Polytope of Type {12,6,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,12}*1728e
if this polytope has a name.
Group : SmallGroup(1728,36999)
Rank : 4
Schlafli Type : {12,6,12}
Number of vertices, edges, etc : 12, 36, 36, 12
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
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 : {6,6,12}*864c, {12,6,6}*864e
3-fold quotients : {12,2,12}*576, {4,6,12}*576b
4-fold quotients : {12,6,3}*432b, {6,6,6}*432c
6-fold quotients : {2,6,12}*288b, {6,2,12}*288, {12,2,6}*288, {4,6,6}*288c
8-fold quotients : {6,6,3}*216b
9-fold quotients : {4,2,12}*192, {12,2,4}*192
12-fold quotients : {3,2,12}*144, {12,2,3}*144, {4,6,3}*144, {2,6,6}*144b, {6,2,6}*144
18-fold quotients : {2,2,12}*96, {12,2,2}*96, {4,2,6}*96, {6,2,4}*96
24-fold quotients : {2,6,3}*72, {3,2,6}*72, {6,2,3}*72
27-fold quotients : {4,2,4}*64
36-fold quotients : {3,2,4}*48, {4,2,3}*48, {2,2,6}*48, {6,2,2}*48
48-fold quotients : {3,2,3}*36
54-fold quotients : {2,2,4}*32, {4,2,2}*32
72-fold quotients : {2,2,3}*24, {3,2,2}*24
108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 4, 7)( 5, 8)( 6, 9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)( 23, 26)
( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)( 49, 52)
( 50, 53)( 51, 54)( 58, 61)( 59, 62)( 60, 63)( 67, 70)( 68, 71)( 69, 72)
( 76, 79)( 77, 80)( 78, 81)( 85, 88)( 86, 89)( 87, 90)( 94, 97)( 95, 98)
( 96, 99)(103,106)(104,107)(105,108)(112,115)(113,116)(114,117)(121,124)
(122,125)(123,126)(130,133)(131,134)(132,135)(139,142)(140,143)(141,144)
(148,151)(149,152)(150,153)(157,160)(158,161)(159,162)(166,169)(167,170)
(168,171)(175,178)(176,179)(177,180)(184,187)(185,188)(186,189)(193,196)
(194,197)(195,198)(202,205)(203,206)(204,207)(211,214)(212,215)(213,216)
(217,244)(218,245)(219,246)(220,250)(221,251)(222,252)(223,247)(224,248)
(225,249)(226,253)(227,254)(228,255)(229,259)(230,260)(231,261)(232,256)
(233,257)(234,258)(235,262)(236,263)(237,264)(238,268)(239,269)(240,270)
(241,265)(242,266)(243,267)(271,298)(272,299)(273,300)(274,304)(275,305)
(276,306)(277,301)(278,302)(279,303)(280,307)(281,308)(282,309)(283,313)
(284,314)(285,315)(286,310)(287,311)(288,312)(289,316)(290,317)(291,318)
(292,322)(293,323)(294,324)(295,319)(296,320)(297,321)(325,352)(326,353)
(327,354)(328,358)(329,359)(330,360)(331,355)(332,356)(333,357)(334,361)
(335,362)(336,363)(337,367)(338,368)(339,369)(340,364)(341,365)(342,366)
(343,370)(344,371)(345,372)(346,376)(347,377)(348,378)(349,373)(350,374)
(351,375)(379,406)(380,407)(381,408)(382,412)(383,413)(384,414)(385,409)
(386,410)(387,411)(388,415)(389,416)(390,417)(391,421)(392,422)(393,423)
(394,418)(395,419)(396,420)(397,424)(398,425)(399,426)(400,430)(401,431)
(402,432)(403,427)(404,428)(405,429)(433,460)(434,461)(435,462)(436,466)
(437,467)(438,468)(439,463)(440,464)(441,465)(442,469)(443,470)(444,471)
(445,475)(446,476)(447,477)(448,472)(449,473)(450,474)(451,478)(452,479)
(453,480)(454,484)(455,485)(456,486)(457,481)(458,482)(459,483)(487,514)
(488,515)(489,516)(490,520)(491,521)(492,522)(493,517)(494,518)(495,519)
(496,523)(497,524)(498,525)(499,529)(500,530)(501,531)(502,526)(503,527)
(504,528)(505,532)(506,533)(507,534)(508,538)(509,539)(510,540)(511,535)
(512,536)(513,537)(541,568)(542,569)(543,570)(544,574)(545,575)(546,576)
(547,571)(548,572)(549,573)(550,577)(551,578)(552,579)(553,583)(554,584)
(555,585)(556,580)(557,581)(558,582)(559,586)(560,587)(561,588)(562,592)
(563,593)(564,594)(565,589)(566,590)(567,591)(595,622)(596,623)(597,624)
(598,628)(599,629)(600,630)(601,625)(602,626)(603,627)(604,631)(605,632)
(606,633)(607,637)(608,638)(609,639)(610,634)(611,635)(612,636)(613,640)
(614,641)(615,642)(616,646)(617,647)(618,648)(619,643)(620,644)(621,645)
(652,655)(653,656)(654,657)(661,664)(662,665)(663,666)(670,673)(671,674)
(672,675)(679,682)(680,683)(681,684)(688,691)(689,692)(690,693)(697,700)
(698,701)(699,702)(706,709)(707,710)(708,711)(715,718)(716,719)(717,720)
(724,727)(725,728)(726,729)(733,736)(734,737)(735,738)(742,745)(743,746)
(744,747)(751,754)(752,755)(753,756)(760,763)(761,764)(762,765)(769,772)
(770,773)(771,774)(778,781)(779,782)(780,783)(787,790)(788,791)(789,792)
(796,799)(797,800)(798,801)(805,808)(806,809)(807,810)(814,817)(815,818)
(816,819)(823,826)(824,827)(825,828)(832,835)(833,836)(834,837)(841,844)
(842,845)(843,846)(850,853)(851,854)(852,855)(859,862)(860,863)(861,864);;
s1 := ( 1,436)( 2,437)( 3,438)( 4,433)( 5,434)( 6,435)( 7,439)( 8,440)
( 9,441)( 10,454)( 11,455)( 12,456)( 13,451)( 14,452)( 15,453)( 16,457)
( 17,458)( 18,459)( 19,445)( 20,446)( 21,447)( 22,442)( 23,443)( 24,444)
( 25,448)( 26,449)( 27,450)( 28,463)( 29,464)( 30,465)( 31,460)( 32,461)
( 33,462)( 34,466)( 35,467)( 36,468)( 37,481)( 38,482)( 39,483)( 40,478)
( 41,479)( 42,480)( 43,484)( 44,485)( 45,486)( 46,472)( 47,473)( 48,474)
( 49,469)( 50,470)( 51,471)( 52,475)( 53,476)( 54,477)( 55,490)( 56,491)
( 57,492)( 58,487)( 59,488)( 60,489)( 61,493)( 62,494)( 63,495)( 64,508)
( 65,509)( 66,510)( 67,505)( 68,506)( 69,507)( 70,511)( 71,512)( 72,513)
( 73,499)( 74,500)( 75,501)( 76,496)( 77,497)( 78,498)( 79,502)( 80,503)
( 81,504)( 82,517)( 83,518)( 84,519)( 85,514)( 86,515)( 87,516)( 88,520)
( 89,521)( 90,522)( 91,535)( 92,536)( 93,537)( 94,532)( 95,533)( 96,534)
( 97,538)( 98,539)( 99,540)(100,526)(101,527)(102,528)(103,523)(104,524)
(105,525)(106,529)(107,530)(108,531)(109,544)(110,545)(111,546)(112,541)
(113,542)(114,543)(115,547)(116,548)(117,549)(118,562)(119,563)(120,564)
(121,559)(122,560)(123,561)(124,565)(125,566)(126,567)(127,553)(128,554)
(129,555)(130,550)(131,551)(132,552)(133,556)(134,557)(135,558)(136,571)
(137,572)(138,573)(139,568)(140,569)(141,570)(142,574)(143,575)(144,576)
(145,589)(146,590)(147,591)(148,586)(149,587)(150,588)(151,592)(152,593)
(153,594)(154,580)(155,581)(156,582)(157,577)(158,578)(159,579)(160,583)
(161,584)(162,585)(163,598)(164,599)(165,600)(166,595)(167,596)(168,597)
(169,601)(170,602)(171,603)(172,616)(173,617)(174,618)(175,613)(176,614)
(177,615)(178,619)(179,620)(180,621)(181,607)(182,608)(183,609)(184,604)
(185,605)(186,606)(187,610)(188,611)(189,612)(190,625)(191,626)(192,627)
(193,622)(194,623)(195,624)(196,628)(197,629)(198,630)(199,643)(200,644)
(201,645)(202,640)(203,641)(204,642)(205,646)(206,647)(207,648)(208,634)
(209,635)(210,636)(211,631)(212,632)(213,633)(214,637)(215,638)(216,639)
(217,679)(218,680)(219,681)(220,676)(221,677)(222,678)(223,682)(224,683)
(225,684)(226,697)(227,698)(228,699)(229,694)(230,695)(231,696)(232,700)
(233,701)(234,702)(235,688)(236,689)(237,690)(238,685)(239,686)(240,687)
(241,691)(242,692)(243,693)(244,652)(245,653)(246,654)(247,649)(248,650)
(249,651)(250,655)(251,656)(252,657)(253,670)(254,671)(255,672)(256,667)
(257,668)(258,669)(259,673)(260,674)(261,675)(262,661)(263,662)(264,663)
(265,658)(266,659)(267,660)(268,664)(269,665)(270,666)(271,733)(272,734)
(273,735)(274,730)(275,731)(276,732)(277,736)(278,737)(279,738)(280,751)
(281,752)(282,753)(283,748)(284,749)(285,750)(286,754)(287,755)(288,756)
(289,742)(290,743)(291,744)(292,739)(293,740)(294,741)(295,745)(296,746)
(297,747)(298,706)(299,707)(300,708)(301,703)(302,704)(303,705)(304,709)
(305,710)(306,711)(307,724)(308,725)(309,726)(310,721)(311,722)(312,723)
(313,727)(314,728)(315,729)(316,715)(317,716)(318,717)(319,712)(320,713)
(321,714)(322,718)(323,719)(324,720)(325,787)(326,788)(327,789)(328,784)
(329,785)(330,786)(331,790)(332,791)(333,792)(334,805)(335,806)(336,807)
(337,802)(338,803)(339,804)(340,808)(341,809)(342,810)(343,796)(344,797)
(345,798)(346,793)(347,794)(348,795)(349,799)(350,800)(351,801)(352,760)
(353,761)(354,762)(355,757)(356,758)(357,759)(358,763)(359,764)(360,765)
(361,778)(362,779)(363,780)(364,775)(365,776)(366,777)(367,781)(368,782)
(369,783)(370,769)(371,770)(372,771)(373,766)(374,767)(375,768)(376,772)
(377,773)(378,774)(379,841)(380,842)(381,843)(382,838)(383,839)(384,840)
(385,844)(386,845)(387,846)(388,859)(389,860)(390,861)(391,856)(392,857)
(393,858)(394,862)(395,863)(396,864)(397,850)(398,851)(399,852)(400,847)
(401,848)(402,849)(403,853)(404,854)(405,855)(406,814)(407,815)(408,816)
(409,811)(410,812)(411,813)(412,817)(413,818)(414,819)(415,832)(416,833)
(417,834)(418,829)(419,830)(420,831)(421,835)(422,836)(423,837)(424,823)
(425,824)(426,825)(427,820)(428,821)(429,822)(430,826)(431,827)(432,828);;
s2 := ( 1,658)( 2,660)( 3,659)( 4,661)( 5,663)( 6,662)( 7,664)( 8,666)
( 9,665)( 10,649)( 11,651)( 12,650)( 13,652)( 14,654)( 15,653)( 16,655)
( 17,657)( 18,656)( 19,667)( 20,669)( 21,668)( 22,670)( 23,672)( 24,671)
( 25,673)( 26,675)( 27,674)( 28,685)( 29,687)( 30,686)( 31,688)( 32,690)
( 33,689)( 34,691)( 35,693)( 36,692)( 37,676)( 38,678)( 39,677)( 40,679)
( 41,681)( 42,680)( 43,682)( 44,684)( 45,683)( 46,694)( 47,696)( 48,695)
( 49,697)( 50,699)( 51,698)( 52,700)( 53,702)( 54,701)( 55,712)( 56,714)
( 57,713)( 58,715)( 59,717)( 60,716)( 61,718)( 62,720)( 63,719)( 64,703)
( 65,705)( 66,704)( 67,706)( 68,708)( 69,707)( 70,709)( 71,711)( 72,710)
( 73,721)( 74,723)( 75,722)( 76,724)( 77,726)( 78,725)( 79,727)( 80,729)
( 81,728)( 82,739)( 83,741)( 84,740)( 85,742)( 86,744)( 87,743)( 88,745)
( 89,747)( 90,746)( 91,730)( 92,732)( 93,731)( 94,733)( 95,735)( 96,734)
( 97,736)( 98,738)( 99,737)(100,748)(101,750)(102,749)(103,751)(104,753)
(105,752)(106,754)(107,756)(108,755)(109,820)(110,822)(111,821)(112,823)
(113,825)(114,824)(115,826)(116,828)(117,827)(118,811)(119,813)(120,812)
(121,814)(122,816)(123,815)(124,817)(125,819)(126,818)(127,829)(128,831)
(129,830)(130,832)(131,834)(132,833)(133,835)(134,837)(135,836)(136,847)
(137,849)(138,848)(139,850)(140,852)(141,851)(142,853)(143,855)(144,854)
(145,838)(146,840)(147,839)(148,841)(149,843)(150,842)(151,844)(152,846)
(153,845)(154,856)(155,858)(156,857)(157,859)(158,861)(159,860)(160,862)
(161,864)(162,863)(163,766)(164,768)(165,767)(166,769)(167,771)(168,770)
(169,772)(170,774)(171,773)(172,757)(173,759)(174,758)(175,760)(176,762)
(177,761)(178,763)(179,765)(180,764)(181,775)(182,777)(183,776)(184,778)
(185,780)(186,779)(187,781)(188,783)(189,782)(190,793)(191,795)(192,794)
(193,796)(194,798)(195,797)(196,799)(197,801)(198,800)(199,784)(200,786)
(201,785)(202,787)(203,789)(204,788)(205,790)(206,792)(207,791)(208,802)
(209,804)(210,803)(211,805)(212,807)(213,806)(214,808)(215,810)(216,809)
(217,469)(218,471)(219,470)(220,472)(221,474)(222,473)(223,475)(224,477)
(225,476)(226,460)(227,462)(228,461)(229,463)(230,465)(231,464)(232,466)
(233,468)(234,467)(235,478)(236,480)(237,479)(238,481)(239,483)(240,482)
(241,484)(242,486)(243,485)(244,442)(245,444)(246,443)(247,445)(248,447)
(249,446)(250,448)(251,450)(252,449)(253,433)(254,435)(255,434)(256,436)
(257,438)(258,437)(259,439)(260,441)(261,440)(262,451)(263,453)(264,452)
(265,454)(266,456)(267,455)(268,457)(269,459)(270,458)(271,523)(272,525)
(273,524)(274,526)(275,528)(276,527)(277,529)(278,531)(279,530)(280,514)
(281,516)(282,515)(283,517)(284,519)(285,518)(286,520)(287,522)(288,521)
(289,532)(290,534)(291,533)(292,535)(293,537)(294,536)(295,538)(296,540)
(297,539)(298,496)(299,498)(300,497)(301,499)(302,501)(303,500)(304,502)
(305,504)(306,503)(307,487)(308,489)(309,488)(310,490)(311,492)(312,491)
(313,493)(314,495)(315,494)(316,505)(317,507)(318,506)(319,508)(320,510)
(321,509)(322,511)(323,513)(324,512)(325,631)(326,633)(327,632)(328,634)
(329,636)(330,635)(331,637)(332,639)(333,638)(334,622)(335,624)(336,623)
(337,625)(338,627)(339,626)(340,628)(341,630)(342,629)(343,640)(344,642)
(345,641)(346,643)(347,645)(348,644)(349,646)(350,648)(351,647)(352,604)
(353,606)(354,605)(355,607)(356,609)(357,608)(358,610)(359,612)(360,611)
(361,595)(362,597)(363,596)(364,598)(365,600)(366,599)(367,601)(368,603)
(369,602)(370,613)(371,615)(372,614)(373,616)(374,618)(375,617)(376,619)
(377,621)(378,620)(379,577)(380,579)(381,578)(382,580)(383,582)(384,581)
(385,583)(386,585)(387,584)(388,568)(389,570)(390,569)(391,571)(392,573)
(393,572)(394,574)(395,576)(396,575)(397,586)(398,588)(399,587)(400,589)
(401,591)(402,590)(403,592)(404,594)(405,593)(406,550)(407,552)(408,551)
(409,553)(410,555)(411,554)(412,556)(413,558)(414,557)(415,541)(416,543)
(417,542)(418,544)(419,546)(420,545)(421,547)(422,549)(423,548)(424,559)
(425,561)(426,560)(427,562)(428,564)(429,563)(430,565)(431,567)(432,566);;
s3 := ( 1,758)( 2,757)( 3,759)( 4,761)( 5,760)( 6,762)( 7,764)( 8,763)
( 9,765)( 10,776)( 11,775)( 12,777)( 13,779)( 14,778)( 15,780)( 16,782)
( 17,781)( 18,783)( 19,767)( 20,766)( 21,768)( 22,770)( 23,769)( 24,771)
( 25,773)( 26,772)( 27,774)( 28,785)( 29,784)( 30,786)( 31,788)( 32,787)
( 33,789)( 34,791)( 35,790)( 36,792)( 37,803)( 38,802)( 39,804)( 40,806)
( 41,805)( 42,807)( 43,809)( 44,808)( 45,810)( 46,794)( 47,793)( 48,795)
( 49,797)( 50,796)( 51,798)( 52,800)( 53,799)( 54,801)( 55,812)( 56,811)
( 57,813)( 58,815)( 59,814)( 60,816)( 61,818)( 62,817)( 63,819)( 64,830)
( 65,829)( 66,831)( 67,833)( 68,832)( 69,834)( 70,836)( 71,835)( 72,837)
( 73,821)( 74,820)( 75,822)( 76,824)( 77,823)( 78,825)( 79,827)( 80,826)
( 81,828)( 82,839)( 83,838)( 84,840)( 85,842)( 86,841)( 87,843)( 88,845)
( 89,844)( 90,846)( 91,857)( 92,856)( 93,858)( 94,860)( 95,859)( 96,861)
( 97,863)( 98,862)( 99,864)(100,848)(101,847)(102,849)(103,851)(104,850)
(105,852)(106,854)(107,853)(108,855)(109,650)(110,649)(111,651)(112,653)
(113,652)(114,654)(115,656)(116,655)(117,657)(118,668)(119,667)(120,669)
(121,671)(122,670)(123,672)(124,674)(125,673)(126,675)(127,659)(128,658)
(129,660)(130,662)(131,661)(132,663)(133,665)(134,664)(135,666)(136,677)
(137,676)(138,678)(139,680)(140,679)(141,681)(142,683)(143,682)(144,684)
(145,695)(146,694)(147,696)(148,698)(149,697)(150,699)(151,701)(152,700)
(153,702)(154,686)(155,685)(156,687)(157,689)(158,688)(159,690)(160,692)
(161,691)(162,693)(163,704)(164,703)(165,705)(166,707)(167,706)(168,708)
(169,710)(170,709)(171,711)(172,722)(173,721)(174,723)(175,725)(176,724)
(177,726)(178,728)(179,727)(180,729)(181,713)(182,712)(183,714)(184,716)
(185,715)(186,717)(187,719)(188,718)(189,720)(190,731)(191,730)(192,732)
(193,734)(194,733)(195,735)(196,737)(197,736)(198,738)(199,749)(200,748)
(201,750)(202,752)(203,751)(204,753)(205,755)(206,754)(207,756)(208,740)
(209,739)(210,741)(211,743)(212,742)(213,744)(214,746)(215,745)(216,747)
(217,569)(218,568)(219,570)(220,572)(221,571)(222,573)(223,575)(224,574)
(225,576)(226,587)(227,586)(228,588)(229,590)(230,589)(231,591)(232,593)
(233,592)(234,594)(235,578)(236,577)(237,579)(238,581)(239,580)(240,582)
(241,584)(242,583)(243,585)(244,542)(245,541)(246,543)(247,545)(248,544)
(249,546)(250,548)(251,547)(252,549)(253,560)(254,559)(255,561)(256,563)
(257,562)(258,564)(259,566)(260,565)(261,567)(262,551)(263,550)(264,552)
(265,554)(266,553)(267,555)(268,557)(269,556)(270,558)(271,623)(272,622)
(273,624)(274,626)(275,625)(276,627)(277,629)(278,628)(279,630)(280,641)
(281,640)(282,642)(283,644)(284,643)(285,645)(286,647)(287,646)(288,648)
(289,632)(290,631)(291,633)(292,635)(293,634)(294,636)(295,638)(296,637)
(297,639)(298,596)(299,595)(300,597)(301,599)(302,598)(303,600)(304,602)
(305,601)(306,603)(307,614)(308,613)(309,615)(310,617)(311,616)(312,618)
(313,620)(314,619)(315,621)(316,605)(317,604)(318,606)(319,608)(320,607)
(321,609)(322,611)(323,610)(324,612)(325,461)(326,460)(327,462)(328,464)
(329,463)(330,465)(331,467)(332,466)(333,468)(334,479)(335,478)(336,480)
(337,482)(338,481)(339,483)(340,485)(341,484)(342,486)(343,470)(344,469)
(345,471)(346,473)(347,472)(348,474)(349,476)(350,475)(351,477)(352,434)
(353,433)(354,435)(355,437)(356,436)(357,438)(358,440)(359,439)(360,441)
(361,452)(362,451)(363,453)(364,455)(365,454)(366,456)(367,458)(368,457)
(369,459)(370,443)(371,442)(372,444)(373,446)(374,445)(375,447)(376,449)
(377,448)(378,450)(379,515)(380,514)(381,516)(382,518)(383,517)(384,519)
(385,521)(386,520)(387,522)(388,533)(389,532)(390,534)(391,536)(392,535)
(393,537)(394,539)(395,538)(396,540)(397,524)(398,523)(399,525)(400,527)
(401,526)(402,528)(403,530)(404,529)(405,531)(406,488)(407,487)(408,489)
(409,491)(410,490)(411,492)(412,494)(413,493)(414,495)(415,506)(416,505)
(417,507)(418,509)(419,508)(420,510)(421,512)(422,511)(423,513)(424,497)
(425,496)(426,498)(427,500)(428,499)(429,501)(430,503)(431,502)(432,504);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 4, 7)( 5, 8)( 6, 9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)
( 23, 26)( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)
( 49, 52)( 50, 53)( 51, 54)( 58, 61)( 59, 62)( 60, 63)( 67, 70)( 68, 71)
( 69, 72)( 76, 79)( 77, 80)( 78, 81)( 85, 88)( 86, 89)( 87, 90)( 94, 97)
( 95, 98)( 96, 99)(103,106)(104,107)(105,108)(112,115)(113,116)(114,117)
(121,124)(122,125)(123,126)(130,133)(131,134)(132,135)(139,142)(140,143)
(141,144)(148,151)(149,152)(150,153)(157,160)(158,161)(159,162)(166,169)
(167,170)(168,171)(175,178)(176,179)(177,180)(184,187)(185,188)(186,189)
(193,196)(194,197)(195,198)(202,205)(203,206)(204,207)(211,214)(212,215)
(213,216)(217,244)(218,245)(219,246)(220,250)(221,251)(222,252)(223,247)
(224,248)(225,249)(226,253)(227,254)(228,255)(229,259)(230,260)(231,261)
(232,256)(233,257)(234,258)(235,262)(236,263)(237,264)(238,268)(239,269)
(240,270)(241,265)(242,266)(243,267)(271,298)(272,299)(273,300)(274,304)
(275,305)(276,306)(277,301)(278,302)(279,303)(280,307)(281,308)(282,309)
(283,313)(284,314)(285,315)(286,310)(287,311)(288,312)(289,316)(290,317)
(291,318)(292,322)(293,323)(294,324)(295,319)(296,320)(297,321)(325,352)
(326,353)(327,354)(328,358)(329,359)(330,360)(331,355)(332,356)(333,357)
(334,361)(335,362)(336,363)(337,367)(338,368)(339,369)(340,364)(341,365)
(342,366)(343,370)(344,371)(345,372)(346,376)(347,377)(348,378)(349,373)
(350,374)(351,375)(379,406)(380,407)(381,408)(382,412)(383,413)(384,414)
(385,409)(386,410)(387,411)(388,415)(389,416)(390,417)(391,421)(392,422)
(393,423)(394,418)(395,419)(396,420)(397,424)(398,425)(399,426)(400,430)
(401,431)(402,432)(403,427)(404,428)(405,429)(433,460)(434,461)(435,462)
(436,466)(437,467)(438,468)(439,463)(440,464)(441,465)(442,469)(443,470)
(444,471)(445,475)(446,476)(447,477)(448,472)(449,473)(450,474)(451,478)
(452,479)(453,480)(454,484)(455,485)(456,486)(457,481)(458,482)(459,483)
(487,514)(488,515)(489,516)(490,520)(491,521)(492,522)(493,517)(494,518)
(495,519)(496,523)(497,524)(498,525)(499,529)(500,530)(501,531)(502,526)
(503,527)(504,528)(505,532)(506,533)(507,534)(508,538)(509,539)(510,540)
(511,535)(512,536)(513,537)(541,568)(542,569)(543,570)(544,574)(545,575)
(546,576)(547,571)(548,572)(549,573)(550,577)(551,578)(552,579)(553,583)
(554,584)(555,585)(556,580)(557,581)(558,582)(559,586)(560,587)(561,588)
(562,592)(563,593)(564,594)(565,589)(566,590)(567,591)(595,622)(596,623)
(597,624)(598,628)(599,629)(600,630)(601,625)(602,626)(603,627)(604,631)
(605,632)(606,633)(607,637)(608,638)(609,639)(610,634)(611,635)(612,636)
(613,640)(614,641)(615,642)(616,646)(617,647)(618,648)(619,643)(620,644)
(621,645)(652,655)(653,656)(654,657)(661,664)(662,665)(663,666)(670,673)
(671,674)(672,675)(679,682)(680,683)(681,684)(688,691)(689,692)(690,693)
(697,700)(698,701)(699,702)(706,709)(707,710)(708,711)(715,718)(716,719)
(717,720)(724,727)(725,728)(726,729)(733,736)(734,737)(735,738)(742,745)
(743,746)(744,747)(751,754)(752,755)(753,756)(760,763)(761,764)(762,765)
(769,772)(770,773)(771,774)(778,781)(779,782)(780,783)(787,790)(788,791)
(789,792)(796,799)(797,800)(798,801)(805,808)(806,809)(807,810)(814,817)
(815,818)(816,819)(823,826)(824,827)(825,828)(832,835)(833,836)(834,837)
(841,844)(842,845)(843,846)(850,853)(851,854)(852,855)(859,862)(860,863)
(861,864);
s1 := Sym(864)!( 1,436)( 2,437)( 3,438)( 4,433)( 5,434)( 6,435)( 7,439)
( 8,440)( 9,441)( 10,454)( 11,455)( 12,456)( 13,451)( 14,452)( 15,453)
( 16,457)( 17,458)( 18,459)( 19,445)( 20,446)( 21,447)( 22,442)( 23,443)
( 24,444)( 25,448)( 26,449)( 27,450)( 28,463)( 29,464)( 30,465)( 31,460)
( 32,461)( 33,462)( 34,466)( 35,467)( 36,468)( 37,481)( 38,482)( 39,483)
( 40,478)( 41,479)( 42,480)( 43,484)( 44,485)( 45,486)( 46,472)( 47,473)
( 48,474)( 49,469)( 50,470)( 51,471)( 52,475)( 53,476)( 54,477)( 55,490)
( 56,491)( 57,492)( 58,487)( 59,488)( 60,489)( 61,493)( 62,494)( 63,495)
( 64,508)( 65,509)( 66,510)( 67,505)( 68,506)( 69,507)( 70,511)( 71,512)
( 72,513)( 73,499)( 74,500)( 75,501)( 76,496)( 77,497)( 78,498)( 79,502)
( 80,503)( 81,504)( 82,517)( 83,518)( 84,519)( 85,514)( 86,515)( 87,516)
( 88,520)( 89,521)( 90,522)( 91,535)( 92,536)( 93,537)( 94,532)( 95,533)
( 96,534)( 97,538)( 98,539)( 99,540)(100,526)(101,527)(102,528)(103,523)
(104,524)(105,525)(106,529)(107,530)(108,531)(109,544)(110,545)(111,546)
(112,541)(113,542)(114,543)(115,547)(116,548)(117,549)(118,562)(119,563)
(120,564)(121,559)(122,560)(123,561)(124,565)(125,566)(126,567)(127,553)
(128,554)(129,555)(130,550)(131,551)(132,552)(133,556)(134,557)(135,558)
(136,571)(137,572)(138,573)(139,568)(140,569)(141,570)(142,574)(143,575)
(144,576)(145,589)(146,590)(147,591)(148,586)(149,587)(150,588)(151,592)
(152,593)(153,594)(154,580)(155,581)(156,582)(157,577)(158,578)(159,579)
(160,583)(161,584)(162,585)(163,598)(164,599)(165,600)(166,595)(167,596)
(168,597)(169,601)(170,602)(171,603)(172,616)(173,617)(174,618)(175,613)
(176,614)(177,615)(178,619)(179,620)(180,621)(181,607)(182,608)(183,609)
(184,604)(185,605)(186,606)(187,610)(188,611)(189,612)(190,625)(191,626)
(192,627)(193,622)(194,623)(195,624)(196,628)(197,629)(198,630)(199,643)
(200,644)(201,645)(202,640)(203,641)(204,642)(205,646)(206,647)(207,648)
(208,634)(209,635)(210,636)(211,631)(212,632)(213,633)(214,637)(215,638)
(216,639)(217,679)(218,680)(219,681)(220,676)(221,677)(222,678)(223,682)
(224,683)(225,684)(226,697)(227,698)(228,699)(229,694)(230,695)(231,696)
(232,700)(233,701)(234,702)(235,688)(236,689)(237,690)(238,685)(239,686)
(240,687)(241,691)(242,692)(243,693)(244,652)(245,653)(246,654)(247,649)
(248,650)(249,651)(250,655)(251,656)(252,657)(253,670)(254,671)(255,672)
(256,667)(257,668)(258,669)(259,673)(260,674)(261,675)(262,661)(263,662)
(264,663)(265,658)(266,659)(267,660)(268,664)(269,665)(270,666)(271,733)
(272,734)(273,735)(274,730)(275,731)(276,732)(277,736)(278,737)(279,738)
(280,751)(281,752)(282,753)(283,748)(284,749)(285,750)(286,754)(287,755)
(288,756)(289,742)(290,743)(291,744)(292,739)(293,740)(294,741)(295,745)
(296,746)(297,747)(298,706)(299,707)(300,708)(301,703)(302,704)(303,705)
(304,709)(305,710)(306,711)(307,724)(308,725)(309,726)(310,721)(311,722)
(312,723)(313,727)(314,728)(315,729)(316,715)(317,716)(318,717)(319,712)
(320,713)(321,714)(322,718)(323,719)(324,720)(325,787)(326,788)(327,789)
(328,784)(329,785)(330,786)(331,790)(332,791)(333,792)(334,805)(335,806)
(336,807)(337,802)(338,803)(339,804)(340,808)(341,809)(342,810)(343,796)
(344,797)(345,798)(346,793)(347,794)(348,795)(349,799)(350,800)(351,801)
(352,760)(353,761)(354,762)(355,757)(356,758)(357,759)(358,763)(359,764)
(360,765)(361,778)(362,779)(363,780)(364,775)(365,776)(366,777)(367,781)
(368,782)(369,783)(370,769)(371,770)(372,771)(373,766)(374,767)(375,768)
(376,772)(377,773)(378,774)(379,841)(380,842)(381,843)(382,838)(383,839)
(384,840)(385,844)(386,845)(387,846)(388,859)(389,860)(390,861)(391,856)
(392,857)(393,858)(394,862)(395,863)(396,864)(397,850)(398,851)(399,852)
(400,847)(401,848)(402,849)(403,853)(404,854)(405,855)(406,814)(407,815)
(408,816)(409,811)(410,812)(411,813)(412,817)(413,818)(414,819)(415,832)
(416,833)(417,834)(418,829)(419,830)(420,831)(421,835)(422,836)(423,837)
(424,823)(425,824)(426,825)(427,820)(428,821)(429,822)(430,826)(431,827)
(432,828);
s2 := Sym(864)!( 1,658)( 2,660)( 3,659)( 4,661)( 5,663)( 6,662)( 7,664)
( 8,666)( 9,665)( 10,649)( 11,651)( 12,650)( 13,652)( 14,654)( 15,653)
( 16,655)( 17,657)( 18,656)( 19,667)( 20,669)( 21,668)( 22,670)( 23,672)
( 24,671)( 25,673)( 26,675)( 27,674)( 28,685)( 29,687)( 30,686)( 31,688)
( 32,690)( 33,689)( 34,691)( 35,693)( 36,692)( 37,676)( 38,678)( 39,677)
( 40,679)( 41,681)( 42,680)( 43,682)( 44,684)( 45,683)( 46,694)( 47,696)
( 48,695)( 49,697)( 50,699)( 51,698)( 52,700)( 53,702)( 54,701)( 55,712)
( 56,714)( 57,713)( 58,715)( 59,717)( 60,716)( 61,718)( 62,720)( 63,719)
( 64,703)( 65,705)( 66,704)( 67,706)( 68,708)( 69,707)( 70,709)( 71,711)
( 72,710)( 73,721)( 74,723)( 75,722)( 76,724)( 77,726)( 78,725)( 79,727)
( 80,729)( 81,728)( 82,739)( 83,741)( 84,740)( 85,742)( 86,744)( 87,743)
( 88,745)( 89,747)( 90,746)( 91,730)( 92,732)( 93,731)( 94,733)( 95,735)
( 96,734)( 97,736)( 98,738)( 99,737)(100,748)(101,750)(102,749)(103,751)
(104,753)(105,752)(106,754)(107,756)(108,755)(109,820)(110,822)(111,821)
(112,823)(113,825)(114,824)(115,826)(116,828)(117,827)(118,811)(119,813)
(120,812)(121,814)(122,816)(123,815)(124,817)(125,819)(126,818)(127,829)
(128,831)(129,830)(130,832)(131,834)(132,833)(133,835)(134,837)(135,836)
(136,847)(137,849)(138,848)(139,850)(140,852)(141,851)(142,853)(143,855)
(144,854)(145,838)(146,840)(147,839)(148,841)(149,843)(150,842)(151,844)
(152,846)(153,845)(154,856)(155,858)(156,857)(157,859)(158,861)(159,860)
(160,862)(161,864)(162,863)(163,766)(164,768)(165,767)(166,769)(167,771)
(168,770)(169,772)(170,774)(171,773)(172,757)(173,759)(174,758)(175,760)
(176,762)(177,761)(178,763)(179,765)(180,764)(181,775)(182,777)(183,776)
(184,778)(185,780)(186,779)(187,781)(188,783)(189,782)(190,793)(191,795)
(192,794)(193,796)(194,798)(195,797)(196,799)(197,801)(198,800)(199,784)
(200,786)(201,785)(202,787)(203,789)(204,788)(205,790)(206,792)(207,791)
(208,802)(209,804)(210,803)(211,805)(212,807)(213,806)(214,808)(215,810)
(216,809)(217,469)(218,471)(219,470)(220,472)(221,474)(222,473)(223,475)
(224,477)(225,476)(226,460)(227,462)(228,461)(229,463)(230,465)(231,464)
(232,466)(233,468)(234,467)(235,478)(236,480)(237,479)(238,481)(239,483)
(240,482)(241,484)(242,486)(243,485)(244,442)(245,444)(246,443)(247,445)
(248,447)(249,446)(250,448)(251,450)(252,449)(253,433)(254,435)(255,434)
(256,436)(257,438)(258,437)(259,439)(260,441)(261,440)(262,451)(263,453)
(264,452)(265,454)(266,456)(267,455)(268,457)(269,459)(270,458)(271,523)
(272,525)(273,524)(274,526)(275,528)(276,527)(277,529)(278,531)(279,530)
(280,514)(281,516)(282,515)(283,517)(284,519)(285,518)(286,520)(287,522)
(288,521)(289,532)(290,534)(291,533)(292,535)(293,537)(294,536)(295,538)
(296,540)(297,539)(298,496)(299,498)(300,497)(301,499)(302,501)(303,500)
(304,502)(305,504)(306,503)(307,487)(308,489)(309,488)(310,490)(311,492)
(312,491)(313,493)(314,495)(315,494)(316,505)(317,507)(318,506)(319,508)
(320,510)(321,509)(322,511)(323,513)(324,512)(325,631)(326,633)(327,632)
(328,634)(329,636)(330,635)(331,637)(332,639)(333,638)(334,622)(335,624)
(336,623)(337,625)(338,627)(339,626)(340,628)(341,630)(342,629)(343,640)
(344,642)(345,641)(346,643)(347,645)(348,644)(349,646)(350,648)(351,647)
(352,604)(353,606)(354,605)(355,607)(356,609)(357,608)(358,610)(359,612)
(360,611)(361,595)(362,597)(363,596)(364,598)(365,600)(366,599)(367,601)
(368,603)(369,602)(370,613)(371,615)(372,614)(373,616)(374,618)(375,617)
(376,619)(377,621)(378,620)(379,577)(380,579)(381,578)(382,580)(383,582)
(384,581)(385,583)(386,585)(387,584)(388,568)(389,570)(390,569)(391,571)
(392,573)(393,572)(394,574)(395,576)(396,575)(397,586)(398,588)(399,587)
(400,589)(401,591)(402,590)(403,592)(404,594)(405,593)(406,550)(407,552)
(408,551)(409,553)(410,555)(411,554)(412,556)(413,558)(414,557)(415,541)
(416,543)(417,542)(418,544)(419,546)(420,545)(421,547)(422,549)(423,548)
(424,559)(425,561)(426,560)(427,562)(428,564)(429,563)(430,565)(431,567)
(432,566);
s3 := Sym(864)!( 1,758)( 2,757)( 3,759)( 4,761)( 5,760)( 6,762)( 7,764)
( 8,763)( 9,765)( 10,776)( 11,775)( 12,777)( 13,779)( 14,778)( 15,780)
( 16,782)( 17,781)( 18,783)( 19,767)( 20,766)( 21,768)( 22,770)( 23,769)
( 24,771)( 25,773)( 26,772)( 27,774)( 28,785)( 29,784)( 30,786)( 31,788)
( 32,787)( 33,789)( 34,791)( 35,790)( 36,792)( 37,803)( 38,802)( 39,804)
( 40,806)( 41,805)( 42,807)( 43,809)( 44,808)( 45,810)( 46,794)( 47,793)
( 48,795)( 49,797)( 50,796)( 51,798)( 52,800)( 53,799)( 54,801)( 55,812)
( 56,811)( 57,813)( 58,815)( 59,814)( 60,816)( 61,818)( 62,817)( 63,819)
( 64,830)( 65,829)( 66,831)( 67,833)( 68,832)( 69,834)( 70,836)( 71,835)
( 72,837)( 73,821)( 74,820)( 75,822)( 76,824)( 77,823)( 78,825)( 79,827)
( 80,826)( 81,828)( 82,839)( 83,838)( 84,840)( 85,842)( 86,841)( 87,843)
( 88,845)( 89,844)( 90,846)( 91,857)( 92,856)( 93,858)( 94,860)( 95,859)
( 96,861)( 97,863)( 98,862)( 99,864)(100,848)(101,847)(102,849)(103,851)
(104,850)(105,852)(106,854)(107,853)(108,855)(109,650)(110,649)(111,651)
(112,653)(113,652)(114,654)(115,656)(116,655)(117,657)(118,668)(119,667)
(120,669)(121,671)(122,670)(123,672)(124,674)(125,673)(126,675)(127,659)
(128,658)(129,660)(130,662)(131,661)(132,663)(133,665)(134,664)(135,666)
(136,677)(137,676)(138,678)(139,680)(140,679)(141,681)(142,683)(143,682)
(144,684)(145,695)(146,694)(147,696)(148,698)(149,697)(150,699)(151,701)
(152,700)(153,702)(154,686)(155,685)(156,687)(157,689)(158,688)(159,690)
(160,692)(161,691)(162,693)(163,704)(164,703)(165,705)(166,707)(167,706)
(168,708)(169,710)(170,709)(171,711)(172,722)(173,721)(174,723)(175,725)
(176,724)(177,726)(178,728)(179,727)(180,729)(181,713)(182,712)(183,714)
(184,716)(185,715)(186,717)(187,719)(188,718)(189,720)(190,731)(191,730)
(192,732)(193,734)(194,733)(195,735)(196,737)(197,736)(198,738)(199,749)
(200,748)(201,750)(202,752)(203,751)(204,753)(205,755)(206,754)(207,756)
(208,740)(209,739)(210,741)(211,743)(212,742)(213,744)(214,746)(215,745)
(216,747)(217,569)(218,568)(219,570)(220,572)(221,571)(222,573)(223,575)
(224,574)(225,576)(226,587)(227,586)(228,588)(229,590)(230,589)(231,591)
(232,593)(233,592)(234,594)(235,578)(236,577)(237,579)(238,581)(239,580)
(240,582)(241,584)(242,583)(243,585)(244,542)(245,541)(246,543)(247,545)
(248,544)(249,546)(250,548)(251,547)(252,549)(253,560)(254,559)(255,561)
(256,563)(257,562)(258,564)(259,566)(260,565)(261,567)(262,551)(263,550)
(264,552)(265,554)(266,553)(267,555)(268,557)(269,556)(270,558)(271,623)
(272,622)(273,624)(274,626)(275,625)(276,627)(277,629)(278,628)(279,630)
(280,641)(281,640)(282,642)(283,644)(284,643)(285,645)(286,647)(287,646)
(288,648)(289,632)(290,631)(291,633)(292,635)(293,634)(294,636)(295,638)
(296,637)(297,639)(298,596)(299,595)(300,597)(301,599)(302,598)(303,600)
(304,602)(305,601)(306,603)(307,614)(308,613)(309,615)(310,617)(311,616)
(312,618)(313,620)(314,619)(315,621)(316,605)(317,604)(318,606)(319,608)
(320,607)(321,609)(322,611)(323,610)(324,612)(325,461)(326,460)(327,462)
(328,464)(329,463)(330,465)(331,467)(332,466)(333,468)(334,479)(335,478)
(336,480)(337,482)(338,481)(339,483)(340,485)(341,484)(342,486)(343,470)
(344,469)(345,471)(346,473)(347,472)(348,474)(349,476)(350,475)(351,477)
(352,434)(353,433)(354,435)(355,437)(356,436)(357,438)(358,440)(359,439)
(360,441)(361,452)(362,451)(363,453)(364,455)(365,454)(366,456)(367,458)
(368,457)(369,459)(370,443)(371,442)(372,444)(373,446)(374,445)(375,447)
(376,449)(377,448)(378,450)(379,515)(380,514)(381,516)(382,518)(383,517)
(384,519)(385,521)(386,520)(387,522)(388,533)(389,532)(390,534)(391,536)
(392,535)(393,537)(394,539)(395,538)(396,540)(397,524)(398,523)(399,525)
(400,527)(401,526)(402,528)(403,530)(404,529)(405,531)(406,488)(407,487)
(408,489)(409,491)(410,490)(411,492)(412,494)(413,493)(414,495)(415,506)
(416,505)(417,507)(418,509)(419,508)(420,510)(421,512)(422,511)(423,513)
(424,497)(425,496)(426,498)(427,500)(428,499)(429,501)(430,503)(431,502)
(432,504);
poly := sub<Sym(864)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope