Polytope of Type {24,9,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,9,2}*1728
if this polytope has a name.
Group : SmallGroup(1728,30249)
Rank : 4
Schlafli Type : {24,9,2}
Number of vertices, edges, etc : 48, 216, 18, 2
Order of s0s1s2s3 : 36
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,9,2}*864
3-fold quotients : {8,9,2}*576, {24,3,2}*576
6-fold quotients : {4,9,2}*288, {12,3,2}*288
8-fold quotients : {6,9,2}*216
9-fold quotients : {8,3,2}*192
12-fold quotients : {4,9,2}*144
18-fold quotients : {4,3,2}*96
24-fold quotients : {2,9,2}*72, {6,3,2}*72
36-fold quotients : {4,3,2}*48
72-fold quotients : {2,3,2}*24
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)
( 9,445)( 10,446)( 11,448)( 12,447)( 13,442)( 14,441)( 15,443)( 16,444)
( 17,453)( 18,454)( 19,456)( 20,455)( 21,450)( 22,449)( 23,451)( 24,452)
( 25,485)( 26,486)( 27,488)( 28,487)( 29,482)( 30,481)( 31,483)( 32,484)
( 33,493)( 34,494)( 35,496)( 36,495)( 37,490)( 38,489)( 39,491)( 40,492)
( 41,501)( 42,502)( 43,504)( 44,503)( 45,498)( 46,497)( 47,499)( 48,500)
( 49,461)( 50,462)( 51,464)( 52,463)( 53,458)( 54,457)( 55,459)( 56,460)
( 57,469)( 58,470)( 59,472)( 60,471)( 61,466)( 62,465)( 63,467)( 64,468)
( 65,477)( 66,478)( 67,480)( 68,479)( 69,474)( 70,473)( 71,475)( 72,476)
( 73,509)( 74,510)( 75,512)( 76,511)( 77,506)( 78,505)( 79,507)( 80,508)
( 81,517)( 82,518)( 83,520)( 84,519)( 85,514)( 86,513)( 87,515)( 88,516)
( 89,525)( 90,526)( 91,528)( 92,527)( 93,522)( 94,521)( 95,523)( 96,524)
( 97,557)( 98,558)( 99,560)(100,559)(101,554)(102,553)(103,555)(104,556)
(105,565)(106,566)(107,568)(108,567)(109,562)(110,561)(111,563)(112,564)
(113,573)(114,574)(115,576)(116,575)(117,570)(118,569)(119,571)(120,572)
(121,533)(122,534)(123,536)(124,535)(125,530)(126,529)(127,531)(128,532)
(129,541)(130,542)(131,544)(132,543)(133,538)(134,537)(135,539)(136,540)
(137,549)(138,550)(139,552)(140,551)(141,546)(142,545)(143,547)(144,548)
(145,581)(146,582)(147,584)(148,583)(149,578)(150,577)(151,579)(152,580)
(153,589)(154,590)(155,592)(156,591)(157,586)(158,585)(159,587)(160,588)
(161,597)(162,598)(163,600)(164,599)(165,594)(166,593)(167,595)(168,596)
(169,629)(170,630)(171,632)(172,631)(173,626)(174,625)(175,627)(176,628)
(177,637)(178,638)(179,640)(180,639)(181,634)(182,633)(183,635)(184,636)
(185,645)(186,646)(187,648)(188,647)(189,642)(190,641)(191,643)(192,644)
(193,605)(194,606)(195,608)(196,607)(197,602)(198,601)(199,603)(200,604)
(201,613)(202,614)(203,616)(204,615)(205,610)(206,609)(207,611)(208,612)
(209,621)(210,622)(211,624)(212,623)(213,618)(214,617)(215,619)(216,620)
(217,654)(218,653)(219,655)(220,656)(221,649)(222,650)(223,652)(224,651)
(225,662)(226,661)(227,663)(228,664)(229,657)(230,658)(231,660)(232,659)
(233,670)(234,669)(235,671)(236,672)(237,665)(238,666)(239,668)(240,667)
(241,702)(242,701)(243,703)(244,704)(245,697)(246,698)(247,700)(248,699)
(249,710)(250,709)(251,711)(252,712)(253,705)(254,706)(255,708)(256,707)
(257,718)(258,717)(259,719)(260,720)(261,713)(262,714)(263,716)(264,715)
(265,678)(266,677)(267,679)(268,680)(269,673)(270,674)(271,676)(272,675)
(273,686)(274,685)(275,687)(276,688)(277,681)(278,682)(279,684)(280,683)
(281,694)(282,693)(283,695)(284,696)(285,689)(286,690)(287,692)(288,691)
(289,726)(290,725)(291,727)(292,728)(293,721)(294,722)(295,724)(296,723)
(297,734)(298,733)(299,735)(300,736)(301,729)(302,730)(303,732)(304,731)
(305,742)(306,741)(307,743)(308,744)(309,737)(310,738)(311,740)(312,739)
(313,774)(314,773)(315,775)(316,776)(317,769)(318,770)(319,772)(320,771)
(321,782)(322,781)(323,783)(324,784)(325,777)(326,778)(327,780)(328,779)
(329,790)(330,789)(331,791)(332,792)(333,785)(334,786)(335,788)(336,787)
(337,750)(338,749)(339,751)(340,752)(341,745)(342,746)(343,748)(344,747)
(345,758)(346,757)(347,759)(348,760)(349,753)(350,754)(351,756)(352,755)
(353,766)(354,765)(355,767)(356,768)(357,761)(358,762)(359,764)(360,763)
(361,798)(362,797)(363,799)(364,800)(365,793)(366,794)(367,796)(368,795)
(369,806)(370,805)(371,807)(372,808)(373,801)(374,802)(375,804)(376,803)
(377,814)(378,813)(379,815)(380,816)(381,809)(382,810)(383,812)(384,811)
(385,846)(386,845)(387,847)(388,848)(389,841)(390,842)(391,844)(392,843)
(393,854)(394,853)(395,855)(396,856)(397,849)(398,850)(399,852)(400,851)
(401,862)(402,861)(403,863)(404,864)(405,857)(406,858)(407,860)(408,859)
(409,822)(410,821)(411,823)(412,824)(413,817)(414,818)(415,820)(416,819)
(417,830)(418,829)(419,831)(420,832)(421,825)(422,826)(423,828)(424,827)
(425,838)(426,837)(427,839)(428,840)(429,833)(430,834)(431,836)(432,835);;
s1 := ( 1,673)( 2,674)( 3,678)( 4,677)( 5,676)( 6,675)( 7,680)( 8,679)
( 9,689)( 10,690)( 11,694)( 12,693)( 13,692)( 14,691)( 15,696)( 16,695)
( 17,681)( 18,682)( 19,686)( 20,685)( 21,684)( 22,683)( 23,688)( 24,687)
( 25,649)( 26,650)( 27,654)( 28,653)( 29,652)( 30,651)( 31,656)( 32,655)
( 33,665)( 34,666)( 35,670)( 36,669)( 37,668)( 38,667)( 39,672)( 40,671)
( 41,657)( 42,658)( 43,662)( 44,661)( 45,660)( 46,659)( 47,664)( 48,663)
( 49,697)( 50,698)( 51,702)( 52,701)( 53,700)( 54,699)( 55,704)( 56,703)
( 57,713)( 58,714)( 59,718)( 60,717)( 61,716)( 62,715)( 63,720)( 64,719)
( 65,705)( 66,706)( 67,710)( 68,709)( 69,708)( 70,707)( 71,712)( 72,711)
( 73,833)( 74,834)( 75,838)( 76,837)( 77,836)( 78,835)( 79,840)( 80,839)
( 81,825)( 82,826)( 83,830)( 84,829)( 85,828)( 86,827)( 87,832)( 88,831)
( 89,817)( 90,818)( 91,822)( 92,821)( 93,820)( 94,819)( 95,824)( 96,823)
( 97,809)( 98,810)( 99,814)(100,813)(101,812)(102,811)(103,816)(104,815)
(105,801)(106,802)(107,806)(108,805)(109,804)(110,803)(111,808)(112,807)
(113,793)(114,794)(115,798)(116,797)(117,796)(118,795)(119,800)(120,799)
(121,857)(122,858)(123,862)(124,861)(125,860)(126,859)(127,864)(128,863)
(129,849)(130,850)(131,854)(132,853)(133,852)(134,851)(135,856)(136,855)
(137,841)(138,842)(139,846)(140,845)(141,844)(142,843)(143,848)(144,847)
(145,761)(146,762)(147,766)(148,765)(149,764)(150,763)(151,768)(152,767)
(153,753)(154,754)(155,758)(156,757)(157,756)(158,755)(159,760)(160,759)
(161,745)(162,746)(163,750)(164,749)(165,748)(166,747)(167,752)(168,751)
(169,737)(170,738)(171,742)(172,741)(173,740)(174,739)(175,744)(176,743)
(177,729)(178,730)(179,734)(180,733)(181,732)(182,731)(183,736)(184,735)
(185,721)(186,722)(187,726)(188,725)(189,724)(190,723)(191,728)(192,727)
(193,785)(194,786)(195,790)(196,789)(197,788)(198,787)(199,792)(200,791)
(201,777)(202,778)(203,782)(204,781)(205,780)(206,779)(207,784)(208,783)
(209,769)(210,770)(211,774)(212,773)(213,772)(214,771)(215,776)(216,775)
(217,458)(218,457)(219,461)(220,462)(221,459)(222,460)(223,463)(224,464)
(225,474)(226,473)(227,477)(228,478)(229,475)(230,476)(231,479)(232,480)
(233,466)(234,465)(235,469)(236,470)(237,467)(238,468)(239,471)(240,472)
(241,434)(242,433)(243,437)(244,438)(245,435)(246,436)(247,439)(248,440)
(249,450)(250,449)(251,453)(252,454)(253,451)(254,452)(255,455)(256,456)
(257,442)(258,441)(259,445)(260,446)(261,443)(262,444)(263,447)(264,448)
(265,482)(266,481)(267,485)(268,486)(269,483)(270,484)(271,487)(272,488)
(273,498)(274,497)(275,501)(276,502)(277,499)(278,500)(279,503)(280,504)
(281,490)(282,489)(283,493)(284,494)(285,491)(286,492)(287,495)(288,496)
(289,618)(290,617)(291,621)(292,622)(293,619)(294,620)(295,623)(296,624)
(297,610)(298,609)(299,613)(300,614)(301,611)(302,612)(303,615)(304,616)
(305,602)(306,601)(307,605)(308,606)(309,603)(310,604)(311,607)(312,608)
(313,594)(314,593)(315,597)(316,598)(317,595)(318,596)(319,599)(320,600)
(321,586)(322,585)(323,589)(324,590)(325,587)(326,588)(327,591)(328,592)
(329,578)(330,577)(331,581)(332,582)(333,579)(334,580)(335,583)(336,584)
(337,642)(338,641)(339,645)(340,646)(341,643)(342,644)(343,647)(344,648)
(345,634)(346,633)(347,637)(348,638)(349,635)(350,636)(351,639)(352,640)
(353,626)(354,625)(355,629)(356,630)(357,627)(358,628)(359,631)(360,632)
(361,546)(362,545)(363,549)(364,550)(365,547)(366,548)(367,551)(368,552)
(369,538)(370,537)(371,541)(372,542)(373,539)(374,540)(375,543)(376,544)
(377,530)(378,529)(379,533)(380,534)(381,531)(382,532)(383,535)(384,536)
(385,522)(386,521)(387,525)(388,526)(389,523)(390,524)(391,527)(392,528)
(393,514)(394,513)(395,517)(396,518)(397,515)(398,516)(399,519)(400,520)
(401,506)(402,505)(403,509)(404,510)(405,507)(406,508)(407,511)(408,512)
(409,570)(410,569)(411,573)(412,574)(413,571)(414,572)(415,575)(416,576)
(417,562)(418,561)(419,565)(420,566)(421,563)(422,564)(423,567)(424,568)
(425,554)(426,553)(427,557)(428,558)(429,555)(430,556)(431,559)(432,560);;
s2 := ( 1,793)( 2,794)( 3,799)( 4,800)( 5,798)( 6,797)( 7,795)( 8,796)
( 9,809)( 10,810)( 11,815)( 12,816)( 13,814)( 14,813)( 15,811)( 16,812)
( 17,801)( 18,802)( 19,807)( 20,808)( 21,806)( 22,805)( 23,803)( 24,804)
( 25,841)( 26,842)( 27,847)( 28,848)( 29,846)( 30,845)( 31,843)( 32,844)
( 33,857)( 34,858)( 35,863)( 36,864)( 37,862)( 38,861)( 39,859)( 40,860)
( 41,849)( 42,850)( 43,855)( 44,856)( 45,854)( 46,853)( 47,851)( 48,852)
( 49,817)( 50,818)( 51,823)( 52,824)( 53,822)( 54,821)( 55,819)( 56,820)
( 57,833)( 58,834)( 59,839)( 60,840)( 61,838)( 62,837)( 63,835)( 64,836)
( 65,825)( 66,826)( 67,831)( 68,832)( 69,830)( 70,829)( 71,827)( 72,828)
( 73,721)( 74,722)( 75,727)( 76,728)( 77,726)( 78,725)( 79,723)( 80,724)
( 81,737)( 82,738)( 83,743)( 84,744)( 85,742)( 86,741)( 87,739)( 88,740)
( 89,729)( 90,730)( 91,735)( 92,736)( 93,734)( 94,733)( 95,731)( 96,732)
( 97,769)( 98,770)( 99,775)(100,776)(101,774)(102,773)(103,771)(104,772)
(105,785)(106,786)(107,791)(108,792)(109,790)(110,789)(111,787)(112,788)
(113,777)(114,778)(115,783)(116,784)(117,782)(118,781)(119,779)(120,780)
(121,745)(122,746)(123,751)(124,752)(125,750)(126,749)(127,747)(128,748)
(129,761)(130,762)(131,767)(132,768)(133,766)(134,765)(135,763)(136,764)
(137,753)(138,754)(139,759)(140,760)(141,758)(142,757)(143,755)(144,756)
(145,649)(146,650)(147,655)(148,656)(149,654)(150,653)(151,651)(152,652)
(153,665)(154,666)(155,671)(156,672)(157,670)(158,669)(159,667)(160,668)
(161,657)(162,658)(163,663)(164,664)(165,662)(166,661)(167,659)(168,660)
(169,697)(170,698)(171,703)(172,704)(173,702)(174,701)(175,699)(176,700)
(177,713)(178,714)(179,719)(180,720)(181,718)(182,717)(183,715)(184,716)
(185,705)(186,706)(187,711)(188,712)(189,710)(190,709)(191,707)(192,708)
(193,673)(194,674)(195,679)(196,680)(197,678)(198,677)(199,675)(200,676)
(201,689)(202,690)(203,695)(204,696)(205,694)(206,693)(207,691)(208,692)
(209,681)(210,682)(211,687)(212,688)(213,686)(214,685)(215,683)(216,684)
(217,578)(218,577)(219,584)(220,583)(221,581)(222,582)(223,580)(224,579)
(225,594)(226,593)(227,600)(228,599)(229,597)(230,598)(231,596)(232,595)
(233,586)(234,585)(235,592)(236,591)(237,589)(238,590)(239,588)(240,587)
(241,626)(242,625)(243,632)(244,631)(245,629)(246,630)(247,628)(248,627)
(249,642)(250,641)(251,648)(252,647)(253,645)(254,646)(255,644)(256,643)
(257,634)(258,633)(259,640)(260,639)(261,637)(262,638)(263,636)(264,635)
(265,602)(266,601)(267,608)(268,607)(269,605)(270,606)(271,604)(272,603)
(273,618)(274,617)(275,624)(276,623)(277,621)(278,622)(279,620)(280,619)
(281,610)(282,609)(283,616)(284,615)(285,613)(286,614)(287,612)(288,611)
(289,506)(290,505)(291,512)(292,511)(293,509)(294,510)(295,508)(296,507)
(297,522)(298,521)(299,528)(300,527)(301,525)(302,526)(303,524)(304,523)
(305,514)(306,513)(307,520)(308,519)(309,517)(310,518)(311,516)(312,515)
(313,554)(314,553)(315,560)(316,559)(317,557)(318,558)(319,556)(320,555)
(321,570)(322,569)(323,576)(324,575)(325,573)(326,574)(327,572)(328,571)
(329,562)(330,561)(331,568)(332,567)(333,565)(334,566)(335,564)(336,563)
(337,530)(338,529)(339,536)(340,535)(341,533)(342,534)(343,532)(344,531)
(345,546)(346,545)(347,552)(348,551)(349,549)(350,550)(351,548)(352,547)
(353,538)(354,537)(355,544)(356,543)(357,541)(358,542)(359,540)(360,539)
(361,434)(362,433)(363,440)(364,439)(365,437)(366,438)(367,436)(368,435)
(369,450)(370,449)(371,456)(372,455)(373,453)(374,454)(375,452)(376,451)
(377,442)(378,441)(379,448)(380,447)(381,445)(382,446)(383,444)(384,443)
(385,482)(386,481)(387,488)(388,487)(389,485)(390,486)(391,484)(392,483)
(393,498)(394,497)(395,504)(396,503)(397,501)(398,502)(399,500)(400,499)
(401,490)(402,489)(403,496)(404,495)(405,493)(406,494)(407,492)(408,491)
(409,458)(410,457)(411,464)(412,463)(413,461)(414,462)(415,460)(416,459)
(417,474)(418,473)(419,480)(420,479)(421,477)(422,478)(423,476)(424,475)
(425,466)(426,465)(427,472)(428,471)(429,469)(430,470)(431,468)(432,467);;
s3 := (865,866);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(866)!( 1,437)( 2,438)( 3,440)( 4,439)( 5,434)( 6,433)( 7,435)
( 8,436)( 9,445)( 10,446)( 11,448)( 12,447)( 13,442)( 14,441)( 15,443)
( 16,444)( 17,453)( 18,454)( 19,456)( 20,455)( 21,450)( 22,449)( 23,451)
( 24,452)( 25,485)( 26,486)( 27,488)( 28,487)( 29,482)( 30,481)( 31,483)
( 32,484)( 33,493)( 34,494)( 35,496)( 36,495)( 37,490)( 38,489)( 39,491)
( 40,492)( 41,501)( 42,502)( 43,504)( 44,503)( 45,498)( 46,497)( 47,499)
( 48,500)( 49,461)( 50,462)( 51,464)( 52,463)( 53,458)( 54,457)( 55,459)
( 56,460)( 57,469)( 58,470)( 59,472)( 60,471)( 61,466)( 62,465)( 63,467)
( 64,468)( 65,477)( 66,478)( 67,480)( 68,479)( 69,474)( 70,473)( 71,475)
( 72,476)( 73,509)( 74,510)( 75,512)( 76,511)( 77,506)( 78,505)( 79,507)
( 80,508)( 81,517)( 82,518)( 83,520)( 84,519)( 85,514)( 86,513)( 87,515)
( 88,516)( 89,525)( 90,526)( 91,528)( 92,527)( 93,522)( 94,521)( 95,523)
( 96,524)( 97,557)( 98,558)( 99,560)(100,559)(101,554)(102,553)(103,555)
(104,556)(105,565)(106,566)(107,568)(108,567)(109,562)(110,561)(111,563)
(112,564)(113,573)(114,574)(115,576)(116,575)(117,570)(118,569)(119,571)
(120,572)(121,533)(122,534)(123,536)(124,535)(125,530)(126,529)(127,531)
(128,532)(129,541)(130,542)(131,544)(132,543)(133,538)(134,537)(135,539)
(136,540)(137,549)(138,550)(139,552)(140,551)(141,546)(142,545)(143,547)
(144,548)(145,581)(146,582)(147,584)(148,583)(149,578)(150,577)(151,579)
(152,580)(153,589)(154,590)(155,592)(156,591)(157,586)(158,585)(159,587)
(160,588)(161,597)(162,598)(163,600)(164,599)(165,594)(166,593)(167,595)
(168,596)(169,629)(170,630)(171,632)(172,631)(173,626)(174,625)(175,627)
(176,628)(177,637)(178,638)(179,640)(180,639)(181,634)(182,633)(183,635)
(184,636)(185,645)(186,646)(187,648)(188,647)(189,642)(190,641)(191,643)
(192,644)(193,605)(194,606)(195,608)(196,607)(197,602)(198,601)(199,603)
(200,604)(201,613)(202,614)(203,616)(204,615)(205,610)(206,609)(207,611)
(208,612)(209,621)(210,622)(211,624)(212,623)(213,618)(214,617)(215,619)
(216,620)(217,654)(218,653)(219,655)(220,656)(221,649)(222,650)(223,652)
(224,651)(225,662)(226,661)(227,663)(228,664)(229,657)(230,658)(231,660)
(232,659)(233,670)(234,669)(235,671)(236,672)(237,665)(238,666)(239,668)
(240,667)(241,702)(242,701)(243,703)(244,704)(245,697)(246,698)(247,700)
(248,699)(249,710)(250,709)(251,711)(252,712)(253,705)(254,706)(255,708)
(256,707)(257,718)(258,717)(259,719)(260,720)(261,713)(262,714)(263,716)
(264,715)(265,678)(266,677)(267,679)(268,680)(269,673)(270,674)(271,676)
(272,675)(273,686)(274,685)(275,687)(276,688)(277,681)(278,682)(279,684)
(280,683)(281,694)(282,693)(283,695)(284,696)(285,689)(286,690)(287,692)
(288,691)(289,726)(290,725)(291,727)(292,728)(293,721)(294,722)(295,724)
(296,723)(297,734)(298,733)(299,735)(300,736)(301,729)(302,730)(303,732)
(304,731)(305,742)(306,741)(307,743)(308,744)(309,737)(310,738)(311,740)
(312,739)(313,774)(314,773)(315,775)(316,776)(317,769)(318,770)(319,772)
(320,771)(321,782)(322,781)(323,783)(324,784)(325,777)(326,778)(327,780)
(328,779)(329,790)(330,789)(331,791)(332,792)(333,785)(334,786)(335,788)
(336,787)(337,750)(338,749)(339,751)(340,752)(341,745)(342,746)(343,748)
(344,747)(345,758)(346,757)(347,759)(348,760)(349,753)(350,754)(351,756)
(352,755)(353,766)(354,765)(355,767)(356,768)(357,761)(358,762)(359,764)
(360,763)(361,798)(362,797)(363,799)(364,800)(365,793)(366,794)(367,796)
(368,795)(369,806)(370,805)(371,807)(372,808)(373,801)(374,802)(375,804)
(376,803)(377,814)(378,813)(379,815)(380,816)(381,809)(382,810)(383,812)
(384,811)(385,846)(386,845)(387,847)(388,848)(389,841)(390,842)(391,844)
(392,843)(393,854)(394,853)(395,855)(396,856)(397,849)(398,850)(399,852)
(400,851)(401,862)(402,861)(403,863)(404,864)(405,857)(406,858)(407,860)
(408,859)(409,822)(410,821)(411,823)(412,824)(413,817)(414,818)(415,820)
(416,819)(417,830)(418,829)(419,831)(420,832)(421,825)(422,826)(423,828)
(424,827)(425,838)(426,837)(427,839)(428,840)(429,833)(430,834)(431,836)
(432,835);
s1 := Sym(866)!( 1,673)( 2,674)( 3,678)( 4,677)( 5,676)( 6,675)( 7,680)
( 8,679)( 9,689)( 10,690)( 11,694)( 12,693)( 13,692)( 14,691)( 15,696)
( 16,695)( 17,681)( 18,682)( 19,686)( 20,685)( 21,684)( 22,683)( 23,688)
( 24,687)( 25,649)( 26,650)( 27,654)( 28,653)( 29,652)( 30,651)( 31,656)
( 32,655)( 33,665)( 34,666)( 35,670)( 36,669)( 37,668)( 38,667)( 39,672)
( 40,671)( 41,657)( 42,658)( 43,662)( 44,661)( 45,660)( 46,659)( 47,664)
( 48,663)( 49,697)( 50,698)( 51,702)( 52,701)( 53,700)( 54,699)( 55,704)
( 56,703)( 57,713)( 58,714)( 59,718)( 60,717)( 61,716)( 62,715)( 63,720)
( 64,719)( 65,705)( 66,706)( 67,710)( 68,709)( 69,708)( 70,707)( 71,712)
( 72,711)( 73,833)( 74,834)( 75,838)( 76,837)( 77,836)( 78,835)( 79,840)
( 80,839)( 81,825)( 82,826)( 83,830)( 84,829)( 85,828)( 86,827)( 87,832)
( 88,831)( 89,817)( 90,818)( 91,822)( 92,821)( 93,820)( 94,819)( 95,824)
( 96,823)( 97,809)( 98,810)( 99,814)(100,813)(101,812)(102,811)(103,816)
(104,815)(105,801)(106,802)(107,806)(108,805)(109,804)(110,803)(111,808)
(112,807)(113,793)(114,794)(115,798)(116,797)(117,796)(118,795)(119,800)
(120,799)(121,857)(122,858)(123,862)(124,861)(125,860)(126,859)(127,864)
(128,863)(129,849)(130,850)(131,854)(132,853)(133,852)(134,851)(135,856)
(136,855)(137,841)(138,842)(139,846)(140,845)(141,844)(142,843)(143,848)
(144,847)(145,761)(146,762)(147,766)(148,765)(149,764)(150,763)(151,768)
(152,767)(153,753)(154,754)(155,758)(156,757)(157,756)(158,755)(159,760)
(160,759)(161,745)(162,746)(163,750)(164,749)(165,748)(166,747)(167,752)
(168,751)(169,737)(170,738)(171,742)(172,741)(173,740)(174,739)(175,744)
(176,743)(177,729)(178,730)(179,734)(180,733)(181,732)(182,731)(183,736)
(184,735)(185,721)(186,722)(187,726)(188,725)(189,724)(190,723)(191,728)
(192,727)(193,785)(194,786)(195,790)(196,789)(197,788)(198,787)(199,792)
(200,791)(201,777)(202,778)(203,782)(204,781)(205,780)(206,779)(207,784)
(208,783)(209,769)(210,770)(211,774)(212,773)(213,772)(214,771)(215,776)
(216,775)(217,458)(218,457)(219,461)(220,462)(221,459)(222,460)(223,463)
(224,464)(225,474)(226,473)(227,477)(228,478)(229,475)(230,476)(231,479)
(232,480)(233,466)(234,465)(235,469)(236,470)(237,467)(238,468)(239,471)
(240,472)(241,434)(242,433)(243,437)(244,438)(245,435)(246,436)(247,439)
(248,440)(249,450)(250,449)(251,453)(252,454)(253,451)(254,452)(255,455)
(256,456)(257,442)(258,441)(259,445)(260,446)(261,443)(262,444)(263,447)
(264,448)(265,482)(266,481)(267,485)(268,486)(269,483)(270,484)(271,487)
(272,488)(273,498)(274,497)(275,501)(276,502)(277,499)(278,500)(279,503)
(280,504)(281,490)(282,489)(283,493)(284,494)(285,491)(286,492)(287,495)
(288,496)(289,618)(290,617)(291,621)(292,622)(293,619)(294,620)(295,623)
(296,624)(297,610)(298,609)(299,613)(300,614)(301,611)(302,612)(303,615)
(304,616)(305,602)(306,601)(307,605)(308,606)(309,603)(310,604)(311,607)
(312,608)(313,594)(314,593)(315,597)(316,598)(317,595)(318,596)(319,599)
(320,600)(321,586)(322,585)(323,589)(324,590)(325,587)(326,588)(327,591)
(328,592)(329,578)(330,577)(331,581)(332,582)(333,579)(334,580)(335,583)
(336,584)(337,642)(338,641)(339,645)(340,646)(341,643)(342,644)(343,647)
(344,648)(345,634)(346,633)(347,637)(348,638)(349,635)(350,636)(351,639)
(352,640)(353,626)(354,625)(355,629)(356,630)(357,627)(358,628)(359,631)
(360,632)(361,546)(362,545)(363,549)(364,550)(365,547)(366,548)(367,551)
(368,552)(369,538)(370,537)(371,541)(372,542)(373,539)(374,540)(375,543)
(376,544)(377,530)(378,529)(379,533)(380,534)(381,531)(382,532)(383,535)
(384,536)(385,522)(386,521)(387,525)(388,526)(389,523)(390,524)(391,527)
(392,528)(393,514)(394,513)(395,517)(396,518)(397,515)(398,516)(399,519)
(400,520)(401,506)(402,505)(403,509)(404,510)(405,507)(406,508)(407,511)
(408,512)(409,570)(410,569)(411,573)(412,574)(413,571)(414,572)(415,575)
(416,576)(417,562)(418,561)(419,565)(420,566)(421,563)(422,564)(423,567)
(424,568)(425,554)(426,553)(427,557)(428,558)(429,555)(430,556)(431,559)
(432,560);
s2 := Sym(866)!( 1,793)( 2,794)( 3,799)( 4,800)( 5,798)( 6,797)( 7,795)
( 8,796)( 9,809)( 10,810)( 11,815)( 12,816)( 13,814)( 14,813)( 15,811)
( 16,812)( 17,801)( 18,802)( 19,807)( 20,808)( 21,806)( 22,805)( 23,803)
( 24,804)( 25,841)( 26,842)( 27,847)( 28,848)( 29,846)( 30,845)( 31,843)
( 32,844)( 33,857)( 34,858)( 35,863)( 36,864)( 37,862)( 38,861)( 39,859)
( 40,860)( 41,849)( 42,850)( 43,855)( 44,856)( 45,854)( 46,853)( 47,851)
( 48,852)( 49,817)( 50,818)( 51,823)( 52,824)( 53,822)( 54,821)( 55,819)
( 56,820)( 57,833)( 58,834)( 59,839)( 60,840)( 61,838)( 62,837)( 63,835)
( 64,836)( 65,825)( 66,826)( 67,831)( 68,832)( 69,830)( 70,829)( 71,827)
( 72,828)( 73,721)( 74,722)( 75,727)( 76,728)( 77,726)( 78,725)( 79,723)
( 80,724)( 81,737)( 82,738)( 83,743)( 84,744)( 85,742)( 86,741)( 87,739)
( 88,740)( 89,729)( 90,730)( 91,735)( 92,736)( 93,734)( 94,733)( 95,731)
( 96,732)( 97,769)( 98,770)( 99,775)(100,776)(101,774)(102,773)(103,771)
(104,772)(105,785)(106,786)(107,791)(108,792)(109,790)(110,789)(111,787)
(112,788)(113,777)(114,778)(115,783)(116,784)(117,782)(118,781)(119,779)
(120,780)(121,745)(122,746)(123,751)(124,752)(125,750)(126,749)(127,747)
(128,748)(129,761)(130,762)(131,767)(132,768)(133,766)(134,765)(135,763)
(136,764)(137,753)(138,754)(139,759)(140,760)(141,758)(142,757)(143,755)
(144,756)(145,649)(146,650)(147,655)(148,656)(149,654)(150,653)(151,651)
(152,652)(153,665)(154,666)(155,671)(156,672)(157,670)(158,669)(159,667)
(160,668)(161,657)(162,658)(163,663)(164,664)(165,662)(166,661)(167,659)
(168,660)(169,697)(170,698)(171,703)(172,704)(173,702)(174,701)(175,699)
(176,700)(177,713)(178,714)(179,719)(180,720)(181,718)(182,717)(183,715)
(184,716)(185,705)(186,706)(187,711)(188,712)(189,710)(190,709)(191,707)
(192,708)(193,673)(194,674)(195,679)(196,680)(197,678)(198,677)(199,675)
(200,676)(201,689)(202,690)(203,695)(204,696)(205,694)(206,693)(207,691)
(208,692)(209,681)(210,682)(211,687)(212,688)(213,686)(214,685)(215,683)
(216,684)(217,578)(218,577)(219,584)(220,583)(221,581)(222,582)(223,580)
(224,579)(225,594)(226,593)(227,600)(228,599)(229,597)(230,598)(231,596)
(232,595)(233,586)(234,585)(235,592)(236,591)(237,589)(238,590)(239,588)
(240,587)(241,626)(242,625)(243,632)(244,631)(245,629)(246,630)(247,628)
(248,627)(249,642)(250,641)(251,648)(252,647)(253,645)(254,646)(255,644)
(256,643)(257,634)(258,633)(259,640)(260,639)(261,637)(262,638)(263,636)
(264,635)(265,602)(266,601)(267,608)(268,607)(269,605)(270,606)(271,604)
(272,603)(273,618)(274,617)(275,624)(276,623)(277,621)(278,622)(279,620)
(280,619)(281,610)(282,609)(283,616)(284,615)(285,613)(286,614)(287,612)
(288,611)(289,506)(290,505)(291,512)(292,511)(293,509)(294,510)(295,508)
(296,507)(297,522)(298,521)(299,528)(300,527)(301,525)(302,526)(303,524)
(304,523)(305,514)(306,513)(307,520)(308,519)(309,517)(310,518)(311,516)
(312,515)(313,554)(314,553)(315,560)(316,559)(317,557)(318,558)(319,556)
(320,555)(321,570)(322,569)(323,576)(324,575)(325,573)(326,574)(327,572)
(328,571)(329,562)(330,561)(331,568)(332,567)(333,565)(334,566)(335,564)
(336,563)(337,530)(338,529)(339,536)(340,535)(341,533)(342,534)(343,532)
(344,531)(345,546)(346,545)(347,552)(348,551)(349,549)(350,550)(351,548)
(352,547)(353,538)(354,537)(355,544)(356,543)(357,541)(358,542)(359,540)
(360,539)(361,434)(362,433)(363,440)(364,439)(365,437)(366,438)(367,436)
(368,435)(369,450)(370,449)(371,456)(372,455)(373,453)(374,454)(375,452)
(376,451)(377,442)(378,441)(379,448)(380,447)(381,445)(382,446)(383,444)
(384,443)(385,482)(386,481)(387,488)(388,487)(389,485)(390,486)(391,484)
(392,483)(393,498)(394,497)(395,504)(396,503)(397,501)(398,502)(399,500)
(400,499)(401,490)(402,489)(403,496)(404,495)(405,493)(406,494)(407,492)
(408,491)(409,458)(410,457)(411,464)(412,463)(413,461)(414,462)(415,460)
(416,459)(417,474)(418,473)(419,480)(420,479)(421,477)(422,478)(423,476)
(424,475)(425,466)(426,465)(427,472)(428,471)(429,469)(430,470)(431,468)
(432,467);
s3 := Sym(866)!(865,866);
poly := sub<Sym(866)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope