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