Polytope of Type {12,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6}*1728i
if this polytope has a name.
Group : SmallGroup(1728,46356)
Rank : 3
Schlafli Type : {12,6}
Number of vertices, edges, etc : 144, 432, 72
Order of s0s1s2 : 12
Order of s0s1s2s1 : 12
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,6}*864c
3-fold quotients : {12,6}*576b, {12,6}*576f
4-fold quotients : {12,6}*432g
6-fold quotients : {12,6}*288a, {12,6}*288b
8-fold quotients : {6,6}*216d
9-fold quotients : {4,6}*192b
12-fold quotients : {12,6}*144a, {12,6}*144b, {12,6}*144c, {12,3}*144, {12,6}*144d
18-fold quotients : {4,6}*96
24-fold quotients : {6,6}*72a, {6,6}*72b, {6,6}*72c
36-fold quotients : {12,2}*48, {4,6}*48a, {4,3}*48, {4,6}*48b, {4,6}*48c
48-fold quotients : {3,6}*36, {6,3}*36
72-fold quotients : {4,3}*24, {2,6}*24, {6,2}*24
108-fold quotients : {4,2}*16
144-fold quotients : {2,3}*12, {3,2}*12
216-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,435)( 2,436)( 3,433)( 4,434)( 5,443)( 6,444)( 7,441)( 8,442)
( 9,439)( 10,440)( 11,437)( 12,438)( 13,459)( 14,460)( 15,457)( 16,458)
( 17,467)( 18,468)( 19,465)( 20,466)( 21,463)( 22,464)( 23,461)( 24,462)
( 25,447)( 26,448)( 27,445)( 28,446)( 29,455)( 30,456)( 31,453)( 32,454)
( 33,451)( 34,452)( 35,449)( 36,450)( 37,471)( 38,472)( 39,469)( 40,470)
( 41,479)( 42,480)( 43,477)( 44,478)( 45,475)( 46,476)( 47,473)( 48,474)
( 49,495)( 50,496)( 51,493)( 52,494)( 53,503)( 54,504)( 55,501)( 56,502)
( 57,499)( 58,500)( 59,497)( 60,498)( 61,483)( 62,484)( 63,481)( 64,482)
( 65,491)( 66,492)( 67,489)( 68,490)( 69,487)( 70,488)( 71,485)( 72,486)
( 73,507)( 74,508)( 75,505)( 76,506)( 77,515)( 78,516)( 79,513)( 80,514)
( 81,511)( 82,512)( 83,509)( 84,510)( 85,531)( 86,532)( 87,529)( 88,530)
( 89,539)( 90,540)( 91,537)( 92,538)( 93,535)( 94,536)( 95,533)( 96,534)
( 97,519)( 98,520)( 99,517)(100,518)(101,527)(102,528)(103,525)(104,526)
(105,523)(106,524)(107,521)(108,522)(109,543)(110,544)(111,541)(112,542)
(113,551)(114,552)(115,549)(116,550)(117,547)(118,548)(119,545)(120,546)
(121,567)(122,568)(123,565)(124,566)(125,575)(126,576)(127,573)(128,574)
(129,571)(130,572)(131,569)(132,570)(133,555)(134,556)(135,553)(136,554)
(137,563)(138,564)(139,561)(140,562)(141,559)(142,560)(143,557)(144,558)
(145,579)(146,580)(147,577)(148,578)(149,587)(150,588)(151,585)(152,586)
(153,583)(154,584)(155,581)(156,582)(157,603)(158,604)(159,601)(160,602)
(161,611)(162,612)(163,609)(164,610)(165,607)(166,608)(167,605)(168,606)
(169,591)(170,592)(171,589)(172,590)(173,599)(174,600)(175,597)(176,598)
(177,595)(178,596)(179,593)(180,594)(181,615)(182,616)(183,613)(184,614)
(185,623)(186,624)(187,621)(188,622)(189,619)(190,620)(191,617)(192,618)
(193,639)(194,640)(195,637)(196,638)(197,647)(198,648)(199,645)(200,646)
(201,643)(202,644)(203,641)(204,642)(205,627)(206,628)(207,625)(208,626)
(209,635)(210,636)(211,633)(212,634)(213,631)(214,632)(215,629)(216,630)
(217,759)(218,760)(219,757)(220,758)(221,767)(222,768)(223,765)(224,766)
(225,763)(226,764)(227,761)(228,762)(229,783)(230,784)(231,781)(232,782)
(233,791)(234,792)(235,789)(236,790)(237,787)(238,788)(239,785)(240,786)
(241,771)(242,772)(243,769)(244,770)(245,779)(246,780)(247,777)(248,778)
(249,775)(250,776)(251,773)(252,774)(253,795)(254,796)(255,793)(256,794)
(257,803)(258,804)(259,801)(260,802)(261,799)(262,800)(263,797)(264,798)
(265,819)(266,820)(267,817)(268,818)(269,827)(270,828)(271,825)(272,826)
(273,823)(274,824)(275,821)(276,822)(277,807)(278,808)(279,805)(280,806)
(281,815)(282,816)(283,813)(284,814)(285,811)(286,812)(287,809)(288,810)
(289,831)(290,832)(291,829)(292,830)(293,839)(294,840)(295,837)(296,838)
(297,835)(298,836)(299,833)(300,834)(301,855)(302,856)(303,853)(304,854)
(305,863)(306,864)(307,861)(308,862)(309,859)(310,860)(311,857)(312,858)
(313,843)(314,844)(315,841)(316,842)(317,851)(318,852)(319,849)(320,850)
(321,847)(322,848)(323,845)(324,846)(325,651)(326,652)(327,649)(328,650)
(329,659)(330,660)(331,657)(332,658)(333,655)(334,656)(335,653)(336,654)
(337,675)(338,676)(339,673)(340,674)(341,683)(342,684)(343,681)(344,682)
(345,679)(346,680)(347,677)(348,678)(349,663)(350,664)(351,661)(352,662)
(353,671)(354,672)(355,669)(356,670)(357,667)(358,668)(359,665)(360,666)
(361,687)(362,688)(363,685)(364,686)(365,695)(366,696)(367,693)(368,694)
(369,691)(370,692)(371,689)(372,690)(373,711)(374,712)(375,709)(376,710)
(377,719)(378,720)(379,717)(380,718)(381,715)(382,716)(383,713)(384,714)
(385,699)(386,700)(387,697)(388,698)(389,707)(390,708)(391,705)(392,706)
(393,703)(394,704)(395,701)(396,702)(397,723)(398,724)(399,721)(400,722)
(401,731)(402,732)(403,729)(404,730)(405,727)(406,728)(407,725)(408,726)
(409,747)(410,748)(411,745)(412,746)(413,755)(414,756)(415,753)(416,754)
(417,751)(418,752)(419,749)(420,750)(421,735)(422,736)(423,733)(424,734)
(425,743)(426,744)(427,741)(428,742)(429,739)(430,740)(431,737)(432,738);;
s1 := ( 1,665)( 2,666)( 3,668)( 4,667)( 5,661)( 6,662)( 7,664)( 8,663)
( 9,669)( 10,670)( 11,672)( 12,671)( 13,653)( 14,654)( 15,656)( 16,655)
( 17,649)( 18,650)( 19,652)( 20,651)( 21,657)( 22,658)( 23,660)( 24,659)
( 25,677)( 26,678)( 27,680)( 28,679)( 29,673)( 30,674)( 31,676)( 32,675)
( 33,681)( 34,682)( 35,684)( 36,683)( 37,737)( 38,738)( 39,740)( 40,739)
( 41,733)( 42,734)( 43,736)( 44,735)( 45,741)( 46,742)( 47,744)( 48,743)
( 49,725)( 50,726)( 51,728)( 52,727)( 53,721)( 54,722)( 55,724)( 56,723)
( 57,729)( 58,730)( 59,732)( 60,731)( 61,749)( 62,750)( 63,752)( 64,751)
( 65,745)( 66,746)( 67,748)( 68,747)( 69,753)( 70,754)( 71,756)( 72,755)
( 73,701)( 74,702)( 75,704)( 76,703)( 77,697)( 78,698)( 79,700)( 80,699)
( 81,705)( 82,706)( 83,708)( 84,707)( 85,689)( 86,690)( 87,692)( 88,691)
( 89,685)( 90,686)( 91,688)( 92,687)( 93,693)( 94,694)( 95,696)( 96,695)
( 97,713)( 98,714)( 99,716)(100,715)(101,709)(102,710)(103,712)(104,711)
(105,717)(106,718)(107,720)(108,719)(109,773)(110,774)(111,776)(112,775)
(113,769)(114,770)(115,772)(116,771)(117,777)(118,778)(119,780)(120,779)
(121,761)(122,762)(123,764)(124,763)(125,757)(126,758)(127,760)(128,759)
(129,765)(130,766)(131,768)(132,767)(133,785)(134,786)(135,788)(136,787)
(137,781)(138,782)(139,784)(140,783)(141,789)(142,790)(143,792)(144,791)
(145,845)(146,846)(147,848)(148,847)(149,841)(150,842)(151,844)(152,843)
(153,849)(154,850)(155,852)(156,851)(157,833)(158,834)(159,836)(160,835)
(161,829)(162,830)(163,832)(164,831)(165,837)(166,838)(167,840)(168,839)
(169,857)(170,858)(171,860)(172,859)(173,853)(174,854)(175,856)(176,855)
(177,861)(178,862)(179,864)(180,863)(181,809)(182,810)(183,812)(184,811)
(185,805)(186,806)(187,808)(188,807)(189,813)(190,814)(191,816)(192,815)
(193,797)(194,798)(195,800)(196,799)(197,793)(198,794)(199,796)(200,795)
(201,801)(202,802)(203,804)(204,803)(205,821)(206,822)(207,824)(208,823)
(209,817)(210,818)(211,820)(212,819)(213,825)(214,826)(215,828)(216,827)
(217,449)(218,450)(219,452)(220,451)(221,445)(222,446)(223,448)(224,447)
(225,453)(226,454)(227,456)(228,455)(229,437)(230,438)(231,440)(232,439)
(233,433)(234,434)(235,436)(236,435)(237,441)(238,442)(239,444)(240,443)
(241,461)(242,462)(243,464)(244,463)(245,457)(246,458)(247,460)(248,459)
(249,465)(250,466)(251,468)(252,467)(253,521)(254,522)(255,524)(256,523)
(257,517)(258,518)(259,520)(260,519)(261,525)(262,526)(263,528)(264,527)
(265,509)(266,510)(267,512)(268,511)(269,505)(270,506)(271,508)(272,507)
(273,513)(274,514)(275,516)(276,515)(277,533)(278,534)(279,536)(280,535)
(281,529)(282,530)(283,532)(284,531)(285,537)(286,538)(287,540)(288,539)
(289,485)(290,486)(291,488)(292,487)(293,481)(294,482)(295,484)(296,483)
(297,489)(298,490)(299,492)(300,491)(301,473)(302,474)(303,476)(304,475)
(305,469)(306,470)(307,472)(308,471)(309,477)(310,478)(311,480)(312,479)
(313,497)(314,498)(315,500)(316,499)(317,493)(318,494)(319,496)(320,495)
(321,501)(322,502)(323,504)(324,503)(325,557)(326,558)(327,560)(328,559)
(329,553)(330,554)(331,556)(332,555)(333,561)(334,562)(335,564)(336,563)
(337,545)(338,546)(339,548)(340,547)(341,541)(342,542)(343,544)(344,543)
(345,549)(346,550)(347,552)(348,551)(349,569)(350,570)(351,572)(352,571)
(353,565)(354,566)(355,568)(356,567)(357,573)(358,574)(359,576)(360,575)
(361,629)(362,630)(363,632)(364,631)(365,625)(366,626)(367,628)(368,627)
(369,633)(370,634)(371,636)(372,635)(373,617)(374,618)(375,620)(376,619)
(377,613)(378,614)(379,616)(380,615)(381,621)(382,622)(383,624)(384,623)
(385,641)(386,642)(387,644)(388,643)(389,637)(390,638)(391,640)(392,639)
(393,645)(394,646)(395,648)(396,647)(397,593)(398,594)(399,596)(400,595)
(401,589)(402,590)(403,592)(404,591)(405,597)(406,598)(407,600)(408,599)
(409,581)(410,582)(411,584)(412,583)(413,577)(414,578)(415,580)(416,579)
(417,585)(418,586)(419,588)(420,587)(421,605)(422,606)(423,608)(424,607)
(425,601)(426,602)(427,604)(428,603)(429,609)(430,610)(431,612)(432,611);;
s2 := ( 1,685)( 2,688)( 3,687)( 4,686)( 5,693)( 6,696)( 7,695)( 8,694)
( 9,689)( 10,692)( 11,691)( 12,690)( 13,697)( 14,700)( 15,699)( 16,698)
( 17,705)( 18,708)( 19,707)( 20,706)( 21,701)( 22,704)( 23,703)( 24,702)
( 25,709)( 26,712)( 27,711)( 28,710)( 29,717)( 30,720)( 31,719)( 32,718)
( 33,713)( 34,716)( 35,715)( 36,714)( 37,649)( 38,652)( 39,651)( 40,650)
( 41,657)( 42,660)( 43,659)( 44,658)( 45,653)( 46,656)( 47,655)( 48,654)
( 49,661)( 50,664)( 51,663)( 52,662)( 53,669)( 54,672)( 55,671)( 56,670)
( 57,665)( 58,668)( 59,667)( 60,666)( 61,673)( 62,676)( 63,675)( 64,674)
( 65,681)( 66,684)( 67,683)( 68,682)( 69,677)( 70,680)( 71,679)( 72,678)
( 73,721)( 74,724)( 75,723)( 76,722)( 77,729)( 78,732)( 79,731)( 80,730)
( 81,725)( 82,728)( 83,727)( 84,726)( 85,733)( 86,736)( 87,735)( 88,734)
( 89,741)( 90,744)( 91,743)( 92,742)( 93,737)( 94,740)( 95,739)( 96,738)
( 97,745)( 98,748)( 99,747)(100,746)(101,753)(102,756)(103,755)(104,754)
(105,749)(106,752)(107,751)(108,750)(109,793)(110,796)(111,795)(112,794)
(113,801)(114,804)(115,803)(116,802)(117,797)(118,800)(119,799)(120,798)
(121,805)(122,808)(123,807)(124,806)(125,813)(126,816)(127,815)(128,814)
(129,809)(130,812)(131,811)(132,810)(133,817)(134,820)(135,819)(136,818)
(137,825)(138,828)(139,827)(140,826)(141,821)(142,824)(143,823)(144,822)
(145,757)(146,760)(147,759)(148,758)(149,765)(150,768)(151,767)(152,766)
(153,761)(154,764)(155,763)(156,762)(157,769)(158,772)(159,771)(160,770)
(161,777)(162,780)(163,779)(164,778)(165,773)(166,776)(167,775)(168,774)
(169,781)(170,784)(171,783)(172,782)(173,789)(174,792)(175,791)(176,790)
(177,785)(178,788)(179,787)(180,786)(181,829)(182,832)(183,831)(184,830)
(185,837)(186,840)(187,839)(188,838)(189,833)(190,836)(191,835)(192,834)
(193,841)(194,844)(195,843)(196,842)(197,849)(198,852)(199,851)(200,850)
(201,845)(202,848)(203,847)(204,846)(205,853)(206,856)(207,855)(208,854)
(209,861)(210,864)(211,863)(212,862)(213,857)(214,860)(215,859)(216,858)
(217,577)(218,580)(219,579)(220,578)(221,585)(222,588)(223,587)(224,586)
(225,581)(226,584)(227,583)(228,582)(229,589)(230,592)(231,591)(232,590)
(233,597)(234,600)(235,599)(236,598)(237,593)(238,596)(239,595)(240,594)
(241,601)(242,604)(243,603)(244,602)(245,609)(246,612)(247,611)(248,610)
(249,605)(250,608)(251,607)(252,606)(253,541)(254,544)(255,543)(256,542)
(257,549)(258,552)(259,551)(260,550)(261,545)(262,548)(263,547)(264,546)
(265,553)(266,556)(267,555)(268,554)(269,561)(270,564)(271,563)(272,562)
(273,557)(274,560)(275,559)(276,558)(277,565)(278,568)(279,567)(280,566)
(281,573)(282,576)(283,575)(284,574)(285,569)(286,572)(287,571)(288,570)
(289,613)(290,616)(291,615)(292,614)(293,621)(294,624)(295,623)(296,622)
(297,617)(298,620)(299,619)(300,618)(301,625)(302,628)(303,627)(304,626)
(305,633)(306,636)(307,635)(308,634)(309,629)(310,632)(311,631)(312,630)
(313,637)(314,640)(315,639)(316,638)(317,645)(318,648)(319,647)(320,646)
(321,641)(322,644)(323,643)(324,642)(325,469)(326,472)(327,471)(328,470)
(329,477)(330,480)(331,479)(332,478)(333,473)(334,476)(335,475)(336,474)
(337,481)(338,484)(339,483)(340,482)(341,489)(342,492)(343,491)(344,490)
(345,485)(346,488)(347,487)(348,486)(349,493)(350,496)(351,495)(352,494)
(353,501)(354,504)(355,503)(356,502)(357,497)(358,500)(359,499)(360,498)
(361,433)(362,436)(363,435)(364,434)(365,441)(366,444)(367,443)(368,442)
(369,437)(370,440)(371,439)(372,438)(373,445)(374,448)(375,447)(376,446)
(377,453)(378,456)(379,455)(380,454)(381,449)(382,452)(383,451)(384,450)
(385,457)(386,460)(387,459)(388,458)(389,465)(390,468)(391,467)(392,466)
(393,461)(394,464)(395,463)(396,462)(397,505)(398,508)(399,507)(400,506)
(401,513)(402,516)(403,515)(404,514)(405,509)(406,512)(407,511)(408,510)
(409,517)(410,520)(411,519)(412,518)(413,525)(414,528)(415,527)(416,526)
(417,521)(418,524)(419,523)(420,522)(421,529)(422,532)(423,531)(424,530)
(425,537)(426,540)(427,539)(428,538)(429,533)(430,536)(431,535)(432,534);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 1,435)( 2,436)( 3,433)( 4,434)( 5,443)( 6,444)( 7,441)
( 8,442)( 9,439)( 10,440)( 11,437)( 12,438)( 13,459)( 14,460)( 15,457)
( 16,458)( 17,467)( 18,468)( 19,465)( 20,466)( 21,463)( 22,464)( 23,461)
( 24,462)( 25,447)( 26,448)( 27,445)( 28,446)( 29,455)( 30,456)( 31,453)
( 32,454)( 33,451)( 34,452)( 35,449)( 36,450)( 37,471)( 38,472)( 39,469)
( 40,470)( 41,479)( 42,480)( 43,477)( 44,478)( 45,475)( 46,476)( 47,473)
( 48,474)( 49,495)( 50,496)( 51,493)( 52,494)( 53,503)( 54,504)( 55,501)
( 56,502)( 57,499)( 58,500)( 59,497)( 60,498)( 61,483)( 62,484)( 63,481)
( 64,482)( 65,491)( 66,492)( 67,489)( 68,490)( 69,487)( 70,488)( 71,485)
( 72,486)( 73,507)( 74,508)( 75,505)( 76,506)( 77,515)( 78,516)( 79,513)
( 80,514)( 81,511)( 82,512)( 83,509)( 84,510)( 85,531)( 86,532)( 87,529)
( 88,530)( 89,539)( 90,540)( 91,537)( 92,538)( 93,535)( 94,536)( 95,533)
( 96,534)( 97,519)( 98,520)( 99,517)(100,518)(101,527)(102,528)(103,525)
(104,526)(105,523)(106,524)(107,521)(108,522)(109,543)(110,544)(111,541)
(112,542)(113,551)(114,552)(115,549)(116,550)(117,547)(118,548)(119,545)
(120,546)(121,567)(122,568)(123,565)(124,566)(125,575)(126,576)(127,573)
(128,574)(129,571)(130,572)(131,569)(132,570)(133,555)(134,556)(135,553)
(136,554)(137,563)(138,564)(139,561)(140,562)(141,559)(142,560)(143,557)
(144,558)(145,579)(146,580)(147,577)(148,578)(149,587)(150,588)(151,585)
(152,586)(153,583)(154,584)(155,581)(156,582)(157,603)(158,604)(159,601)
(160,602)(161,611)(162,612)(163,609)(164,610)(165,607)(166,608)(167,605)
(168,606)(169,591)(170,592)(171,589)(172,590)(173,599)(174,600)(175,597)
(176,598)(177,595)(178,596)(179,593)(180,594)(181,615)(182,616)(183,613)
(184,614)(185,623)(186,624)(187,621)(188,622)(189,619)(190,620)(191,617)
(192,618)(193,639)(194,640)(195,637)(196,638)(197,647)(198,648)(199,645)
(200,646)(201,643)(202,644)(203,641)(204,642)(205,627)(206,628)(207,625)
(208,626)(209,635)(210,636)(211,633)(212,634)(213,631)(214,632)(215,629)
(216,630)(217,759)(218,760)(219,757)(220,758)(221,767)(222,768)(223,765)
(224,766)(225,763)(226,764)(227,761)(228,762)(229,783)(230,784)(231,781)
(232,782)(233,791)(234,792)(235,789)(236,790)(237,787)(238,788)(239,785)
(240,786)(241,771)(242,772)(243,769)(244,770)(245,779)(246,780)(247,777)
(248,778)(249,775)(250,776)(251,773)(252,774)(253,795)(254,796)(255,793)
(256,794)(257,803)(258,804)(259,801)(260,802)(261,799)(262,800)(263,797)
(264,798)(265,819)(266,820)(267,817)(268,818)(269,827)(270,828)(271,825)
(272,826)(273,823)(274,824)(275,821)(276,822)(277,807)(278,808)(279,805)
(280,806)(281,815)(282,816)(283,813)(284,814)(285,811)(286,812)(287,809)
(288,810)(289,831)(290,832)(291,829)(292,830)(293,839)(294,840)(295,837)
(296,838)(297,835)(298,836)(299,833)(300,834)(301,855)(302,856)(303,853)
(304,854)(305,863)(306,864)(307,861)(308,862)(309,859)(310,860)(311,857)
(312,858)(313,843)(314,844)(315,841)(316,842)(317,851)(318,852)(319,849)
(320,850)(321,847)(322,848)(323,845)(324,846)(325,651)(326,652)(327,649)
(328,650)(329,659)(330,660)(331,657)(332,658)(333,655)(334,656)(335,653)
(336,654)(337,675)(338,676)(339,673)(340,674)(341,683)(342,684)(343,681)
(344,682)(345,679)(346,680)(347,677)(348,678)(349,663)(350,664)(351,661)
(352,662)(353,671)(354,672)(355,669)(356,670)(357,667)(358,668)(359,665)
(360,666)(361,687)(362,688)(363,685)(364,686)(365,695)(366,696)(367,693)
(368,694)(369,691)(370,692)(371,689)(372,690)(373,711)(374,712)(375,709)
(376,710)(377,719)(378,720)(379,717)(380,718)(381,715)(382,716)(383,713)
(384,714)(385,699)(386,700)(387,697)(388,698)(389,707)(390,708)(391,705)
(392,706)(393,703)(394,704)(395,701)(396,702)(397,723)(398,724)(399,721)
(400,722)(401,731)(402,732)(403,729)(404,730)(405,727)(406,728)(407,725)
(408,726)(409,747)(410,748)(411,745)(412,746)(413,755)(414,756)(415,753)
(416,754)(417,751)(418,752)(419,749)(420,750)(421,735)(422,736)(423,733)
(424,734)(425,743)(426,744)(427,741)(428,742)(429,739)(430,740)(431,737)
(432,738);
s1 := Sym(864)!( 1,665)( 2,666)( 3,668)( 4,667)( 5,661)( 6,662)( 7,664)
( 8,663)( 9,669)( 10,670)( 11,672)( 12,671)( 13,653)( 14,654)( 15,656)
( 16,655)( 17,649)( 18,650)( 19,652)( 20,651)( 21,657)( 22,658)( 23,660)
( 24,659)( 25,677)( 26,678)( 27,680)( 28,679)( 29,673)( 30,674)( 31,676)
( 32,675)( 33,681)( 34,682)( 35,684)( 36,683)( 37,737)( 38,738)( 39,740)
( 40,739)( 41,733)( 42,734)( 43,736)( 44,735)( 45,741)( 46,742)( 47,744)
( 48,743)( 49,725)( 50,726)( 51,728)( 52,727)( 53,721)( 54,722)( 55,724)
( 56,723)( 57,729)( 58,730)( 59,732)( 60,731)( 61,749)( 62,750)( 63,752)
( 64,751)( 65,745)( 66,746)( 67,748)( 68,747)( 69,753)( 70,754)( 71,756)
( 72,755)( 73,701)( 74,702)( 75,704)( 76,703)( 77,697)( 78,698)( 79,700)
( 80,699)( 81,705)( 82,706)( 83,708)( 84,707)( 85,689)( 86,690)( 87,692)
( 88,691)( 89,685)( 90,686)( 91,688)( 92,687)( 93,693)( 94,694)( 95,696)
( 96,695)( 97,713)( 98,714)( 99,716)(100,715)(101,709)(102,710)(103,712)
(104,711)(105,717)(106,718)(107,720)(108,719)(109,773)(110,774)(111,776)
(112,775)(113,769)(114,770)(115,772)(116,771)(117,777)(118,778)(119,780)
(120,779)(121,761)(122,762)(123,764)(124,763)(125,757)(126,758)(127,760)
(128,759)(129,765)(130,766)(131,768)(132,767)(133,785)(134,786)(135,788)
(136,787)(137,781)(138,782)(139,784)(140,783)(141,789)(142,790)(143,792)
(144,791)(145,845)(146,846)(147,848)(148,847)(149,841)(150,842)(151,844)
(152,843)(153,849)(154,850)(155,852)(156,851)(157,833)(158,834)(159,836)
(160,835)(161,829)(162,830)(163,832)(164,831)(165,837)(166,838)(167,840)
(168,839)(169,857)(170,858)(171,860)(172,859)(173,853)(174,854)(175,856)
(176,855)(177,861)(178,862)(179,864)(180,863)(181,809)(182,810)(183,812)
(184,811)(185,805)(186,806)(187,808)(188,807)(189,813)(190,814)(191,816)
(192,815)(193,797)(194,798)(195,800)(196,799)(197,793)(198,794)(199,796)
(200,795)(201,801)(202,802)(203,804)(204,803)(205,821)(206,822)(207,824)
(208,823)(209,817)(210,818)(211,820)(212,819)(213,825)(214,826)(215,828)
(216,827)(217,449)(218,450)(219,452)(220,451)(221,445)(222,446)(223,448)
(224,447)(225,453)(226,454)(227,456)(228,455)(229,437)(230,438)(231,440)
(232,439)(233,433)(234,434)(235,436)(236,435)(237,441)(238,442)(239,444)
(240,443)(241,461)(242,462)(243,464)(244,463)(245,457)(246,458)(247,460)
(248,459)(249,465)(250,466)(251,468)(252,467)(253,521)(254,522)(255,524)
(256,523)(257,517)(258,518)(259,520)(260,519)(261,525)(262,526)(263,528)
(264,527)(265,509)(266,510)(267,512)(268,511)(269,505)(270,506)(271,508)
(272,507)(273,513)(274,514)(275,516)(276,515)(277,533)(278,534)(279,536)
(280,535)(281,529)(282,530)(283,532)(284,531)(285,537)(286,538)(287,540)
(288,539)(289,485)(290,486)(291,488)(292,487)(293,481)(294,482)(295,484)
(296,483)(297,489)(298,490)(299,492)(300,491)(301,473)(302,474)(303,476)
(304,475)(305,469)(306,470)(307,472)(308,471)(309,477)(310,478)(311,480)
(312,479)(313,497)(314,498)(315,500)(316,499)(317,493)(318,494)(319,496)
(320,495)(321,501)(322,502)(323,504)(324,503)(325,557)(326,558)(327,560)
(328,559)(329,553)(330,554)(331,556)(332,555)(333,561)(334,562)(335,564)
(336,563)(337,545)(338,546)(339,548)(340,547)(341,541)(342,542)(343,544)
(344,543)(345,549)(346,550)(347,552)(348,551)(349,569)(350,570)(351,572)
(352,571)(353,565)(354,566)(355,568)(356,567)(357,573)(358,574)(359,576)
(360,575)(361,629)(362,630)(363,632)(364,631)(365,625)(366,626)(367,628)
(368,627)(369,633)(370,634)(371,636)(372,635)(373,617)(374,618)(375,620)
(376,619)(377,613)(378,614)(379,616)(380,615)(381,621)(382,622)(383,624)
(384,623)(385,641)(386,642)(387,644)(388,643)(389,637)(390,638)(391,640)
(392,639)(393,645)(394,646)(395,648)(396,647)(397,593)(398,594)(399,596)
(400,595)(401,589)(402,590)(403,592)(404,591)(405,597)(406,598)(407,600)
(408,599)(409,581)(410,582)(411,584)(412,583)(413,577)(414,578)(415,580)
(416,579)(417,585)(418,586)(419,588)(420,587)(421,605)(422,606)(423,608)
(424,607)(425,601)(426,602)(427,604)(428,603)(429,609)(430,610)(431,612)
(432,611);
s2 := Sym(864)!( 1,685)( 2,688)( 3,687)( 4,686)( 5,693)( 6,696)( 7,695)
( 8,694)( 9,689)( 10,692)( 11,691)( 12,690)( 13,697)( 14,700)( 15,699)
( 16,698)( 17,705)( 18,708)( 19,707)( 20,706)( 21,701)( 22,704)( 23,703)
( 24,702)( 25,709)( 26,712)( 27,711)( 28,710)( 29,717)( 30,720)( 31,719)
( 32,718)( 33,713)( 34,716)( 35,715)( 36,714)( 37,649)( 38,652)( 39,651)
( 40,650)( 41,657)( 42,660)( 43,659)( 44,658)( 45,653)( 46,656)( 47,655)
( 48,654)( 49,661)( 50,664)( 51,663)( 52,662)( 53,669)( 54,672)( 55,671)
( 56,670)( 57,665)( 58,668)( 59,667)( 60,666)( 61,673)( 62,676)( 63,675)
( 64,674)( 65,681)( 66,684)( 67,683)( 68,682)( 69,677)( 70,680)( 71,679)
( 72,678)( 73,721)( 74,724)( 75,723)( 76,722)( 77,729)( 78,732)( 79,731)
( 80,730)( 81,725)( 82,728)( 83,727)( 84,726)( 85,733)( 86,736)( 87,735)
( 88,734)( 89,741)( 90,744)( 91,743)( 92,742)( 93,737)( 94,740)( 95,739)
( 96,738)( 97,745)( 98,748)( 99,747)(100,746)(101,753)(102,756)(103,755)
(104,754)(105,749)(106,752)(107,751)(108,750)(109,793)(110,796)(111,795)
(112,794)(113,801)(114,804)(115,803)(116,802)(117,797)(118,800)(119,799)
(120,798)(121,805)(122,808)(123,807)(124,806)(125,813)(126,816)(127,815)
(128,814)(129,809)(130,812)(131,811)(132,810)(133,817)(134,820)(135,819)
(136,818)(137,825)(138,828)(139,827)(140,826)(141,821)(142,824)(143,823)
(144,822)(145,757)(146,760)(147,759)(148,758)(149,765)(150,768)(151,767)
(152,766)(153,761)(154,764)(155,763)(156,762)(157,769)(158,772)(159,771)
(160,770)(161,777)(162,780)(163,779)(164,778)(165,773)(166,776)(167,775)
(168,774)(169,781)(170,784)(171,783)(172,782)(173,789)(174,792)(175,791)
(176,790)(177,785)(178,788)(179,787)(180,786)(181,829)(182,832)(183,831)
(184,830)(185,837)(186,840)(187,839)(188,838)(189,833)(190,836)(191,835)
(192,834)(193,841)(194,844)(195,843)(196,842)(197,849)(198,852)(199,851)
(200,850)(201,845)(202,848)(203,847)(204,846)(205,853)(206,856)(207,855)
(208,854)(209,861)(210,864)(211,863)(212,862)(213,857)(214,860)(215,859)
(216,858)(217,577)(218,580)(219,579)(220,578)(221,585)(222,588)(223,587)
(224,586)(225,581)(226,584)(227,583)(228,582)(229,589)(230,592)(231,591)
(232,590)(233,597)(234,600)(235,599)(236,598)(237,593)(238,596)(239,595)
(240,594)(241,601)(242,604)(243,603)(244,602)(245,609)(246,612)(247,611)
(248,610)(249,605)(250,608)(251,607)(252,606)(253,541)(254,544)(255,543)
(256,542)(257,549)(258,552)(259,551)(260,550)(261,545)(262,548)(263,547)
(264,546)(265,553)(266,556)(267,555)(268,554)(269,561)(270,564)(271,563)
(272,562)(273,557)(274,560)(275,559)(276,558)(277,565)(278,568)(279,567)
(280,566)(281,573)(282,576)(283,575)(284,574)(285,569)(286,572)(287,571)
(288,570)(289,613)(290,616)(291,615)(292,614)(293,621)(294,624)(295,623)
(296,622)(297,617)(298,620)(299,619)(300,618)(301,625)(302,628)(303,627)
(304,626)(305,633)(306,636)(307,635)(308,634)(309,629)(310,632)(311,631)
(312,630)(313,637)(314,640)(315,639)(316,638)(317,645)(318,648)(319,647)
(320,646)(321,641)(322,644)(323,643)(324,642)(325,469)(326,472)(327,471)
(328,470)(329,477)(330,480)(331,479)(332,478)(333,473)(334,476)(335,475)
(336,474)(337,481)(338,484)(339,483)(340,482)(341,489)(342,492)(343,491)
(344,490)(345,485)(346,488)(347,487)(348,486)(349,493)(350,496)(351,495)
(352,494)(353,501)(354,504)(355,503)(356,502)(357,497)(358,500)(359,499)
(360,498)(361,433)(362,436)(363,435)(364,434)(365,441)(366,444)(367,443)
(368,442)(369,437)(370,440)(371,439)(372,438)(373,445)(374,448)(375,447)
(376,446)(377,453)(378,456)(379,455)(380,454)(381,449)(382,452)(383,451)
(384,450)(385,457)(386,460)(387,459)(388,458)(389,465)(390,468)(391,467)
(392,466)(393,461)(394,464)(395,463)(396,462)(397,505)(398,508)(399,507)
(400,506)(401,513)(402,516)(403,515)(404,514)(405,509)(406,512)(407,511)
(408,510)(409,517)(410,520)(411,519)(412,518)(413,525)(414,528)(415,527)
(416,526)(417,521)(418,524)(419,523)(420,522)(421,529)(422,532)(423,531)
(424,530)(425,537)(426,540)(427,539)(428,538)(429,533)(430,536)(431,535)
(432,534);
poly := sub<Sym(864)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope