Polytope of Type {6,156}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope