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