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