Polytope of Type {3,24,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,24,2}*1728
if this polytope has a name.
Group : SmallGroup(1728,30267)
Rank : 4
Schlafli Type : {3,24,2}
Number of vertices, edges, etc : 18, 216, 144, 2
Order of s0s1s2s3 : 12
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 : {3,12,2}*864
3-fold quotients : {3,24,2}*576
6-fold quotients : {3,12,2}*288
8-fold quotients : {3,6,2}*216
9-fold quotients : {3,8,2}*192
18-fold quotients : {3,4,2}*96
24-fold quotients : {3,6,2}*72
36-fold quotients : {3,4,2}*48
72-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,649)( 2,650)( 3,654)( 4,653)( 5,652)( 6,651)( 7,656)( 8,655)
( 9,657)( 10,658)( 11,662)( 12,661)( 13,660)( 14,659)( 15,664)( 16,663)
( 17,665)( 18,666)( 19,670)( 20,669)( 21,668)( 22,667)( 23,672)( 24,671)
( 25,697)( 26,698)( 27,702)( 28,701)( 29,700)( 30,699)( 31,704)( 32,703)
( 33,705)( 34,706)( 35,710)( 36,709)( 37,708)( 38,707)( 39,712)( 40,711)
( 41,713)( 42,714)( 43,718)( 44,717)( 45,716)( 46,715)( 47,720)( 48,719)
( 49,673)( 50,674)( 51,678)( 52,677)( 53,676)( 54,675)( 55,680)( 56,679)
( 57,681)( 58,682)( 59,686)( 60,685)( 61,684)( 62,683)( 63,688)( 64,687)
( 65,689)( 66,690)( 67,694)( 68,693)( 69,692)( 70,691)( 71,696)( 72,695)
( 73,793)( 74,794)( 75,798)( 76,797)( 77,796)( 78,795)( 79,800)( 80,799)
( 81,801)( 82,802)( 83,806)( 84,805)( 85,804)( 86,803)( 87,808)( 88,807)
( 89,809)( 90,810)( 91,814)( 92,813)( 93,812)( 94,811)( 95,816)( 96,815)
( 97,841)( 98,842)( 99,846)(100,845)(101,844)(102,843)(103,848)(104,847)
(105,849)(106,850)(107,854)(108,853)(109,852)(110,851)(111,856)(112,855)
(113,857)(114,858)(115,862)(116,861)(117,860)(118,859)(119,864)(120,863)
(121,817)(122,818)(123,822)(124,821)(125,820)(126,819)(127,824)(128,823)
(129,825)(130,826)(131,830)(132,829)(133,828)(134,827)(135,832)(136,831)
(137,833)(138,834)(139,838)(140,837)(141,836)(142,835)(143,840)(144,839)
(145,721)(146,722)(147,726)(148,725)(149,724)(150,723)(151,728)(152,727)
(153,729)(154,730)(155,734)(156,733)(157,732)(158,731)(159,736)(160,735)
(161,737)(162,738)(163,742)(164,741)(165,740)(166,739)(167,744)(168,743)
(169,769)(170,770)(171,774)(172,773)(173,772)(174,771)(175,776)(176,775)
(177,777)(178,778)(179,782)(180,781)(181,780)(182,779)(183,784)(184,783)
(185,785)(186,786)(187,790)(188,789)(189,788)(190,787)(191,792)(192,791)
(193,745)(194,746)(195,750)(196,749)(197,748)(198,747)(199,752)(200,751)
(201,753)(202,754)(203,758)(204,757)(205,756)(206,755)(207,760)(208,759)
(209,761)(210,762)(211,766)(212,765)(213,764)(214,763)(215,768)(216,767)
(217,434)(218,433)(219,437)(220,438)(221,435)(222,436)(223,439)(224,440)
(225,442)(226,441)(227,445)(228,446)(229,443)(230,444)(231,447)(232,448)
(233,450)(234,449)(235,453)(236,454)(237,451)(238,452)(239,455)(240,456)
(241,482)(242,481)(243,485)(244,486)(245,483)(246,484)(247,487)(248,488)
(249,490)(250,489)(251,493)(252,494)(253,491)(254,492)(255,495)(256,496)
(257,498)(258,497)(259,501)(260,502)(261,499)(262,500)(263,503)(264,504)
(265,458)(266,457)(267,461)(268,462)(269,459)(270,460)(271,463)(272,464)
(273,466)(274,465)(275,469)(276,470)(277,467)(278,468)(279,471)(280,472)
(281,474)(282,473)(283,477)(284,478)(285,475)(286,476)(287,479)(288,480)
(289,578)(290,577)(291,581)(292,582)(293,579)(294,580)(295,583)(296,584)
(297,586)(298,585)(299,589)(300,590)(301,587)(302,588)(303,591)(304,592)
(305,594)(306,593)(307,597)(308,598)(309,595)(310,596)(311,599)(312,600)
(313,626)(314,625)(315,629)(316,630)(317,627)(318,628)(319,631)(320,632)
(321,634)(322,633)(323,637)(324,638)(325,635)(326,636)(327,639)(328,640)
(329,642)(330,641)(331,645)(332,646)(333,643)(334,644)(335,647)(336,648)
(337,602)(338,601)(339,605)(340,606)(341,603)(342,604)(343,607)(344,608)
(345,610)(346,609)(347,613)(348,614)(349,611)(350,612)(351,615)(352,616)
(353,618)(354,617)(355,621)(356,622)(357,619)(358,620)(359,623)(360,624)
(361,506)(362,505)(363,509)(364,510)(365,507)(366,508)(367,511)(368,512)
(369,514)(370,513)(371,517)(372,518)(373,515)(374,516)(375,519)(376,520)
(377,522)(378,521)(379,525)(380,526)(381,523)(382,524)(383,527)(384,528)
(385,554)(386,553)(387,557)(388,558)(389,555)(390,556)(391,559)(392,560)
(393,562)(394,561)(395,565)(396,566)(397,563)(398,564)(399,567)(400,568)
(401,570)(402,569)(403,573)(404,574)(405,571)(406,572)(407,575)(408,576)
(409,530)(410,529)(411,533)(412,534)(413,531)(414,532)(415,535)(416,536)
(417,538)(418,537)(419,541)(420,542)(421,539)(422,540)(423,543)(424,544)
(425,546)(426,545)(427,549)(428,550)(429,547)(430,548)(431,551)(432,552);;
s1 := ( 1,825)( 2,826)( 3,831)( 4,832)( 5,830)( 6,829)( 7,827)( 8,828)
( 9,833)( 10,834)( 11,839)( 12,840)( 13,838)( 14,837)( 15,835)( 16,836)
( 17,817)( 18,818)( 19,823)( 20,824)( 21,822)( 22,821)( 23,819)( 24,820)
( 25,809)( 26,810)( 27,815)( 28,816)( 29,814)( 30,813)( 31,811)( 32,812)
( 33,793)( 34,794)( 35,799)( 36,800)( 37,798)( 38,797)( 39,795)( 40,796)
( 41,801)( 42,802)( 43,807)( 44,808)( 45,806)( 46,805)( 47,803)( 48,804)
( 49,841)( 50,842)( 51,847)( 52,848)( 53,846)( 54,845)( 55,843)( 56,844)
( 57,849)( 58,850)( 59,855)( 60,856)( 61,854)( 62,853)( 63,851)( 64,852)
( 65,857)( 66,858)( 67,863)( 68,864)( 69,862)( 70,861)( 71,859)( 72,860)
( 73,753)( 74,754)( 75,759)( 76,760)( 77,758)( 78,757)( 79,755)( 80,756)
( 81,761)( 82,762)( 83,767)( 84,768)( 85,766)( 86,765)( 87,763)( 88,764)
( 89,745)( 90,746)( 91,751)( 92,752)( 93,750)( 94,749)( 95,747)( 96,748)
( 97,737)( 98,738)( 99,743)(100,744)(101,742)(102,741)(103,739)(104,740)
(105,721)(106,722)(107,727)(108,728)(109,726)(110,725)(111,723)(112,724)
(113,729)(114,730)(115,735)(116,736)(117,734)(118,733)(119,731)(120,732)
(121,769)(122,770)(123,775)(124,776)(125,774)(126,773)(127,771)(128,772)
(129,777)(130,778)(131,783)(132,784)(133,782)(134,781)(135,779)(136,780)
(137,785)(138,786)(139,791)(140,792)(141,790)(142,789)(143,787)(144,788)
(145,681)(146,682)(147,687)(148,688)(149,686)(150,685)(151,683)(152,684)
(153,689)(154,690)(155,695)(156,696)(157,694)(158,693)(159,691)(160,692)
(161,673)(162,674)(163,679)(164,680)(165,678)(166,677)(167,675)(168,676)
(169,665)(170,666)(171,671)(172,672)(173,670)(174,669)(175,667)(176,668)
(177,649)(178,650)(179,655)(180,656)(181,654)(182,653)(183,651)(184,652)
(185,657)(186,658)(187,663)(188,664)(189,662)(190,661)(191,659)(192,660)
(193,697)(194,698)(195,703)(196,704)(197,702)(198,701)(199,699)(200,700)
(201,705)(202,706)(203,711)(204,712)(205,710)(206,709)(207,707)(208,708)
(209,713)(210,714)(211,719)(212,720)(213,718)(214,717)(215,715)(216,716)
(217,610)(218,609)(219,616)(220,615)(221,613)(222,614)(223,612)(224,611)
(225,618)(226,617)(227,624)(228,623)(229,621)(230,622)(231,620)(232,619)
(233,602)(234,601)(235,608)(236,607)(237,605)(238,606)(239,604)(240,603)
(241,594)(242,593)(243,600)(244,599)(245,597)(246,598)(247,596)(248,595)
(249,578)(250,577)(251,584)(252,583)(253,581)(254,582)(255,580)(256,579)
(257,586)(258,585)(259,592)(260,591)(261,589)(262,590)(263,588)(264,587)
(265,626)(266,625)(267,632)(268,631)(269,629)(270,630)(271,628)(272,627)
(273,634)(274,633)(275,640)(276,639)(277,637)(278,638)(279,636)(280,635)
(281,642)(282,641)(283,648)(284,647)(285,645)(286,646)(287,644)(288,643)
(289,538)(290,537)(291,544)(292,543)(293,541)(294,542)(295,540)(296,539)
(297,546)(298,545)(299,552)(300,551)(301,549)(302,550)(303,548)(304,547)
(305,530)(306,529)(307,536)(308,535)(309,533)(310,534)(311,532)(312,531)
(313,522)(314,521)(315,528)(316,527)(317,525)(318,526)(319,524)(320,523)
(321,506)(322,505)(323,512)(324,511)(325,509)(326,510)(327,508)(328,507)
(329,514)(330,513)(331,520)(332,519)(333,517)(334,518)(335,516)(336,515)
(337,554)(338,553)(339,560)(340,559)(341,557)(342,558)(343,556)(344,555)
(345,562)(346,561)(347,568)(348,567)(349,565)(350,566)(351,564)(352,563)
(353,570)(354,569)(355,576)(356,575)(357,573)(358,574)(359,572)(360,571)
(361,466)(362,465)(363,472)(364,471)(365,469)(366,470)(367,468)(368,467)
(369,474)(370,473)(371,480)(372,479)(373,477)(374,478)(375,476)(376,475)
(377,458)(378,457)(379,464)(380,463)(381,461)(382,462)(383,460)(384,459)
(385,450)(386,449)(387,456)(388,455)(389,453)(390,454)(391,452)(392,451)
(393,434)(394,433)(395,440)(396,439)(397,437)(398,438)(399,436)(400,435)
(401,442)(402,441)(403,448)(404,447)(405,445)(406,446)(407,444)(408,443)
(409,482)(410,481)(411,488)(412,487)(413,485)(414,486)(415,484)(416,483)
(417,490)(418,489)(419,496)(420,495)(421,493)(422,494)(423,492)(424,491)
(425,498)(426,497)(427,504)(428,503)(429,501)(430,502)(431,500)(432,499);;
s2 := ( 1,439)( 2,440)( 3,437)( 4,438)( 5,436)( 6,435)( 7,434)( 8,433)
( 9,455)( 10,456)( 11,453)( 12,454)( 13,452)( 14,451)( 15,450)( 16,449)
( 17,447)( 18,448)( 19,445)( 20,446)( 21,444)( 22,443)( 23,442)( 24,441)
( 25,487)( 26,488)( 27,485)( 28,486)( 29,484)( 30,483)( 31,482)( 32,481)
( 33,503)( 34,504)( 35,501)( 36,502)( 37,500)( 38,499)( 39,498)( 40,497)
( 41,495)( 42,496)( 43,493)( 44,494)( 45,492)( 46,491)( 47,490)( 48,489)
( 49,463)( 50,464)( 51,461)( 52,462)( 53,460)( 54,459)( 55,458)( 56,457)
( 57,479)( 58,480)( 59,477)( 60,478)( 61,476)( 62,475)( 63,474)( 64,473)
( 65,471)( 66,472)( 67,469)( 68,470)( 69,468)( 70,467)( 71,466)( 72,465)
( 73,511)( 74,512)( 75,509)( 76,510)( 77,508)( 78,507)( 79,506)( 80,505)
( 81,527)( 82,528)( 83,525)( 84,526)( 85,524)( 86,523)( 87,522)( 88,521)
( 89,519)( 90,520)( 91,517)( 92,518)( 93,516)( 94,515)( 95,514)( 96,513)
( 97,559)( 98,560)( 99,557)(100,558)(101,556)(102,555)(103,554)(104,553)
(105,575)(106,576)(107,573)(108,574)(109,572)(110,571)(111,570)(112,569)
(113,567)(114,568)(115,565)(116,566)(117,564)(118,563)(119,562)(120,561)
(121,535)(122,536)(123,533)(124,534)(125,532)(126,531)(127,530)(128,529)
(129,551)(130,552)(131,549)(132,550)(133,548)(134,547)(135,546)(136,545)
(137,543)(138,544)(139,541)(140,542)(141,540)(142,539)(143,538)(144,537)
(145,583)(146,584)(147,581)(148,582)(149,580)(150,579)(151,578)(152,577)
(153,599)(154,600)(155,597)(156,598)(157,596)(158,595)(159,594)(160,593)
(161,591)(162,592)(163,589)(164,590)(165,588)(166,587)(167,586)(168,585)
(169,631)(170,632)(171,629)(172,630)(173,628)(174,627)(175,626)(176,625)
(177,647)(178,648)(179,645)(180,646)(181,644)(182,643)(183,642)(184,641)
(185,639)(186,640)(187,637)(188,638)(189,636)(190,635)(191,634)(192,633)
(193,607)(194,608)(195,605)(196,606)(197,604)(198,603)(199,602)(200,601)
(201,623)(202,624)(203,621)(204,622)(205,620)(206,619)(207,618)(208,617)
(209,615)(210,616)(211,613)(212,614)(213,612)(214,611)(215,610)(216,609)
(217,656)(218,655)(219,654)(220,653)(221,651)(222,652)(223,649)(224,650)
(225,672)(226,671)(227,670)(228,669)(229,667)(230,668)(231,665)(232,666)
(233,664)(234,663)(235,662)(236,661)(237,659)(238,660)(239,657)(240,658)
(241,704)(242,703)(243,702)(244,701)(245,699)(246,700)(247,697)(248,698)
(249,720)(250,719)(251,718)(252,717)(253,715)(254,716)(255,713)(256,714)
(257,712)(258,711)(259,710)(260,709)(261,707)(262,708)(263,705)(264,706)
(265,680)(266,679)(267,678)(268,677)(269,675)(270,676)(271,673)(272,674)
(273,696)(274,695)(275,694)(276,693)(277,691)(278,692)(279,689)(280,690)
(281,688)(282,687)(283,686)(284,685)(285,683)(286,684)(287,681)(288,682)
(289,728)(290,727)(291,726)(292,725)(293,723)(294,724)(295,721)(296,722)
(297,744)(298,743)(299,742)(300,741)(301,739)(302,740)(303,737)(304,738)
(305,736)(306,735)(307,734)(308,733)(309,731)(310,732)(311,729)(312,730)
(313,776)(314,775)(315,774)(316,773)(317,771)(318,772)(319,769)(320,770)
(321,792)(322,791)(323,790)(324,789)(325,787)(326,788)(327,785)(328,786)
(329,784)(330,783)(331,782)(332,781)(333,779)(334,780)(335,777)(336,778)
(337,752)(338,751)(339,750)(340,749)(341,747)(342,748)(343,745)(344,746)
(345,768)(346,767)(347,766)(348,765)(349,763)(350,764)(351,761)(352,762)
(353,760)(354,759)(355,758)(356,757)(357,755)(358,756)(359,753)(360,754)
(361,800)(362,799)(363,798)(364,797)(365,795)(366,796)(367,793)(368,794)
(369,816)(370,815)(371,814)(372,813)(373,811)(374,812)(375,809)(376,810)
(377,808)(378,807)(379,806)(380,805)(381,803)(382,804)(383,801)(384,802)
(385,848)(386,847)(387,846)(388,845)(389,843)(390,844)(391,841)(392,842)
(393,864)(394,863)(395,862)(396,861)(397,859)(398,860)(399,857)(400,858)
(401,856)(402,855)(403,854)(404,853)(405,851)(406,852)(407,849)(408,850)
(409,824)(410,823)(411,822)(412,821)(413,819)(414,820)(415,817)(416,818)
(417,840)(418,839)(419,838)(420,837)(421,835)(422,836)(423,833)(424,834)
(425,832)(426,831)(427,830)(428,829)(429,827)(430,828)(431,825)(432,826);;
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, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(866)!( 1,649)( 2,650)( 3,654)( 4,653)( 5,652)( 6,651)( 7,656)
( 8,655)( 9,657)( 10,658)( 11,662)( 12,661)( 13,660)( 14,659)( 15,664)
( 16,663)( 17,665)( 18,666)( 19,670)( 20,669)( 21,668)( 22,667)( 23,672)
( 24,671)( 25,697)( 26,698)( 27,702)( 28,701)( 29,700)( 30,699)( 31,704)
( 32,703)( 33,705)( 34,706)( 35,710)( 36,709)( 37,708)( 38,707)( 39,712)
( 40,711)( 41,713)( 42,714)( 43,718)( 44,717)( 45,716)( 46,715)( 47,720)
( 48,719)( 49,673)( 50,674)( 51,678)( 52,677)( 53,676)( 54,675)( 55,680)
( 56,679)( 57,681)( 58,682)( 59,686)( 60,685)( 61,684)( 62,683)( 63,688)
( 64,687)( 65,689)( 66,690)( 67,694)( 68,693)( 69,692)( 70,691)( 71,696)
( 72,695)( 73,793)( 74,794)( 75,798)( 76,797)( 77,796)( 78,795)( 79,800)
( 80,799)( 81,801)( 82,802)( 83,806)( 84,805)( 85,804)( 86,803)( 87,808)
( 88,807)( 89,809)( 90,810)( 91,814)( 92,813)( 93,812)( 94,811)( 95,816)
( 96,815)( 97,841)( 98,842)( 99,846)(100,845)(101,844)(102,843)(103,848)
(104,847)(105,849)(106,850)(107,854)(108,853)(109,852)(110,851)(111,856)
(112,855)(113,857)(114,858)(115,862)(116,861)(117,860)(118,859)(119,864)
(120,863)(121,817)(122,818)(123,822)(124,821)(125,820)(126,819)(127,824)
(128,823)(129,825)(130,826)(131,830)(132,829)(133,828)(134,827)(135,832)
(136,831)(137,833)(138,834)(139,838)(140,837)(141,836)(142,835)(143,840)
(144,839)(145,721)(146,722)(147,726)(148,725)(149,724)(150,723)(151,728)
(152,727)(153,729)(154,730)(155,734)(156,733)(157,732)(158,731)(159,736)
(160,735)(161,737)(162,738)(163,742)(164,741)(165,740)(166,739)(167,744)
(168,743)(169,769)(170,770)(171,774)(172,773)(173,772)(174,771)(175,776)
(176,775)(177,777)(178,778)(179,782)(180,781)(181,780)(182,779)(183,784)
(184,783)(185,785)(186,786)(187,790)(188,789)(189,788)(190,787)(191,792)
(192,791)(193,745)(194,746)(195,750)(196,749)(197,748)(198,747)(199,752)
(200,751)(201,753)(202,754)(203,758)(204,757)(205,756)(206,755)(207,760)
(208,759)(209,761)(210,762)(211,766)(212,765)(213,764)(214,763)(215,768)
(216,767)(217,434)(218,433)(219,437)(220,438)(221,435)(222,436)(223,439)
(224,440)(225,442)(226,441)(227,445)(228,446)(229,443)(230,444)(231,447)
(232,448)(233,450)(234,449)(235,453)(236,454)(237,451)(238,452)(239,455)
(240,456)(241,482)(242,481)(243,485)(244,486)(245,483)(246,484)(247,487)
(248,488)(249,490)(250,489)(251,493)(252,494)(253,491)(254,492)(255,495)
(256,496)(257,498)(258,497)(259,501)(260,502)(261,499)(262,500)(263,503)
(264,504)(265,458)(266,457)(267,461)(268,462)(269,459)(270,460)(271,463)
(272,464)(273,466)(274,465)(275,469)(276,470)(277,467)(278,468)(279,471)
(280,472)(281,474)(282,473)(283,477)(284,478)(285,475)(286,476)(287,479)
(288,480)(289,578)(290,577)(291,581)(292,582)(293,579)(294,580)(295,583)
(296,584)(297,586)(298,585)(299,589)(300,590)(301,587)(302,588)(303,591)
(304,592)(305,594)(306,593)(307,597)(308,598)(309,595)(310,596)(311,599)
(312,600)(313,626)(314,625)(315,629)(316,630)(317,627)(318,628)(319,631)
(320,632)(321,634)(322,633)(323,637)(324,638)(325,635)(326,636)(327,639)
(328,640)(329,642)(330,641)(331,645)(332,646)(333,643)(334,644)(335,647)
(336,648)(337,602)(338,601)(339,605)(340,606)(341,603)(342,604)(343,607)
(344,608)(345,610)(346,609)(347,613)(348,614)(349,611)(350,612)(351,615)
(352,616)(353,618)(354,617)(355,621)(356,622)(357,619)(358,620)(359,623)
(360,624)(361,506)(362,505)(363,509)(364,510)(365,507)(366,508)(367,511)
(368,512)(369,514)(370,513)(371,517)(372,518)(373,515)(374,516)(375,519)
(376,520)(377,522)(378,521)(379,525)(380,526)(381,523)(382,524)(383,527)
(384,528)(385,554)(386,553)(387,557)(388,558)(389,555)(390,556)(391,559)
(392,560)(393,562)(394,561)(395,565)(396,566)(397,563)(398,564)(399,567)
(400,568)(401,570)(402,569)(403,573)(404,574)(405,571)(406,572)(407,575)
(408,576)(409,530)(410,529)(411,533)(412,534)(413,531)(414,532)(415,535)
(416,536)(417,538)(418,537)(419,541)(420,542)(421,539)(422,540)(423,543)
(424,544)(425,546)(426,545)(427,549)(428,550)(429,547)(430,548)(431,551)
(432,552);
s1 := Sym(866)!( 1,825)( 2,826)( 3,831)( 4,832)( 5,830)( 6,829)( 7,827)
( 8,828)( 9,833)( 10,834)( 11,839)( 12,840)( 13,838)( 14,837)( 15,835)
( 16,836)( 17,817)( 18,818)( 19,823)( 20,824)( 21,822)( 22,821)( 23,819)
( 24,820)( 25,809)( 26,810)( 27,815)( 28,816)( 29,814)( 30,813)( 31,811)
( 32,812)( 33,793)( 34,794)( 35,799)( 36,800)( 37,798)( 38,797)( 39,795)
( 40,796)( 41,801)( 42,802)( 43,807)( 44,808)( 45,806)( 46,805)( 47,803)
( 48,804)( 49,841)( 50,842)( 51,847)( 52,848)( 53,846)( 54,845)( 55,843)
( 56,844)( 57,849)( 58,850)( 59,855)( 60,856)( 61,854)( 62,853)( 63,851)
( 64,852)( 65,857)( 66,858)( 67,863)( 68,864)( 69,862)( 70,861)( 71,859)
( 72,860)( 73,753)( 74,754)( 75,759)( 76,760)( 77,758)( 78,757)( 79,755)
( 80,756)( 81,761)( 82,762)( 83,767)( 84,768)( 85,766)( 86,765)( 87,763)
( 88,764)( 89,745)( 90,746)( 91,751)( 92,752)( 93,750)( 94,749)( 95,747)
( 96,748)( 97,737)( 98,738)( 99,743)(100,744)(101,742)(102,741)(103,739)
(104,740)(105,721)(106,722)(107,727)(108,728)(109,726)(110,725)(111,723)
(112,724)(113,729)(114,730)(115,735)(116,736)(117,734)(118,733)(119,731)
(120,732)(121,769)(122,770)(123,775)(124,776)(125,774)(126,773)(127,771)
(128,772)(129,777)(130,778)(131,783)(132,784)(133,782)(134,781)(135,779)
(136,780)(137,785)(138,786)(139,791)(140,792)(141,790)(142,789)(143,787)
(144,788)(145,681)(146,682)(147,687)(148,688)(149,686)(150,685)(151,683)
(152,684)(153,689)(154,690)(155,695)(156,696)(157,694)(158,693)(159,691)
(160,692)(161,673)(162,674)(163,679)(164,680)(165,678)(166,677)(167,675)
(168,676)(169,665)(170,666)(171,671)(172,672)(173,670)(174,669)(175,667)
(176,668)(177,649)(178,650)(179,655)(180,656)(181,654)(182,653)(183,651)
(184,652)(185,657)(186,658)(187,663)(188,664)(189,662)(190,661)(191,659)
(192,660)(193,697)(194,698)(195,703)(196,704)(197,702)(198,701)(199,699)
(200,700)(201,705)(202,706)(203,711)(204,712)(205,710)(206,709)(207,707)
(208,708)(209,713)(210,714)(211,719)(212,720)(213,718)(214,717)(215,715)
(216,716)(217,610)(218,609)(219,616)(220,615)(221,613)(222,614)(223,612)
(224,611)(225,618)(226,617)(227,624)(228,623)(229,621)(230,622)(231,620)
(232,619)(233,602)(234,601)(235,608)(236,607)(237,605)(238,606)(239,604)
(240,603)(241,594)(242,593)(243,600)(244,599)(245,597)(246,598)(247,596)
(248,595)(249,578)(250,577)(251,584)(252,583)(253,581)(254,582)(255,580)
(256,579)(257,586)(258,585)(259,592)(260,591)(261,589)(262,590)(263,588)
(264,587)(265,626)(266,625)(267,632)(268,631)(269,629)(270,630)(271,628)
(272,627)(273,634)(274,633)(275,640)(276,639)(277,637)(278,638)(279,636)
(280,635)(281,642)(282,641)(283,648)(284,647)(285,645)(286,646)(287,644)
(288,643)(289,538)(290,537)(291,544)(292,543)(293,541)(294,542)(295,540)
(296,539)(297,546)(298,545)(299,552)(300,551)(301,549)(302,550)(303,548)
(304,547)(305,530)(306,529)(307,536)(308,535)(309,533)(310,534)(311,532)
(312,531)(313,522)(314,521)(315,528)(316,527)(317,525)(318,526)(319,524)
(320,523)(321,506)(322,505)(323,512)(324,511)(325,509)(326,510)(327,508)
(328,507)(329,514)(330,513)(331,520)(332,519)(333,517)(334,518)(335,516)
(336,515)(337,554)(338,553)(339,560)(340,559)(341,557)(342,558)(343,556)
(344,555)(345,562)(346,561)(347,568)(348,567)(349,565)(350,566)(351,564)
(352,563)(353,570)(354,569)(355,576)(356,575)(357,573)(358,574)(359,572)
(360,571)(361,466)(362,465)(363,472)(364,471)(365,469)(366,470)(367,468)
(368,467)(369,474)(370,473)(371,480)(372,479)(373,477)(374,478)(375,476)
(376,475)(377,458)(378,457)(379,464)(380,463)(381,461)(382,462)(383,460)
(384,459)(385,450)(386,449)(387,456)(388,455)(389,453)(390,454)(391,452)
(392,451)(393,434)(394,433)(395,440)(396,439)(397,437)(398,438)(399,436)
(400,435)(401,442)(402,441)(403,448)(404,447)(405,445)(406,446)(407,444)
(408,443)(409,482)(410,481)(411,488)(412,487)(413,485)(414,486)(415,484)
(416,483)(417,490)(418,489)(419,496)(420,495)(421,493)(422,494)(423,492)
(424,491)(425,498)(426,497)(427,504)(428,503)(429,501)(430,502)(431,500)
(432,499);
s2 := Sym(866)!( 1,439)( 2,440)( 3,437)( 4,438)( 5,436)( 6,435)( 7,434)
( 8,433)( 9,455)( 10,456)( 11,453)( 12,454)( 13,452)( 14,451)( 15,450)
( 16,449)( 17,447)( 18,448)( 19,445)( 20,446)( 21,444)( 22,443)( 23,442)
( 24,441)( 25,487)( 26,488)( 27,485)( 28,486)( 29,484)( 30,483)( 31,482)
( 32,481)( 33,503)( 34,504)( 35,501)( 36,502)( 37,500)( 38,499)( 39,498)
( 40,497)( 41,495)( 42,496)( 43,493)( 44,494)( 45,492)( 46,491)( 47,490)
( 48,489)( 49,463)( 50,464)( 51,461)( 52,462)( 53,460)( 54,459)( 55,458)
( 56,457)( 57,479)( 58,480)( 59,477)( 60,478)( 61,476)( 62,475)( 63,474)
( 64,473)( 65,471)( 66,472)( 67,469)( 68,470)( 69,468)( 70,467)( 71,466)
( 72,465)( 73,511)( 74,512)( 75,509)( 76,510)( 77,508)( 78,507)( 79,506)
( 80,505)( 81,527)( 82,528)( 83,525)( 84,526)( 85,524)( 86,523)( 87,522)
( 88,521)( 89,519)( 90,520)( 91,517)( 92,518)( 93,516)( 94,515)( 95,514)
( 96,513)( 97,559)( 98,560)( 99,557)(100,558)(101,556)(102,555)(103,554)
(104,553)(105,575)(106,576)(107,573)(108,574)(109,572)(110,571)(111,570)
(112,569)(113,567)(114,568)(115,565)(116,566)(117,564)(118,563)(119,562)
(120,561)(121,535)(122,536)(123,533)(124,534)(125,532)(126,531)(127,530)
(128,529)(129,551)(130,552)(131,549)(132,550)(133,548)(134,547)(135,546)
(136,545)(137,543)(138,544)(139,541)(140,542)(141,540)(142,539)(143,538)
(144,537)(145,583)(146,584)(147,581)(148,582)(149,580)(150,579)(151,578)
(152,577)(153,599)(154,600)(155,597)(156,598)(157,596)(158,595)(159,594)
(160,593)(161,591)(162,592)(163,589)(164,590)(165,588)(166,587)(167,586)
(168,585)(169,631)(170,632)(171,629)(172,630)(173,628)(174,627)(175,626)
(176,625)(177,647)(178,648)(179,645)(180,646)(181,644)(182,643)(183,642)
(184,641)(185,639)(186,640)(187,637)(188,638)(189,636)(190,635)(191,634)
(192,633)(193,607)(194,608)(195,605)(196,606)(197,604)(198,603)(199,602)
(200,601)(201,623)(202,624)(203,621)(204,622)(205,620)(206,619)(207,618)
(208,617)(209,615)(210,616)(211,613)(212,614)(213,612)(214,611)(215,610)
(216,609)(217,656)(218,655)(219,654)(220,653)(221,651)(222,652)(223,649)
(224,650)(225,672)(226,671)(227,670)(228,669)(229,667)(230,668)(231,665)
(232,666)(233,664)(234,663)(235,662)(236,661)(237,659)(238,660)(239,657)
(240,658)(241,704)(242,703)(243,702)(244,701)(245,699)(246,700)(247,697)
(248,698)(249,720)(250,719)(251,718)(252,717)(253,715)(254,716)(255,713)
(256,714)(257,712)(258,711)(259,710)(260,709)(261,707)(262,708)(263,705)
(264,706)(265,680)(266,679)(267,678)(268,677)(269,675)(270,676)(271,673)
(272,674)(273,696)(274,695)(275,694)(276,693)(277,691)(278,692)(279,689)
(280,690)(281,688)(282,687)(283,686)(284,685)(285,683)(286,684)(287,681)
(288,682)(289,728)(290,727)(291,726)(292,725)(293,723)(294,724)(295,721)
(296,722)(297,744)(298,743)(299,742)(300,741)(301,739)(302,740)(303,737)
(304,738)(305,736)(306,735)(307,734)(308,733)(309,731)(310,732)(311,729)
(312,730)(313,776)(314,775)(315,774)(316,773)(317,771)(318,772)(319,769)
(320,770)(321,792)(322,791)(323,790)(324,789)(325,787)(326,788)(327,785)
(328,786)(329,784)(330,783)(331,782)(332,781)(333,779)(334,780)(335,777)
(336,778)(337,752)(338,751)(339,750)(340,749)(341,747)(342,748)(343,745)
(344,746)(345,768)(346,767)(347,766)(348,765)(349,763)(350,764)(351,761)
(352,762)(353,760)(354,759)(355,758)(356,757)(357,755)(358,756)(359,753)
(360,754)(361,800)(362,799)(363,798)(364,797)(365,795)(366,796)(367,793)
(368,794)(369,816)(370,815)(371,814)(372,813)(373,811)(374,812)(375,809)
(376,810)(377,808)(378,807)(379,806)(380,805)(381,803)(382,804)(383,801)
(384,802)(385,848)(386,847)(387,846)(388,845)(389,843)(390,844)(391,841)
(392,842)(393,864)(394,863)(395,862)(396,861)(397,859)(398,860)(399,857)
(400,858)(401,856)(402,855)(403,854)(404,853)(405,851)(406,852)(407,849)
(408,850)(409,824)(410,823)(411,822)(412,821)(413,819)(414,820)(415,817)
(416,818)(417,840)(418,839)(419,838)(420,837)(421,835)(422,836)(423,833)
(424,834)(425,832)(426,831)(427,830)(428,829)(429,827)(430,828)(431,825)
(432,826);
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, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1 >;
to this polytope