Polytope of Type {12,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12}*1728y
if this polytope has a name.
Group : SmallGroup(1728,46356)
Rank : 3
Schlafli Type : {12,12}
Number of vertices, edges, etc : 72, 432, 72
Order of s₀s₁s₂ : 6
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 : {12,12}*576i, {12,12}*576k
   6-fold quotients : {12,6}*288a, {12,6}*288b
   8-fold quotients : {6,6}*216d
   9-fold quotients : {4,12}*192c
   12-fold quotients : {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 : {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
   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 := (  1,253)(  2,256)(  3,255)(  4,254)(  5,257)(  6,260)(  7,259)(  8,258)
(  9,261)( 10,264)( 11,263)( 12,262)( 13,277)( 14,280)( 15,279)( 16,278)
( 17,281)( 18,284)( 19,283)( 20,282)( 21,285)( 22,288)( 23,287)( 24,286)
( 25,265)( 26,268)( 27,267)( 28,266)( 29,269)( 30,272)( 31,271)( 32,270)
( 33,273)( 34,276)( 35,275)( 36,274)( 37,217)( 38,220)( 39,219)( 40,218)
( 41,221)( 42,224)( 43,223)( 44,222)( 45,225)( 46,228)( 47,227)( 48,226)
( 49,241)( 50,244)( 51,243)( 52,242)( 53,245)( 54,248)( 55,247)( 56,246)
( 57,249)( 58,252)( 59,251)( 60,250)( 61,229)( 62,232)( 63,231)( 64,230)
( 65,233)( 66,236)( 67,235)( 68,234)( 69,237)( 70,240)( 71,239)( 72,238)
( 73,289)( 74,292)( 75,291)( 76,290)( 77,293)( 78,296)( 79,295)( 80,294)
( 81,297)( 82,300)( 83,299)( 84,298)( 85,313)( 86,316)( 87,315)( 88,314)
( 89,317)( 90,320)( 91,319)( 92,318)( 93,321)( 94,324)( 95,323)( 96,322)
( 97,301)( 98,304)( 99,303)(100,302)(101,305)(102,308)(103,307)(104,306)
(105,309)(106,312)(107,311)(108,310)(109,361)(110,364)(111,363)(112,362)
(113,365)(114,368)(115,367)(116,366)(117,369)(118,372)(119,371)(120,370)
(121,385)(122,388)(123,387)(124,386)(125,389)(126,392)(127,391)(128,390)
(129,393)(130,396)(131,395)(132,394)(133,373)(134,376)(135,375)(136,374)
(137,377)(138,380)(139,379)(140,378)(141,381)(142,384)(143,383)(144,382)
(145,325)(146,328)(147,327)(148,326)(149,329)(150,332)(151,331)(152,330)
(153,333)(154,336)(155,335)(156,334)(157,349)(158,352)(159,351)(160,350)
(161,353)(162,356)(163,355)(164,354)(165,357)(166,360)(167,359)(168,358)
(169,337)(170,340)(171,339)(172,338)(173,341)(174,344)(175,343)(176,342)
(177,345)(178,348)(179,347)(180,346)(181,397)(182,400)(183,399)(184,398)
(185,401)(186,404)(187,403)(188,402)(189,405)(190,408)(191,407)(192,406)
(193,421)(194,424)(195,423)(196,422)(197,425)(198,428)(199,427)(200,426)
(201,429)(202,432)(203,431)(204,430)(205,409)(206,412)(207,411)(208,410)
(209,413)(210,416)(211,415)(212,414)(213,417)(214,420)(215,419)(216,418)
(433,793)(434,796)(435,795)(436,794)(437,797)(438,800)(439,799)(440,798)
(441,801)(442,804)(443,803)(444,802)(445,817)(446,820)(447,819)(448,818)
(449,821)(450,824)(451,823)(452,822)(453,825)(454,828)(455,827)(456,826)
(457,805)(458,808)(459,807)(460,806)(461,809)(462,812)(463,811)(464,810)
(465,813)(466,816)(467,815)(468,814)(469,757)(470,760)(471,759)(472,758)
(473,761)(474,764)(475,763)(476,762)(477,765)(478,768)(479,767)(480,766)
(481,781)(482,784)(483,783)(484,782)(485,785)(486,788)(487,787)(488,786)
(489,789)(490,792)(491,791)(492,790)(493,769)(494,772)(495,771)(496,770)
(497,773)(498,776)(499,775)(500,774)(501,777)(502,780)(503,779)(504,778)
(505,829)(506,832)(507,831)(508,830)(509,833)(510,836)(511,835)(512,834)
(513,837)(514,840)(515,839)(516,838)(517,853)(518,856)(519,855)(520,854)
(521,857)(522,860)(523,859)(524,858)(525,861)(526,864)(527,863)(528,862)
(529,841)(530,844)(531,843)(532,842)(533,845)(534,848)(535,847)(536,846)
(537,849)(538,852)(539,851)(540,850)(541,685)(542,688)(543,687)(544,686)
(545,689)(546,692)(547,691)(548,690)(549,693)(550,696)(551,695)(552,694)
(553,709)(554,712)(555,711)(556,710)(557,713)(558,716)(559,715)(560,714)
(561,717)(562,720)(563,719)(564,718)(565,697)(566,700)(567,699)(568,698)
(569,701)(570,704)(571,703)(572,702)(573,705)(574,708)(575,707)(576,706)
(577,649)(578,652)(579,651)(580,650)(581,653)(582,656)(583,655)(584,654)
(585,657)(586,660)(587,659)(588,658)(589,673)(590,676)(591,675)(592,674)
(593,677)(594,680)(595,679)(596,678)(597,681)(598,684)(599,683)(600,682)
(601,661)(602,664)(603,663)(604,662)(605,665)(606,668)(607,667)(608,666)
(609,669)(610,672)(611,671)(612,670)(613,721)(614,724)(615,723)(616,722)
(617,725)(618,728)(619,727)(620,726)(621,729)(622,732)(623,731)(624,730)
(625,745)(626,748)(627,747)(628,746)(629,749)(630,752)(631,751)(632,750)
(633,753)(634,756)(635,755)(636,754)(637,733)(638,736)(639,735)(640,734)
(641,737)(642,740)(643,739)(644,738)(645,741)(646,744)(647,743)(648,742);;
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, s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*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 ];;
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)!(  1,253)(  2,256)(  3,255)(  4,254)(  5,257)(  6,260)(  7,259)
(  8,258)(  9,261)( 10,264)( 11,263)( 12,262)( 13,277)( 14,280)( 15,279)
( 16,278)( 17,281)( 18,284)( 19,283)( 20,282)( 21,285)( 22,288)( 23,287)
( 24,286)( 25,265)( 26,268)( 27,267)( 28,266)( 29,269)( 30,272)( 31,271)
( 32,270)( 33,273)( 34,276)( 35,275)( 36,274)( 37,217)( 38,220)( 39,219)
( 40,218)( 41,221)( 42,224)( 43,223)( 44,222)( 45,225)( 46,228)( 47,227)
( 48,226)( 49,241)( 50,244)( 51,243)( 52,242)( 53,245)( 54,248)( 55,247)
( 56,246)( 57,249)( 58,252)( 59,251)( 60,250)( 61,229)( 62,232)( 63,231)
( 64,230)( 65,233)( 66,236)( 67,235)( 68,234)( 69,237)( 70,240)( 71,239)
( 72,238)( 73,289)( 74,292)( 75,291)( 76,290)( 77,293)( 78,296)( 79,295)
( 80,294)( 81,297)( 82,300)( 83,299)( 84,298)( 85,313)( 86,316)( 87,315)
( 88,314)( 89,317)( 90,320)( 91,319)( 92,318)( 93,321)( 94,324)( 95,323)
( 96,322)( 97,301)( 98,304)( 99,303)(100,302)(101,305)(102,308)(103,307)
(104,306)(105,309)(106,312)(107,311)(108,310)(109,361)(110,364)(111,363)
(112,362)(113,365)(114,368)(115,367)(116,366)(117,369)(118,372)(119,371)
(120,370)(121,385)(122,388)(123,387)(124,386)(125,389)(126,392)(127,391)
(128,390)(129,393)(130,396)(131,395)(132,394)(133,373)(134,376)(135,375)
(136,374)(137,377)(138,380)(139,379)(140,378)(141,381)(142,384)(143,383)
(144,382)(145,325)(146,328)(147,327)(148,326)(149,329)(150,332)(151,331)
(152,330)(153,333)(154,336)(155,335)(156,334)(157,349)(158,352)(159,351)
(160,350)(161,353)(162,356)(163,355)(164,354)(165,357)(166,360)(167,359)
(168,358)(169,337)(170,340)(171,339)(172,338)(173,341)(174,344)(175,343)
(176,342)(177,345)(178,348)(179,347)(180,346)(181,397)(182,400)(183,399)
(184,398)(185,401)(186,404)(187,403)(188,402)(189,405)(190,408)(191,407)
(192,406)(193,421)(194,424)(195,423)(196,422)(197,425)(198,428)(199,427)
(200,426)(201,429)(202,432)(203,431)(204,430)(205,409)(206,412)(207,411)
(208,410)(209,413)(210,416)(211,415)(212,414)(213,417)(214,420)(215,419)
(216,418)(433,793)(434,796)(435,795)(436,794)(437,797)(438,800)(439,799)
(440,798)(441,801)(442,804)(443,803)(444,802)(445,817)(446,820)(447,819)
(448,818)(449,821)(450,824)(451,823)(452,822)(453,825)(454,828)(455,827)
(456,826)(457,805)(458,808)(459,807)(460,806)(461,809)(462,812)(463,811)
(464,810)(465,813)(466,816)(467,815)(468,814)(469,757)(470,760)(471,759)
(472,758)(473,761)(474,764)(475,763)(476,762)(477,765)(478,768)(479,767)
(480,766)(481,781)(482,784)(483,783)(484,782)(485,785)(486,788)(487,787)
(488,786)(489,789)(490,792)(491,791)(492,790)(493,769)(494,772)(495,771)
(496,770)(497,773)(498,776)(499,775)(500,774)(501,777)(502,780)(503,779)
(504,778)(505,829)(506,832)(507,831)(508,830)(509,833)(510,836)(511,835)
(512,834)(513,837)(514,840)(515,839)(516,838)(517,853)(518,856)(519,855)
(520,854)(521,857)(522,860)(523,859)(524,858)(525,861)(526,864)(527,863)
(528,862)(529,841)(530,844)(531,843)(532,842)(533,845)(534,848)(535,847)
(536,846)(537,849)(538,852)(539,851)(540,850)(541,685)(542,688)(543,687)
(544,686)(545,689)(546,692)(547,691)(548,690)(549,693)(550,696)(551,695)
(552,694)(553,709)(554,712)(555,711)(556,710)(557,713)(558,716)(559,715)
(560,714)(561,717)(562,720)(563,719)(564,718)(565,697)(566,700)(567,699)
(568,698)(569,701)(570,704)(571,703)(572,702)(573,705)(574,708)(575,707)
(576,706)(577,649)(578,652)(579,651)(580,650)(581,653)(582,656)(583,655)
(584,654)(585,657)(586,660)(587,659)(588,658)(589,673)(590,676)(591,675)
(592,674)(593,677)(594,680)(595,679)(596,678)(597,681)(598,684)(599,683)
(600,682)(601,661)(602,664)(603,663)(604,662)(605,665)(606,668)(607,667)
(608,666)(609,669)(610,672)(611,671)(612,670)(613,721)(614,724)(615,723)
(616,722)(617,725)(618,728)(619,727)(620,726)(621,729)(622,732)(623,731)
(624,730)(625,745)(626,748)(627,747)(628,746)(629,749)(630,752)(631,751)
(632,750)(633,753)(634,756)(635,755)(636,754)(637,733)(638,736)(639,735)
(640,734)(641,737)(642,740)(643,739)(644,738)(645,741)(646,744)(647,743)
(648,742);
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, s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*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 >;

References : None.
to this polytope