Polytope of Type {156,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {156,6}*1872a
if this polytope has a name.
Group : SmallGroup(1872,696)
Rank : 3
Schlafli Type : {156,6}
Number of vertices, edges, etc : 156, 468, 6
Order of s₀s₁s₂ : 156
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
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 : {78,6}*936a
   3-fold quotients : {52,6}*624a
   6-fold quotients : {26,6}*312
   9-fold quotients : {52,2}*208
   13-fold quotients : {12,6}*144c
   18-fold quotients : {26,2}*104
   26-fold quotients : {6,6}*72b
   36-fold quotients : {13,2}*52
   39-fold quotients : {4,6}*48a
   52-fold quotients : {6,3}*36
   78-fold quotients : {2,6}*24
   117-fold quotients : {4,2}*16
   156-fold quotients : {2,3}*12
   234-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,469)(  2,481)(  3,480)(  4,479)(  5,478)(  6,477)(  7,476)(  8,475)
(  9,474)( 10,473)( 11,472)( 12,471)( 13,470)( 14,482)( 15,494)( 16,493)
( 17,492)( 18,491)( 19,490)( 20,489)( 21,488)( 22,487)( 23,486)( 24,485)
( 25,484)( 26,483)( 27,495)( 28,507)( 29,506)( 30,505)( 31,504)( 32,503)
( 33,502)( 34,501)( 35,500)( 36,499)( 37,498)( 38,497)( 39,496)( 40,547)
( 41,559)( 42,558)( 43,557)( 44,556)( 45,555)( 46,554)( 47,553)( 48,552)
( 49,551)( 50,550)( 51,549)( 52,548)( 53,560)( 54,572)( 55,571)( 56,570)
( 57,569)( 58,568)( 59,567)( 60,566)( 61,565)( 62,564)( 63,563)( 64,562)
( 65,561)( 66,573)( 67,585)( 68,584)( 69,583)( 70,582)( 71,581)( 72,580)
( 73,579)( 74,578)( 75,577)( 76,576)( 77,575)( 78,574)( 79,508)( 80,520)
( 81,519)( 82,518)( 83,517)( 84,516)( 85,515)( 86,514)( 87,513)( 88,512)
( 89,511)( 90,510)( 91,509)( 92,521)( 93,533)( 94,532)( 95,531)( 96,530)
( 97,529)( 98,528)( 99,527)(100,526)(101,525)(102,524)(103,523)(104,522)
(105,534)(106,546)(107,545)(108,544)(109,543)(110,542)(111,541)(112,540)
(113,539)(114,538)(115,537)(116,536)(117,535)(118,586)(119,598)(120,597)
(121,596)(122,595)(123,594)(124,593)(125,592)(126,591)(127,590)(128,589)
(129,588)(130,587)(131,599)(132,611)(133,610)(134,609)(135,608)(136,607)
(137,606)(138,605)(139,604)(140,603)(141,602)(142,601)(143,600)(144,612)
(145,624)(146,623)(147,622)(148,621)(149,620)(150,619)(151,618)(152,617)
(153,616)(154,615)(155,614)(156,613)(157,664)(158,676)(159,675)(160,674)
(161,673)(162,672)(163,671)(164,670)(165,669)(166,668)(167,667)(168,666)
(169,665)(170,677)(171,689)(172,688)(173,687)(174,686)(175,685)(176,684)
(177,683)(178,682)(179,681)(180,680)(181,679)(182,678)(183,690)(184,702)
(185,701)(186,700)(187,699)(188,698)(189,697)(190,696)(191,695)(192,694)
(193,693)(194,692)(195,691)(196,625)(197,637)(198,636)(199,635)(200,634)
(201,633)(202,632)(203,631)(204,630)(205,629)(206,628)(207,627)(208,626)
(209,638)(210,650)(211,649)(212,648)(213,647)(214,646)(215,645)(216,644)
(217,643)(218,642)(219,641)(220,640)(221,639)(222,651)(223,663)(224,662)
(225,661)(226,660)(227,659)(228,658)(229,657)(230,656)(231,655)(232,654)
(233,653)(234,652)(235,820)(236,832)(237,831)(238,830)(239,829)(240,828)
(241,827)(242,826)(243,825)(244,824)(245,823)(246,822)(247,821)(248,833)
(249,845)(250,844)(251,843)(252,842)(253,841)(254,840)(255,839)(256,838)
(257,837)(258,836)(259,835)(260,834)(261,846)(262,858)(263,857)(264,856)
(265,855)(266,854)(267,853)(268,852)(269,851)(270,850)(271,849)(272,848)
(273,847)(274,898)(275,910)(276,909)(277,908)(278,907)(279,906)(280,905)
(281,904)(282,903)(283,902)(284,901)(285,900)(286,899)(287,911)(288,923)
(289,922)(290,921)(291,920)(292,919)(293,918)(294,917)(295,916)(296,915)
(297,914)(298,913)(299,912)(300,924)(301,936)(302,935)(303,934)(304,933)
(305,932)(306,931)(307,930)(308,929)(309,928)(310,927)(311,926)(312,925)
(313,859)(314,871)(315,870)(316,869)(317,868)(318,867)(319,866)(320,865)
(321,864)(322,863)(323,862)(324,861)(325,860)(326,872)(327,884)(328,883)
(329,882)(330,881)(331,880)(332,879)(333,878)(334,877)(335,876)(336,875)
(337,874)(338,873)(339,885)(340,897)(341,896)(342,895)(343,894)(344,893)
(345,892)(346,891)(347,890)(348,889)(349,888)(350,887)(351,886)(352,703)
(353,715)(354,714)(355,713)(356,712)(357,711)(358,710)(359,709)(360,708)
(361,707)(362,706)(363,705)(364,704)(365,716)(366,728)(367,727)(368,726)
(369,725)(370,724)(371,723)(372,722)(373,721)(374,720)(375,719)(376,718)
(377,717)(378,729)(379,741)(380,740)(381,739)(382,738)(383,737)(384,736)
(385,735)(386,734)(387,733)(388,732)(389,731)(390,730)(391,781)(392,793)
(393,792)(394,791)(395,790)(396,789)(397,788)(398,787)(399,786)(400,785)
(401,784)(402,783)(403,782)(404,794)(405,806)(406,805)(407,804)(408,803)
(409,802)(410,801)(411,800)(412,799)(413,798)(414,797)(415,796)(416,795)
(417,807)(418,819)(419,818)(420,817)(421,816)(422,815)(423,814)(424,813)
(425,812)(426,811)(427,810)(428,809)(429,808)(430,742)(431,754)(432,753)
(433,752)(434,751)(435,750)(436,749)(437,748)(438,747)(439,746)(440,745)
(441,744)(442,743)(443,755)(444,767)(445,766)(446,765)(447,764)(448,763)
(449,762)(450,761)(451,760)(452,759)(453,758)(454,757)(455,756)(456,768)
(457,780)(458,779)(459,778)(460,777)(461,776)(462,775)(463,774)(464,773)
(465,772)(466,771)(467,770)(468,769);;
s1 := (  1,743)(  2,742)(  3,754)(  4,753)(  5,752)(  6,751)(  7,750)(  8,749)
(  9,748)( 10,747)( 11,746)( 12,745)( 13,744)( 14,769)( 15,768)( 16,780)
( 17,779)( 18,778)( 19,777)( 20,776)( 21,775)( 22,774)( 23,773)( 24,772)
( 25,771)( 26,770)( 27,756)( 28,755)( 29,767)( 30,766)( 31,765)( 32,764)
( 33,763)( 34,762)( 35,761)( 36,760)( 37,759)( 38,758)( 39,757)( 40,704)
( 41,703)( 42,715)( 43,714)( 44,713)( 45,712)( 46,711)( 47,710)( 48,709)
( 49,708)( 50,707)( 51,706)( 52,705)( 53,730)( 54,729)( 55,741)( 56,740)
( 57,739)( 58,738)( 59,737)( 60,736)( 61,735)( 62,734)( 63,733)( 64,732)
( 65,731)( 66,717)( 67,716)( 68,728)( 69,727)( 70,726)( 71,725)( 72,724)
( 73,723)( 74,722)( 75,721)( 76,720)( 77,719)( 78,718)( 79,782)( 80,781)
( 81,793)( 82,792)( 83,791)( 84,790)( 85,789)( 86,788)( 87,787)( 88,786)
( 89,785)( 90,784)( 91,783)( 92,808)( 93,807)( 94,819)( 95,818)( 96,817)
( 97,816)( 98,815)( 99,814)(100,813)(101,812)(102,811)(103,810)(104,809)
(105,795)(106,794)(107,806)(108,805)(109,804)(110,803)(111,802)(112,801)
(113,800)(114,799)(115,798)(116,797)(117,796)(118,860)(119,859)(120,871)
(121,870)(122,869)(123,868)(124,867)(125,866)(126,865)(127,864)(128,863)
(129,862)(130,861)(131,886)(132,885)(133,897)(134,896)(135,895)(136,894)
(137,893)(138,892)(139,891)(140,890)(141,889)(142,888)(143,887)(144,873)
(145,872)(146,884)(147,883)(148,882)(149,881)(150,880)(151,879)(152,878)
(153,877)(154,876)(155,875)(156,874)(157,821)(158,820)(159,832)(160,831)
(161,830)(162,829)(163,828)(164,827)(165,826)(166,825)(167,824)(168,823)
(169,822)(170,847)(171,846)(172,858)(173,857)(174,856)(175,855)(176,854)
(177,853)(178,852)(179,851)(180,850)(181,849)(182,848)(183,834)(184,833)
(185,845)(186,844)(187,843)(188,842)(189,841)(190,840)(191,839)(192,838)
(193,837)(194,836)(195,835)(196,899)(197,898)(198,910)(199,909)(200,908)
(201,907)(202,906)(203,905)(204,904)(205,903)(206,902)(207,901)(208,900)
(209,925)(210,924)(211,936)(212,935)(213,934)(214,933)(215,932)(216,931)
(217,930)(218,929)(219,928)(220,927)(221,926)(222,912)(223,911)(224,923)
(225,922)(226,921)(227,920)(228,919)(229,918)(230,917)(231,916)(232,915)
(233,914)(234,913)(235,509)(236,508)(237,520)(238,519)(239,518)(240,517)
(241,516)(242,515)(243,514)(244,513)(245,512)(246,511)(247,510)(248,535)
(249,534)(250,546)(251,545)(252,544)(253,543)(254,542)(255,541)(256,540)
(257,539)(258,538)(259,537)(260,536)(261,522)(262,521)(263,533)(264,532)
(265,531)(266,530)(267,529)(268,528)(269,527)(270,526)(271,525)(272,524)
(273,523)(274,470)(275,469)(276,481)(277,480)(278,479)(279,478)(280,477)
(281,476)(282,475)(283,474)(284,473)(285,472)(286,471)(287,496)(288,495)
(289,507)(290,506)(291,505)(292,504)(293,503)(294,502)(295,501)(296,500)
(297,499)(298,498)(299,497)(300,483)(301,482)(302,494)(303,493)(304,492)
(305,491)(306,490)(307,489)(308,488)(309,487)(310,486)(311,485)(312,484)
(313,548)(314,547)(315,559)(316,558)(317,557)(318,556)(319,555)(320,554)
(321,553)(322,552)(323,551)(324,550)(325,549)(326,574)(327,573)(328,585)
(329,584)(330,583)(331,582)(332,581)(333,580)(334,579)(335,578)(336,577)
(337,576)(338,575)(339,561)(340,560)(341,572)(342,571)(343,570)(344,569)
(345,568)(346,567)(347,566)(348,565)(349,564)(350,563)(351,562)(352,626)
(353,625)(354,637)(355,636)(356,635)(357,634)(358,633)(359,632)(360,631)
(361,630)(362,629)(363,628)(364,627)(365,652)(366,651)(367,663)(368,662)
(369,661)(370,660)(371,659)(372,658)(373,657)(374,656)(375,655)(376,654)
(377,653)(378,639)(379,638)(380,650)(381,649)(382,648)(383,647)(384,646)
(385,645)(386,644)(387,643)(388,642)(389,641)(390,640)(391,587)(392,586)
(393,598)(394,597)(395,596)(396,595)(397,594)(398,593)(399,592)(400,591)
(401,590)(402,589)(403,588)(404,613)(405,612)(406,624)(407,623)(408,622)
(409,621)(410,620)(411,619)(412,618)(413,617)(414,616)(415,615)(416,614)
(417,600)(418,599)(419,611)(420,610)(421,609)(422,608)(423,607)(424,606)
(425,605)(426,604)(427,603)(428,602)(429,601)(430,665)(431,664)(432,676)
(433,675)(434,674)(435,673)(436,672)(437,671)(438,670)(439,669)(440,668)
(441,667)(442,666)(443,691)(444,690)(445,702)(446,701)(447,700)(448,699)
(449,698)(450,697)(451,696)(452,695)(453,694)(454,693)(455,692)(456,678)
(457,677)(458,689)(459,688)(460,687)(461,686)(462,685)(463,684)(464,683)
(465,682)(466,681)(467,680)(468,679);;
s2 := (  1,716)(  2,717)(  3,718)(  4,719)(  5,720)(  6,721)(  7,722)(  8,723)
(  9,724)( 10,725)( 11,726)( 12,727)( 13,728)( 14,703)( 15,704)( 16,705)
( 17,706)( 18,707)( 19,708)( 20,709)( 21,710)( 22,711)( 23,712)( 24,713)
( 25,714)( 26,715)( 27,729)( 28,730)( 29,731)( 30,732)( 31,733)( 32,734)
( 33,735)( 34,736)( 35,737)( 36,738)( 37,739)( 38,740)( 39,741)( 40,794)
( 41,795)( 42,796)( 43,797)( 44,798)( 45,799)( 46,800)( 47,801)( 48,802)
( 49,803)( 50,804)( 51,805)( 52,806)( 53,781)( 54,782)( 55,783)( 56,784)
( 57,785)( 58,786)( 59,787)( 60,788)( 61,789)( 62,790)( 63,791)( 64,792)
( 65,793)( 66,807)( 67,808)( 68,809)( 69,810)( 70,811)( 71,812)( 72,813)
( 73,814)( 74,815)( 75,816)( 76,817)( 77,818)( 78,819)( 79,755)( 80,756)
( 81,757)( 82,758)( 83,759)( 84,760)( 85,761)( 86,762)( 87,763)( 88,764)
( 89,765)( 90,766)( 91,767)( 92,742)( 93,743)( 94,744)( 95,745)( 96,746)
( 97,747)( 98,748)( 99,749)(100,750)(101,751)(102,752)(103,753)(104,754)
(105,768)(106,769)(107,770)(108,771)(109,772)(110,773)(111,774)(112,775)
(113,776)(114,777)(115,778)(116,779)(117,780)(118,833)(119,834)(120,835)
(121,836)(122,837)(123,838)(124,839)(125,840)(126,841)(127,842)(128,843)
(129,844)(130,845)(131,820)(132,821)(133,822)(134,823)(135,824)(136,825)
(137,826)(138,827)(139,828)(140,829)(141,830)(142,831)(143,832)(144,846)
(145,847)(146,848)(147,849)(148,850)(149,851)(150,852)(151,853)(152,854)
(153,855)(154,856)(155,857)(156,858)(157,911)(158,912)(159,913)(160,914)
(161,915)(162,916)(163,917)(164,918)(165,919)(166,920)(167,921)(168,922)
(169,923)(170,898)(171,899)(172,900)(173,901)(174,902)(175,903)(176,904)
(177,905)(178,906)(179,907)(180,908)(181,909)(182,910)(183,924)(184,925)
(185,926)(186,927)(187,928)(188,929)(189,930)(190,931)(191,932)(192,933)
(193,934)(194,935)(195,936)(196,872)(197,873)(198,874)(199,875)(200,876)
(201,877)(202,878)(203,879)(204,880)(205,881)(206,882)(207,883)(208,884)
(209,859)(210,860)(211,861)(212,862)(213,863)(214,864)(215,865)(216,866)
(217,867)(218,868)(219,869)(220,870)(221,871)(222,885)(223,886)(224,887)
(225,888)(226,889)(227,890)(228,891)(229,892)(230,893)(231,894)(232,895)
(233,896)(234,897)(235,599)(236,600)(237,601)(238,602)(239,603)(240,604)
(241,605)(242,606)(243,607)(244,608)(245,609)(246,610)(247,611)(248,586)
(249,587)(250,588)(251,589)(252,590)(253,591)(254,592)(255,593)(256,594)
(257,595)(258,596)(259,597)(260,598)(261,612)(262,613)(263,614)(264,615)
(265,616)(266,617)(267,618)(268,619)(269,620)(270,621)(271,622)(272,623)
(273,624)(274,677)(275,678)(276,679)(277,680)(278,681)(279,682)(280,683)
(281,684)(282,685)(283,686)(284,687)(285,688)(286,689)(287,664)(288,665)
(289,666)(290,667)(291,668)(292,669)(293,670)(294,671)(295,672)(296,673)
(297,674)(298,675)(299,676)(300,690)(301,691)(302,692)(303,693)(304,694)
(305,695)(306,696)(307,697)(308,698)(309,699)(310,700)(311,701)(312,702)
(313,638)(314,639)(315,640)(316,641)(317,642)(318,643)(319,644)(320,645)
(321,646)(322,647)(323,648)(324,649)(325,650)(326,625)(327,626)(328,627)
(329,628)(330,629)(331,630)(332,631)(333,632)(334,633)(335,634)(336,635)
(337,636)(338,637)(339,651)(340,652)(341,653)(342,654)(343,655)(344,656)
(345,657)(346,658)(347,659)(348,660)(349,661)(350,662)(351,663)(352,482)
(353,483)(354,484)(355,485)(356,486)(357,487)(358,488)(359,489)(360,490)
(361,491)(362,492)(363,493)(364,494)(365,469)(366,470)(367,471)(368,472)
(369,473)(370,474)(371,475)(372,476)(373,477)(374,478)(375,479)(376,480)
(377,481)(378,495)(379,496)(380,497)(381,498)(382,499)(383,500)(384,501)
(385,502)(386,503)(387,504)(388,505)(389,506)(390,507)(391,560)(392,561)
(393,562)(394,563)(395,564)(396,565)(397,566)(398,567)(399,568)(400,569)
(401,570)(402,571)(403,572)(404,547)(405,548)(406,549)(407,550)(408,551)
(409,552)(410,553)(411,554)(412,555)(413,556)(414,557)(415,558)(416,559)
(417,573)(418,574)(419,575)(420,576)(421,577)(422,578)(423,579)(424,580)
(425,581)(426,582)(427,583)(428,584)(429,585)(430,521)(431,522)(432,523)
(433,524)(434,525)(435,526)(436,527)(437,528)(438,529)(439,530)(440,531)
(441,532)(442,533)(443,508)(444,509)(445,510)(446,511)(447,512)(448,513)
(449,514)(450,515)(451,516)(452,517)(453,518)(454,519)(455,520)(456,534)
(457,535)(458,536)(459,537)(460,538)(461,539)(462,540)(463,541)(464,542)
(465,543)(466,544)(467,545)(468,546);;
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*s2*s1*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*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*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*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(936)!(  1,469)(  2,481)(  3,480)(  4,479)(  5,478)(  6,477)(  7,476)
(  8,475)(  9,474)( 10,473)( 11,472)( 12,471)( 13,470)( 14,482)( 15,494)
( 16,493)( 17,492)( 18,491)( 19,490)( 20,489)( 21,488)( 22,487)( 23,486)
( 24,485)( 25,484)( 26,483)( 27,495)( 28,507)( 29,506)( 30,505)( 31,504)
( 32,503)( 33,502)( 34,501)( 35,500)( 36,499)( 37,498)( 38,497)( 39,496)
( 40,547)( 41,559)( 42,558)( 43,557)( 44,556)( 45,555)( 46,554)( 47,553)
( 48,552)( 49,551)( 50,550)( 51,549)( 52,548)( 53,560)( 54,572)( 55,571)
( 56,570)( 57,569)( 58,568)( 59,567)( 60,566)( 61,565)( 62,564)( 63,563)
( 64,562)( 65,561)( 66,573)( 67,585)( 68,584)( 69,583)( 70,582)( 71,581)
( 72,580)( 73,579)( 74,578)( 75,577)( 76,576)( 77,575)( 78,574)( 79,508)
( 80,520)( 81,519)( 82,518)( 83,517)( 84,516)( 85,515)( 86,514)( 87,513)
( 88,512)( 89,511)( 90,510)( 91,509)( 92,521)( 93,533)( 94,532)( 95,531)
( 96,530)( 97,529)( 98,528)( 99,527)(100,526)(101,525)(102,524)(103,523)
(104,522)(105,534)(106,546)(107,545)(108,544)(109,543)(110,542)(111,541)
(112,540)(113,539)(114,538)(115,537)(116,536)(117,535)(118,586)(119,598)
(120,597)(121,596)(122,595)(123,594)(124,593)(125,592)(126,591)(127,590)
(128,589)(129,588)(130,587)(131,599)(132,611)(133,610)(134,609)(135,608)
(136,607)(137,606)(138,605)(139,604)(140,603)(141,602)(142,601)(143,600)
(144,612)(145,624)(146,623)(147,622)(148,621)(149,620)(150,619)(151,618)
(152,617)(153,616)(154,615)(155,614)(156,613)(157,664)(158,676)(159,675)
(160,674)(161,673)(162,672)(163,671)(164,670)(165,669)(166,668)(167,667)
(168,666)(169,665)(170,677)(171,689)(172,688)(173,687)(174,686)(175,685)
(176,684)(177,683)(178,682)(179,681)(180,680)(181,679)(182,678)(183,690)
(184,702)(185,701)(186,700)(187,699)(188,698)(189,697)(190,696)(191,695)
(192,694)(193,693)(194,692)(195,691)(196,625)(197,637)(198,636)(199,635)
(200,634)(201,633)(202,632)(203,631)(204,630)(205,629)(206,628)(207,627)
(208,626)(209,638)(210,650)(211,649)(212,648)(213,647)(214,646)(215,645)
(216,644)(217,643)(218,642)(219,641)(220,640)(221,639)(222,651)(223,663)
(224,662)(225,661)(226,660)(227,659)(228,658)(229,657)(230,656)(231,655)
(232,654)(233,653)(234,652)(235,820)(236,832)(237,831)(238,830)(239,829)
(240,828)(241,827)(242,826)(243,825)(244,824)(245,823)(246,822)(247,821)
(248,833)(249,845)(250,844)(251,843)(252,842)(253,841)(254,840)(255,839)
(256,838)(257,837)(258,836)(259,835)(260,834)(261,846)(262,858)(263,857)
(264,856)(265,855)(266,854)(267,853)(268,852)(269,851)(270,850)(271,849)
(272,848)(273,847)(274,898)(275,910)(276,909)(277,908)(278,907)(279,906)
(280,905)(281,904)(282,903)(283,902)(284,901)(285,900)(286,899)(287,911)
(288,923)(289,922)(290,921)(291,920)(292,919)(293,918)(294,917)(295,916)
(296,915)(297,914)(298,913)(299,912)(300,924)(301,936)(302,935)(303,934)
(304,933)(305,932)(306,931)(307,930)(308,929)(309,928)(310,927)(311,926)
(312,925)(313,859)(314,871)(315,870)(316,869)(317,868)(318,867)(319,866)
(320,865)(321,864)(322,863)(323,862)(324,861)(325,860)(326,872)(327,884)
(328,883)(329,882)(330,881)(331,880)(332,879)(333,878)(334,877)(335,876)
(336,875)(337,874)(338,873)(339,885)(340,897)(341,896)(342,895)(343,894)
(344,893)(345,892)(346,891)(347,890)(348,889)(349,888)(350,887)(351,886)
(352,703)(353,715)(354,714)(355,713)(356,712)(357,711)(358,710)(359,709)
(360,708)(361,707)(362,706)(363,705)(364,704)(365,716)(366,728)(367,727)
(368,726)(369,725)(370,724)(371,723)(372,722)(373,721)(374,720)(375,719)
(376,718)(377,717)(378,729)(379,741)(380,740)(381,739)(382,738)(383,737)
(384,736)(385,735)(386,734)(387,733)(388,732)(389,731)(390,730)(391,781)
(392,793)(393,792)(394,791)(395,790)(396,789)(397,788)(398,787)(399,786)
(400,785)(401,784)(402,783)(403,782)(404,794)(405,806)(406,805)(407,804)
(408,803)(409,802)(410,801)(411,800)(412,799)(413,798)(414,797)(415,796)
(416,795)(417,807)(418,819)(419,818)(420,817)(421,816)(422,815)(423,814)
(424,813)(425,812)(426,811)(427,810)(428,809)(429,808)(430,742)(431,754)
(432,753)(433,752)(434,751)(435,750)(436,749)(437,748)(438,747)(439,746)
(440,745)(441,744)(442,743)(443,755)(444,767)(445,766)(446,765)(447,764)
(448,763)(449,762)(450,761)(451,760)(452,759)(453,758)(454,757)(455,756)
(456,768)(457,780)(458,779)(459,778)(460,777)(461,776)(462,775)(463,774)
(464,773)(465,772)(466,771)(467,770)(468,769);
s1 := Sym(936)!(  1,743)(  2,742)(  3,754)(  4,753)(  5,752)(  6,751)(  7,750)
(  8,749)(  9,748)( 10,747)( 11,746)( 12,745)( 13,744)( 14,769)( 15,768)
( 16,780)( 17,779)( 18,778)( 19,777)( 20,776)( 21,775)( 22,774)( 23,773)
( 24,772)( 25,771)( 26,770)( 27,756)( 28,755)( 29,767)( 30,766)( 31,765)
( 32,764)( 33,763)( 34,762)( 35,761)( 36,760)( 37,759)( 38,758)( 39,757)
( 40,704)( 41,703)( 42,715)( 43,714)( 44,713)( 45,712)( 46,711)( 47,710)
( 48,709)( 49,708)( 50,707)( 51,706)( 52,705)( 53,730)( 54,729)( 55,741)
( 56,740)( 57,739)( 58,738)( 59,737)( 60,736)( 61,735)( 62,734)( 63,733)
( 64,732)( 65,731)( 66,717)( 67,716)( 68,728)( 69,727)( 70,726)( 71,725)
( 72,724)( 73,723)( 74,722)( 75,721)( 76,720)( 77,719)( 78,718)( 79,782)
( 80,781)( 81,793)( 82,792)( 83,791)( 84,790)( 85,789)( 86,788)( 87,787)
( 88,786)( 89,785)( 90,784)( 91,783)( 92,808)( 93,807)( 94,819)( 95,818)
( 96,817)( 97,816)( 98,815)( 99,814)(100,813)(101,812)(102,811)(103,810)
(104,809)(105,795)(106,794)(107,806)(108,805)(109,804)(110,803)(111,802)
(112,801)(113,800)(114,799)(115,798)(116,797)(117,796)(118,860)(119,859)
(120,871)(121,870)(122,869)(123,868)(124,867)(125,866)(126,865)(127,864)
(128,863)(129,862)(130,861)(131,886)(132,885)(133,897)(134,896)(135,895)
(136,894)(137,893)(138,892)(139,891)(140,890)(141,889)(142,888)(143,887)
(144,873)(145,872)(146,884)(147,883)(148,882)(149,881)(150,880)(151,879)
(152,878)(153,877)(154,876)(155,875)(156,874)(157,821)(158,820)(159,832)
(160,831)(161,830)(162,829)(163,828)(164,827)(165,826)(166,825)(167,824)
(168,823)(169,822)(170,847)(171,846)(172,858)(173,857)(174,856)(175,855)
(176,854)(177,853)(178,852)(179,851)(180,850)(181,849)(182,848)(183,834)
(184,833)(185,845)(186,844)(187,843)(188,842)(189,841)(190,840)(191,839)
(192,838)(193,837)(194,836)(195,835)(196,899)(197,898)(198,910)(199,909)
(200,908)(201,907)(202,906)(203,905)(204,904)(205,903)(206,902)(207,901)
(208,900)(209,925)(210,924)(211,936)(212,935)(213,934)(214,933)(215,932)
(216,931)(217,930)(218,929)(219,928)(220,927)(221,926)(222,912)(223,911)
(224,923)(225,922)(226,921)(227,920)(228,919)(229,918)(230,917)(231,916)
(232,915)(233,914)(234,913)(235,509)(236,508)(237,520)(238,519)(239,518)
(240,517)(241,516)(242,515)(243,514)(244,513)(245,512)(246,511)(247,510)
(248,535)(249,534)(250,546)(251,545)(252,544)(253,543)(254,542)(255,541)
(256,540)(257,539)(258,538)(259,537)(260,536)(261,522)(262,521)(263,533)
(264,532)(265,531)(266,530)(267,529)(268,528)(269,527)(270,526)(271,525)
(272,524)(273,523)(274,470)(275,469)(276,481)(277,480)(278,479)(279,478)
(280,477)(281,476)(282,475)(283,474)(284,473)(285,472)(286,471)(287,496)
(288,495)(289,507)(290,506)(291,505)(292,504)(293,503)(294,502)(295,501)
(296,500)(297,499)(298,498)(299,497)(300,483)(301,482)(302,494)(303,493)
(304,492)(305,491)(306,490)(307,489)(308,488)(309,487)(310,486)(311,485)
(312,484)(313,548)(314,547)(315,559)(316,558)(317,557)(318,556)(319,555)
(320,554)(321,553)(322,552)(323,551)(324,550)(325,549)(326,574)(327,573)
(328,585)(329,584)(330,583)(331,582)(332,581)(333,580)(334,579)(335,578)
(336,577)(337,576)(338,575)(339,561)(340,560)(341,572)(342,571)(343,570)
(344,569)(345,568)(346,567)(347,566)(348,565)(349,564)(350,563)(351,562)
(352,626)(353,625)(354,637)(355,636)(356,635)(357,634)(358,633)(359,632)
(360,631)(361,630)(362,629)(363,628)(364,627)(365,652)(366,651)(367,663)
(368,662)(369,661)(370,660)(371,659)(372,658)(373,657)(374,656)(375,655)
(376,654)(377,653)(378,639)(379,638)(380,650)(381,649)(382,648)(383,647)
(384,646)(385,645)(386,644)(387,643)(388,642)(389,641)(390,640)(391,587)
(392,586)(393,598)(394,597)(395,596)(396,595)(397,594)(398,593)(399,592)
(400,591)(401,590)(402,589)(403,588)(404,613)(405,612)(406,624)(407,623)
(408,622)(409,621)(410,620)(411,619)(412,618)(413,617)(414,616)(415,615)
(416,614)(417,600)(418,599)(419,611)(420,610)(421,609)(422,608)(423,607)
(424,606)(425,605)(426,604)(427,603)(428,602)(429,601)(430,665)(431,664)
(432,676)(433,675)(434,674)(435,673)(436,672)(437,671)(438,670)(439,669)
(440,668)(441,667)(442,666)(443,691)(444,690)(445,702)(446,701)(447,700)
(448,699)(449,698)(450,697)(451,696)(452,695)(453,694)(454,693)(455,692)
(456,678)(457,677)(458,689)(459,688)(460,687)(461,686)(462,685)(463,684)
(464,683)(465,682)(466,681)(467,680)(468,679);
s2 := Sym(936)!(  1,716)(  2,717)(  3,718)(  4,719)(  5,720)(  6,721)(  7,722)
(  8,723)(  9,724)( 10,725)( 11,726)( 12,727)( 13,728)( 14,703)( 15,704)
( 16,705)( 17,706)( 18,707)( 19,708)( 20,709)( 21,710)( 22,711)( 23,712)
( 24,713)( 25,714)( 26,715)( 27,729)( 28,730)( 29,731)( 30,732)( 31,733)
( 32,734)( 33,735)( 34,736)( 35,737)( 36,738)( 37,739)( 38,740)( 39,741)
( 40,794)( 41,795)( 42,796)( 43,797)( 44,798)( 45,799)( 46,800)( 47,801)
( 48,802)( 49,803)( 50,804)( 51,805)( 52,806)( 53,781)( 54,782)( 55,783)
( 56,784)( 57,785)( 58,786)( 59,787)( 60,788)( 61,789)( 62,790)( 63,791)
( 64,792)( 65,793)( 66,807)( 67,808)( 68,809)( 69,810)( 70,811)( 71,812)
( 72,813)( 73,814)( 74,815)( 75,816)( 76,817)( 77,818)( 78,819)( 79,755)
( 80,756)( 81,757)( 82,758)( 83,759)( 84,760)( 85,761)( 86,762)( 87,763)
( 88,764)( 89,765)( 90,766)( 91,767)( 92,742)( 93,743)( 94,744)( 95,745)
( 96,746)( 97,747)( 98,748)( 99,749)(100,750)(101,751)(102,752)(103,753)
(104,754)(105,768)(106,769)(107,770)(108,771)(109,772)(110,773)(111,774)
(112,775)(113,776)(114,777)(115,778)(116,779)(117,780)(118,833)(119,834)
(120,835)(121,836)(122,837)(123,838)(124,839)(125,840)(126,841)(127,842)
(128,843)(129,844)(130,845)(131,820)(132,821)(133,822)(134,823)(135,824)
(136,825)(137,826)(138,827)(139,828)(140,829)(141,830)(142,831)(143,832)
(144,846)(145,847)(146,848)(147,849)(148,850)(149,851)(150,852)(151,853)
(152,854)(153,855)(154,856)(155,857)(156,858)(157,911)(158,912)(159,913)
(160,914)(161,915)(162,916)(163,917)(164,918)(165,919)(166,920)(167,921)
(168,922)(169,923)(170,898)(171,899)(172,900)(173,901)(174,902)(175,903)
(176,904)(177,905)(178,906)(179,907)(180,908)(181,909)(182,910)(183,924)
(184,925)(185,926)(186,927)(187,928)(188,929)(189,930)(190,931)(191,932)
(192,933)(193,934)(194,935)(195,936)(196,872)(197,873)(198,874)(199,875)
(200,876)(201,877)(202,878)(203,879)(204,880)(205,881)(206,882)(207,883)
(208,884)(209,859)(210,860)(211,861)(212,862)(213,863)(214,864)(215,865)
(216,866)(217,867)(218,868)(219,869)(220,870)(221,871)(222,885)(223,886)
(224,887)(225,888)(226,889)(227,890)(228,891)(229,892)(230,893)(231,894)
(232,895)(233,896)(234,897)(235,599)(236,600)(237,601)(238,602)(239,603)
(240,604)(241,605)(242,606)(243,607)(244,608)(245,609)(246,610)(247,611)
(248,586)(249,587)(250,588)(251,589)(252,590)(253,591)(254,592)(255,593)
(256,594)(257,595)(258,596)(259,597)(260,598)(261,612)(262,613)(263,614)
(264,615)(265,616)(266,617)(267,618)(268,619)(269,620)(270,621)(271,622)
(272,623)(273,624)(274,677)(275,678)(276,679)(277,680)(278,681)(279,682)
(280,683)(281,684)(282,685)(283,686)(284,687)(285,688)(286,689)(287,664)
(288,665)(289,666)(290,667)(291,668)(292,669)(293,670)(294,671)(295,672)
(296,673)(297,674)(298,675)(299,676)(300,690)(301,691)(302,692)(303,693)
(304,694)(305,695)(306,696)(307,697)(308,698)(309,699)(310,700)(311,701)
(312,702)(313,638)(314,639)(315,640)(316,641)(317,642)(318,643)(319,644)
(320,645)(321,646)(322,647)(323,648)(324,649)(325,650)(326,625)(327,626)
(328,627)(329,628)(330,629)(331,630)(332,631)(333,632)(334,633)(335,634)
(336,635)(337,636)(338,637)(339,651)(340,652)(341,653)(342,654)(343,655)
(344,656)(345,657)(346,658)(347,659)(348,660)(349,661)(350,662)(351,663)
(352,482)(353,483)(354,484)(355,485)(356,486)(357,487)(358,488)(359,489)
(360,490)(361,491)(362,492)(363,493)(364,494)(365,469)(366,470)(367,471)
(368,472)(369,473)(370,474)(371,475)(372,476)(373,477)(374,478)(375,479)
(376,480)(377,481)(378,495)(379,496)(380,497)(381,498)(382,499)(383,500)
(384,501)(385,502)(386,503)(387,504)(388,505)(389,506)(390,507)(391,560)
(392,561)(393,562)(394,563)(395,564)(396,565)(397,566)(398,567)(399,568)
(400,569)(401,570)(402,571)(403,572)(404,547)(405,548)(406,549)(407,550)
(408,551)(409,552)(410,553)(411,554)(412,555)(413,556)(414,557)(415,558)
(416,559)(417,573)(418,574)(419,575)(420,576)(421,577)(422,578)(423,579)
(424,580)(425,581)(426,582)(427,583)(428,584)(429,585)(430,521)(431,522)
(432,523)(433,524)(434,525)(435,526)(436,527)(437,528)(438,529)(439,530)
(440,531)(441,532)(442,533)(443,508)(444,509)(445,510)(446,511)(447,512)
(448,513)(449,514)(450,515)(451,516)(452,517)(453,518)(454,519)(455,520)
(456,534)(457,535)(458,536)(459,537)(460,538)(461,539)(462,540)(463,541)
(464,542)(465,543)(466,544)(467,545)(468,546);
poly := sub<Sym(936)|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*s2*s1*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*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*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*s0*s1 >;

References : None.
to this polytope