,810)(190,812)(191,811)(192,759)(193,761)
(194,760)(195,780)(196,782)(197,781)(198,774)(199,776)(200,775)(201,777)
(202,779)(203,778)(204,771)(205,773)(206,772)(207,765)(208,767)(209,766)
(210,768)(211,770)(212,769)(213,762)(214,764)(215,763)(216,783)(217,785)
(218,784)(219,462)(220,464)(221,463)(222,483)(223,485)(224,484)(225,477)
(226,479)(227,478)(228,480)(229,482)(230,481)(231,474)(232,476)(233,475)
(234,468)(235,470)(236,469)(237,471)(238,473)(239,472)(240,465)(241,467)
(242,466)(243,486)(244,488)(245,487)(246,435)(247,437)(248,436)(249,456)
(250,458)(251,457)(252,450)(253,452)(254,451)(255,453)(256,455)(257,454)
(258,447)(259,449)(260,448)(261,441)(262,443)(263,442)(264,444)(265,446)
(266,445)(267,438)(268,440)(269,439)(270,459)(271,461)(272,460)(273,489)
(274,491)(275,490)(276,510)(277,512)(278,511)(279,504)(280,506)(281,505)
(282,507)(283,509)(284,508)(285,501)(286,503)(287,502)(288,495)(289,497)
(290,496)(291,498)(292,500)(293,499)(294,492)(295,494)(296,493)(297,513)
(298,515)(299,514)(300,516)(301,518)(302,517)(303,537)(304,539)(305,538)
(306,531)(307,533)(308,532)(309,534)(310,536)(311,535)(312,528)(313,530)
(314,529)(315,522)(316,524)(317,523)(318,525)(319,527)(320,526)(321,519)
(322,521)(323,520)(324,540)(325,542)(326,541)(327,597)(328,599)(329,598)
(330,618)(331,620)(332,619)(333,612)(334,614)(335,613)(336,615)(337,617)
(338,616)(339,609)(340,611)(341,610)(342,603)(343,605)(344,604)(345,606)
(346,608)(347,607)(348,600)(349,602)(350,601)(351,621)(352,623)(353,622)
(354,624)(355,626)(356,625)(357,645)(358,647)(359,646)(360,639)(361,641)
(362,640)(363,642)(364,644)(365,643)(366,636)(367,638)(368,637)(369,630)
(370,632)(371,631)(372,633)(373,635)(374,634)(375,627)(376,629)(377,628)
(378,648)(379,650)(380,649)(381,543)(382,545)(383,544)(384,564)(385,566)
(386,565)(387,558)(388,560)(389,559)(390,561)(391,563)(392,562)(393,555)
(394,557)(395,556)(396,549)(397,551)(398,550)(399,552)(400,554)(401,553)
(402,546)(403,548)(404,547)(405,567)(406,569)(407,568)(408,570)(409,572)
(410,571)(411,591)(412,593)(413,592)(414,585)(415,587)(416,586)(417,588)
(418,590)(419,589)(420,582)(421,584)(422,583)(423,576)(424,578)(425,577)
(426,579)(427,581)(428,580)(429,573)(430,575)(431,574)(432,594)(433,596)
(434,595);
s2 := Sym(866)!(  3,544)(  4,543)(  5,545)(  6,547)(  7,546)(  8,548)(  9,550)
( 10,549)( 11,551)( 12,568)( 13,567)( 14,569)( 15,562)( 16,561)( 17,563)
( 18,565)( 19,564)( 20,566)( 21,556)( 22,555)( 23,557)( 24,559)( 25,558)
( 26,560)( 27,553)( 28,552)( 29,554)( 30,571)( 31,570)( 32,572)( 33,574)
( 34,573)( 35,575)( 36,577)( 37,576)( 38,578)( 39,595)( 40,594)( 41,596)
( 42,589)( 43,588)( 44,590)( 45,592)( 46,591)( 47,593)( 48,583)( 49,582)
( 50,584)( 51,586)( 52,585)( 53,587)( 54,580)( 55,579)( 56,581)( 57,625)
( 58,624)( 59,626)( 60,628)( 61,627)( 62,629)( 63,631)( 64,630)( 65,632)
( 66,649)( 67,648)( 68,650)( 69,643)( 70,642)( 71,644)( 72,646)( 73,645)
( 74,647)( 75,637)( 76,636)( 77,638)( 78,640)( 79,639)( 80,641)( 81,634)
( 82,633)( 83,635)( 84,598)( 85,597)( 86,599)( 87,601)( 88,600)( 89,602)
( 90,604)( 91,603)( 92,605)( 93,622)( 94,621)( 95,623)( 96,616)( 97,615)
( 98,617)( 99,619)(100,618)(101,620)(102,610)(103,609)(104,611)(105,613)
(106,612)(107,614)(108,607)(109,606)(110,608)(111,463)(112,462)(113,464)
(114,466)(115,465)(116,467)(117,469)(118,468)(119,470)(120,487)(121,486)
(122,488)(123,481)(124,480)(125,482)(126,484)(127,483)(128,485)(129,475)
(130,474)(131,476)(132,478)(133,477)(134,479)(135,472)(136,471)(137,473)
(138,436)(139,435)(140,437)(141,439)(142,438)(143,440)(144,442)(145,441)
(146,443)(147,460)(148,459)(149,461)(150,454)(151,453)(152,455)(153,457)
(154,456)(155,458)(156,448)(157,447)(158,449)(159,451)(160,450)(161,452)
(162,445)(163,444)(164,446)(165,490)(166,489)(167,491)(168,493)(169,492)
(170,494)(171,496)(172,495)(173,497)(174,514)(175,513)(176,515)(177,508)
(178,507)(179,509)(180,511)(181,510)(182,512)(183,502)(184,501)(185,503)
(186,505)(187,504)(188,506)(189,499)(190,498)(191,500)(192,517)(193,516)
(194,518)(195,520)(196,519)(197,521)(198,523)(199,522)(200,524)(201,541)
(202,540)(203,542)(204,535)(205,534)(206,536)(207,538)(208,537)(209,539)
(210,529)(211,528)(212,530)(213,532)(214,531)(215,533)(216,526)(217,525)
(218,527)(219,787)(220,786)(221,788)(222,790)(223,789)(224,791)(225,793)
(226,792)(227,794)(228,811)(229,810)(230,812)(231,805)(232,804)(233,806)
(234,808)(235,807)(236,809)(237,799)(238,798)(239,800)(240,802)(241,801)
(242,803)(243,796)(244,795)(245,797)(246,760)(247,759)(248,761)(249,763)
(250,762)(251,764)(252,766)(253,765)(254,767)(255,784)(256,783)(257,785)
(258,778)(259,777)(260,779)(261,781)(262,780)(263,782)(264,772)(265,771)
(266,773)(267,775)(268,774)(269,776)(270,769)(271,768)(272,770)(273,814)
(274,813)(275,815)(276,817)(277,816)(278,818)(279,820)(280,819)(281,821)
(282,838)(283,837)(284,839)(285,832)(286,831)(287,833)(288,835)(289,834)
(290,836)(291,826)(292,825)(293,827)(294,829)(295,828)(296,830)(297,823)
(298,822)(299,824)(300,841)(301,840)(302,842)(303,844)(304,843)(305,845)
(306,847)(307,846)(308,848)(309,865)(310,864)(311,866)(312,859)(313,858)
(314,860)(315,862)(316,861)(317,863)(318,853)(319,852)(320,854)(321,856)
(322,855)(323,857)(324,850)(325,849)(326,851)(327,652)(328,651)(329,653)
(330,655)(331,654)(332,656)(333,658)(334,657)(335,659)(336,676)(337,675)
(338,677)(339,670)(340,669)(341,671)(342,673)(343,672)(344,674)(345,664)
(346,663)(347,665)(348,667)(349,666)(350,668)(351,661)(352,660)(353,662)
(354,679)(355,678)(356,680)(357,682)(358,681)(359,683)(360,685)(361,684)
(362,686)(363,703)(364,702)(365,704)(366,697)(367,696)(368,698)(369,700)
(370,699)(371,701)(372,691)(373,690)(374,692)(375,694)(376,693)(377,695)
(378,688)(379,687)(380,689)(381,733)(382,732)(383,734)(384,736)(385,735)
(386,737)(387,739)(388,738)(389,740)(390,757)(391,756)(392,758)(393,751)
(394,750)(395,752)(396,754)(397,753)(398,755)(399,745)(400,744)(401,746)
(402,748)(403,747)(404,749)(405,742)(406,741)(407,743)(408,706)(409,705)
(410,707)(411,709)(412,708)(413,710)(414,712)(415,711)(416,713)(417,730)
(418,729)(419,731)(420,724)(421,723)(422,725)(423,727)(424,726)(425,728)
(426,718)(427,717)(428,719)(429,721)(430,720)(431,722)(432,715)(433,714)
(434,716);
s3 := Sym(866)!(  3,501)(  4,503)(  5,502)(  6,498)(  7,500)(  8,499)(  9,504)
( 10,506)( 11,505)( 12,492)( 13,494)( 14,493)( 15,489)( 16,491)( 17,490)
( 18,495)( 19,497)( 20,496)( 21,510)( 22,512)( 23,511)( 24,507)( 25,509)
( 26,508)( 27,513)( 28,515)( 29,514)( 30,528)( 31,530)( 32,529)( 33,525)
( 34,527)( 35,526)( 36,531)( 37,533)( 38,532)( 39,519)( 40,521)( 41,520)
( 42,516)( 43,518)( 44,517)( 45,522)( 46,524)( 47,523)( 48,537)( 49,539)
( 50,538)( 51,534)( 52,536)( 53,535)( 54,540)( 55,542)( 56,541)( 57,474)
( 58,476)( 59,475)( 60,471)( 61,473)( 62,472)( 63,477)( 64,479)( 65,478)
( 66,465)( 67,467)( 68,466)( 69,462)( 70,464)( 71,463)( 72,468)( 73,470)
( 74,469)( 75,483)( 76,485)( 77,484)( 78,480)( 79,482)( 80,481)( 81,486)
( 82,488)( 83,487)( 84,447)( 85,449)( 86,448)( 87,444)( 88,446)( 89,445)
( 90,450)( 91,452)( 92,451)( 93,438)( 94,440)( 95,439)( 96,435)( 97,437)
( 98,436)( 99,441)(100,443)(101,442)(102,456)(103,458)(104,457)(105,453)
(106,455)(107,454)(108,459)(109,461)(110,460)(111,636)(112,638)(113,637)
(114,633)(115,635)(116,634)(117,639)(118,641)(119,640)(120,627)(121,629)
(122,628)(123,624)(124,626)(125,625)(126,630)(127,632)(128,631)(129,645)
(130,647)(131,646)(132,642)(133,644)(134,643)(135,648)(136,650)(137,649)
(138,609)(139,611)(140,610)(141,606)(142,608)(143,607)(144,612)(145,614)
(146,613)(147,600)(148,602)(149,601)(150,597)(151,599)(152,598)(153,603)
(154,605)(155,604)(156,618)(157,620)(158,619)(159,615)(160,617)(161,616)
(162,621)(163,623)(164,622)(165,555)(166,557)(167,556)(168,552)(169,554)
(170,553)(171,558)(172,560)(173,559)(174,546)(175,548)(176,547)(177,543)
(178,545)(179,544)(180,549)(181,551)(182,550)(183,564)(184,566)(185,565)
(186,561)(187,563)(188,562)(189,567)(190,569)(191,568)(192,582)(193,584)
(194,583)(195,579)(196,581)(197,580)(198,585)(199,587)(200,586)(201,573)
(202,575)(203,574)(204,570)(205,572)(206,571)(207,576)(208,578)(209,577)
(210,591)(211,593)(212,592)(213,588)(214,590)(215,589)(216,594)(217,596)
(218,595)(219,744)(220,746)(221,745)(222,741)(223,743)(224,742)(225,747)
(226,749)(227,748)(228,735)(229,737)(230,736)(231,732)(232,734)(233,733)
(234,738)(235,740)(236,739)(237,753)(238,755)(239,754)(240,750)(241,752)
(242,751)(243,756)(244,758)(245,757)(246,717)(247,719)(248,718)(249,714)
(250,716)(251,715)(252,720)(253,722)(254,721)(255,708)(256,710)(257,709)
(258,705)(259,707)(260,706)(261,711)(262,713)(263,712)(264,726)(265,728)
(266,727)(267,723)(268,725)(269,724)(270,729)(271,731)(272,730)(273,663)
(274,665)(275,664)(276,660)(277,662)(278,661)(279,666)(280,668)(281,667)
(282,654)(283,656)(284,655)(285,651)(286,653)(287,652)(288,657)(289,659)
(290,658)(291,672)(292,674)(293,673)(294,669)(295,671)(296,670)(297,675)
(298,677)(299,676)(300,690)(301,692)(302,691)(303,687)(304,689)(305,688)
(306,693)(307,695)(308,694)(309,681)(310,683)(311,682)(312,678)(313,680)
(314,679)(315,684)(316,686)(317,685)(318,699)(319,701)(320,700)(321,696)
(322,698)(323,697)(324,702)(325,704)(326,703)(327,825)(328,827)(329,826)
(330,822)(331,824)(332,823)(333,828)(334,830)(335,829)(336,816)(337,818)
(338,817)(339,813)(340,815)(341,814)(342,819)(343,821)(344,820)(345,834)
(346,836)(347,835)(348,831)(349,833)(350,832)(351,837)(352,839)(353,838)
(354,852)(355,854)(356,853)(357,849)(358,851)(359,850)(360,855)(361,857)
(362,856)(363,843)(364,845)(365,844)(366,840)(367,842)(368,841)(369,846)
(370,848)(371,847)(372,861)(373,863)(374,862)(375,858)(376,860)(377,859)
(378,864)(379,866)(380,865)(381,798)(382,800)(383,799)(384,795)(385,797)
(386,796)(387,801)(388,803)(389,802)(390,789)(391,791)(392,790)(393,786)
(394,788)(395,787)(396,792)(397,794)(398,793)(399,807)(400,809)(401,808)
(402,804)(403,806)(404,805)(405,810)(406,812)(407,811)(408,771)(409,773)
(410,772)(411,768)(412,770)(413,769)(414,774)(415,776)(416,775)(417,762)
(418,764)(419,763)(420,759)(421,761)(422,760)(423,765)(424,767)(425,766)
(426,780)(427,782)(428,781)(429,777)(430,779)(431,778)(432,783)(433,785)
(434,784);
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2*s3*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2 >; 
 

to this polytope