Polytope of Type {12,12,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12,6}*1728g
if this polytope has a name.
Group : SmallGroup(1728,38778)
Rank : 4
Schlafli Type : {12,12,6}
Number of vertices, edges, etc : 12, 72, 36, 6
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 : {12,6,6}*864e, {6,12,6}*864g
3-fold quotients : {12,4,6}*576, {4,12,6}*576c
4-fold quotients : {12,6,3}*432b, {6,6,6}*432c
6-fold quotients : {12,2,6}*288, {6,4,6}*288, {4,6,6}*288c, {2,12,6}*288c
8-fold quotients : {6,6,3}*216b
9-fold quotients : {12,4,2}*192a, {4,4,6}*192
12-fold quotients : {12,2,3}*144, {4,6,3}*144, {2,6,6}*144b, {6,2,6}*144
18-fold quotients : {12,2,2}*96, {2,4,6}*96a, {4,2,6}*96, {6,4,2}*96a
24-fold quotients : {2,6,3}*72, {3,2,6}*72, {6,2,3}*72
27-fold quotients : {4,4,2}*64
36-fold quotients : {4,2,3}*48, {2,2,6}*48, {6,2,2}*48
48-fold quotients : {3,2,3}*36
54-fold quotients : {2,4,2}*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)(109,598)(110,599)(111,600)(112,595)
(113,596)(114,597)(115,601)(116,602)(117,603)(118,616)(119,617)(120,618)
(121,613)(122,614)(123,615)(124,619)(125,620)(126,621)(127,607)(128,608)
(129,609)(130,604)(131,605)(132,606)(133,610)(134,611)(135,612)(136,625)
(137,626)(138,627)(139,622)(140,623)(141,624)(142,628)(143,629)(144,630)
(145,643)(146,644)(147,645)(148,640)(149,641)(150,642)(151,646)(152,647)
(153,648)(154,634)(155,635)(156,636)(157,631)(158,632)(159,633)(160,637)
(161,638)(162,639)(163,544)(164,545)(165,546)(166,541)(167,542)(168,543)
(169,547)(170,548)(171,549)(172,562)(173,563)(174,564)(175,559)(176,560)
(177,561)(178,565)(179,566)(180,567)(181,553)(182,554)(183,555)(184,550)
(185,551)(186,552)(187,556)(188,557)(189,558)(190,571)(191,572)(192,573)
(193,568)(194,569)(195,570)(196,574)(197,575)(198,576)(199,589)(200,590)
(201,591)(202,586)(203,587)(204,588)(205,592)(206,593)(207,594)(208,580)
(209,581)(210,582)(211,577)(212,578)(213,579)(214,583)(215,584)(216,585)
(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)(325,841)(326,842)(327,843)(328,838)
(329,839)(330,840)(331,844)(332,845)(333,846)(334,859)(335,860)(336,861)
(337,856)(338,857)(339,858)(340,862)(341,863)(342,864)(343,850)(344,851)
(345,852)(346,847)(347,848)(348,849)(349,853)(350,854)(351,855)(352,814)
(353,815)(354,816)(355,811)(356,812)(357,813)(358,817)(359,818)(360,819)
(361,832)(362,833)(363,834)(364,829)(365,830)(366,831)(367,835)(368,836)
(369,837)(370,823)(371,824)(372,825)(373,820)(374,821)(375,822)(376,826)
(377,827)(378,828)(379,787)(380,788)(381,789)(382,784)(383,785)(384,786)
(385,790)(386,791)(387,792)(388,805)(389,806)(390,807)(391,802)(392,803)
(393,804)(394,808)(395,809)(396,810)(397,796)(398,797)(399,798)(400,793)
(401,794)(402,795)(403,799)(404,800)(405,801)(406,760)(407,761)(408,762)
(409,757)(410,758)(411,759)(412,763)(413,764)(414,765)(415,778)(416,779)
(417,780)(418,775)(419,776)(420,777)(421,781)(422,782)(423,783)(424,769)
(425,770)(426,771)(427,766)(428,767)(429,768)(430,772)(431,773)(432,774);;
s2 := ( 1,766)( 2,768)( 3,767)( 4,769)( 5,771)( 6,770)( 7,772)( 8,774)
( 9,773)( 10,757)( 11,759)( 12,758)( 13,760)( 14,762)( 15,761)( 16,763)
( 17,765)( 18,764)( 19,775)( 20,777)( 21,776)( 22,778)( 23,780)( 24,779)
( 25,781)( 26,783)( 27,782)( 28,793)( 29,795)( 30,794)( 31,796)( 32,798)
( 33,797)( 34,799)( 35,801)( 36,800)( 37,784)( 38,786)( 39,785)( 40,787)
( 41,789)( 42,788)( 43,790)( 44,792)( 45,791)( 46,802)( 47,804)( 48,803)
( 49,805)( 50,807)( 51,806)( 52,808)( 53,810)( 54,809)( 55,820)( 56,822)
( 57,821)( 58,823)( 59,825)( 60,824)( 61,826)( 62,828)( 63,827)( 64,811)
( 65,813)( 66,812)( 67,814)( 68,816)( 69,815)( 70,817)( 71,819)( 72,818)
( 73,829)( 74,831)( 75,830)( 76,832)( 77,834)( 78,833)( 79,835)( 80,837)
( 81,836)( 82,847)( 83,849)( 84,848)( 85,850)( 86,852)( 87,851)( 88,853)
( 89,855)( 90,854)( 91,838)( 92,840)( 93,839)( 94,841)( 95,843)( 96,842)
( 97,844)( 98,846)( 99,845)(100,856)(101,858)(102,857)(103,859)(104,861)
(105,860)(106,862)(107,864)(108,863)(109,658)(110,660)(111,659)(112,661)
(113,663)(114,662)(115,664)(116,666)(117,665)(118,649)(119,651)(120,650)
(121,652)(122,654)(123,653)(124,655)(125,657)(126,656)(127,667)(128,669)
(129,668)(130,670)(131,672)(132,671)(133,673)(134,675)(135,674)(136,685)
(137,687)(138,686)(139,688)(140,690)(141,689)(142,691)(143,693)(144,692)
(145,676)(146,678)(147,677)(148,679)(149,681)(150,680)(151,682)(152,684)
(153,683)(154,694)(155,696)(156,695)(157,697)(158,699)(159,698)(160,700)
(161,702)(162,701)(163,712)(164,714)(165,713)(166,715)(167,717)(168,716)
(169,718)(170,720)(171,719)(172,703)(173,705)(174,704)(175,706)(176,708)
(177,707)(178,709)(179,711)(180,710)(181,721)(182,723)(183,722)(184,724)
(185,726)(186,725)(187,727)(188,729)(189,728)(190,739)(191,741)(192,740)
(193,742)(194,744)(195,743)(196,745)(197,747)(198,746)(199,730)(200,732)
(201,731)(202,733)(203,735)(204,734)(205,736)(206,738)(207,737)(208,748)
(209,750)(210,749)(211,751)(212,753)(213,752)(214,754)(215,756)(216,755)
(217,577)(218,579)(219,578)(220,580)(221,582)(222,581)(223,583)(224,585)
(225,584)(226,568)(227,570)(228,569)(229,571)(230,573)(231,572)(232,574)
(233,576)(234,575)(235,586)(236,588)(237,587)(238,589)(239,591)(240,590)
(241,592)(242,594)(243,593)(244,550)(245,552)(246,551)(247,553)(248,555)
(249,554)(250,556)(251,558)(252,557)(253,541)(254,543)(255,542)(256,544)
(257,546)(258,545)(259,547)(260,549)(261,548)(262,559)(263,561)(264,560)
(265,562)(266,564)(267,563)(268,565)(269,567)(270,566)(271,631)(272,633)
(273,632)(274,634)(275,636)(276,635)(277,637)(278,639)(279,638)(280,622)
(281,624)(282,623)(283,625)(284,627)(285,626)(286,628)(287,630)(288,629)
(289,640)(290,642)(291,641)(292,643)(293,645)(294,644)(295,646)(296,648)
(297,647)(298,604)(299,606)(300,605)(301,607)(302,609)(303,608)(304,610)
(305,612)(306,611)(307,595)(308,597)(309,596)(310,598)(311,600)(312,599)
(313,601)(314,603)(315,602)(316,613)(317,615)(318,614)(319,616)(320,618)
(321,617)(322,619)(323,621)(324,620)(325,469)(326,471)(327,470)(328,472)
(329,474)(330,473)(331,475)(332,477)(333,476)(334,460)(335,462)(336,461)
(337,463)(338,465)(339,464)(340,466)(341,468)(342,467)(343,478)(344,480)
(345,479)(346,481)(347,483)(348,482)(349,484)(350,486)(351,485)(352,442)
(353,444)(354,443)(355,445)(356,447)(357,446)(358,448)(359,450)(360,449)
(361,433)(362,435)(363,434)(364,436)(365,438)(366,437)(367,439)(368,441)
(369,440)(370,451)(371,453)(372,452)(373,454)(374,456)(375,455)(376,457)
(377,459)(378,458)(379,523)(380,525)(381,524)(382,526)(383,528)(384,527)
(385,529)(386,531)(387,530)(388,514)(389,516)(390,515)(391,517)(392,519)
(393,518)(394,520)(395,522)(396,521)(397,532)(398,534)(399,533)(400,535)
(401,537)(402,536)(403,538)(404,540)(405,539)(406,496)(407,498)(408,497)
(409,499)(410,501)(411,500)(412,502)(413,504)(414,503)(415,487)(416,489)
(417,488)(418,490)(419,492)(420,491)(421,493)(422,495)(423,494)(424,505)
(425,507)(426,506)(427,508)(428,510)(429,509)(430,511)(431,513)(432,512);;
s3 := ( 1,650)( 2,649)( 3,651)( 4,653)( 5,652)( 6,654)( 7,656)( 8,655)
( 9,657)( 10,668)( 11,667)( 12,669)( 13,671)( 14,670)( 15,672)( 16,674)
( 17,673)( 18,675)( 19,659)( 20,658)( 21,660)( 22,662)( 23,661)( 24,663)
( 25,665)( 26,664)( 27,666)( 28,677)( 29,676)( 30,678)( 31,680)( 32,679)
( 33,681)( 34,683)( 35,682)( 36,684)( 37,695)( 38,694)( 39,696)( 40,698)
( 41,697)( 42,699)( 43,701)( 44,700)( 45,702)( 46,686)( 47,685)( 48,687)
( 49,689)( 50,688)( 51,690)( 52,692)( 53,691)( 54,693)( 55,704)( 56,703)
( 57,705)( 58,707)( 59,706)( 60,708)( 61,710)( 62,709)( 63,711)( 64,722)
( 65,721)( 66,723)( 67,725)( 68,724)( 69,726)( 70,728)( 71,727)( 72,729)
( 73,713)( 74,712)( 75,714)( 76,716)( 77,715)( 78,717)( 79,719)( 80,718)
( 81,720)( 82,731)( 83,730)( 84,732)( 85,734)( 86,733)( 87,735)( 88,737)
( 89,736)( 90,738)( 91,749)( 92,748)( 93,750)( 94,752)( 95,751)( 96,753)
( 97,755)( 98,754)( 99,756)(100,740)(101,739)(102,741)(103,743)(104,742)
(105,744)(106,746)(107,745)(108,747)(109,758)(110,757)(111,759)(112,761)
(113,760)(114,762)(115,764)(116,763)(117,765)(118,776)(119,775)(120,777)
(121,779)(122,778)(123,780)(124,782)(125,781)(126,783)(127,767)(128,766)
(129,768)(130,770)(131,769)(132,771)(133,773)(134,772)(135,774)(136,785)
(137,784)(138,786)(139,788)(140,787)(141,789)(142,791)(143,790)(144,792)
(145,803)(146,802)(147,804)(148,806)(149,805)(150,807)(151,809)(152,808)
(153,810)(154,794)(155,793)(156,795)(157,797)(158,796)(159,798)(160,800)
(161,799)(162,801)(163,812)(164,811)(165,813)(166,815)(167,814)(168,816)
(169,818)(170,817)(171,819)(172,830)(173,829)(174,831)(175,833)(176,832)
(177,834)(178,836)(179,835)(180,837)(181,821)(182,820)(183,822)(184,824)
(185,823)(186,825)(187,827)(188,826)(189,828)(190,839)(191,838)(192,840)
(193,842)(194,841)(195,843)(196,845)(197,844)(198,846)(199,857)(200,856)
(201,858)(202,860)(203,859)(204,861)(205,863)(206,862)(207,864)(208,848)
(209,847)(210,849)(211,851)(212,850)(213,852)(214,854)(215,853)(216,855)
(217,461)(218,460)(219,462)(220,464)(221,463)(222,465)(223,467)(224,466)
(225,468)(226,479)(227,478)(228,480)(229,482)(230,481)(231,483)(232,485)
(233,484)(234,486)(235,470)(236,469)(237,471)(238,473)(239,472)(240,474)
(241,476)(242,475)(243,477)(244,434)(245,433)(246,435)(247,437)(248,436)
(249,438)(250,440)(251,439)(252,441)(253,452)(254,451)(255,453)(256,455)
(257,454)(258,456)(259,458)(260,457)(261,459)(262,443)(263,442)(264,444)
(265,446)(266,445)(267,447)(268,449)(269,448)(270,450)(271,515)(272,514)
(273,516)(274,518)(275,517)(276,519)(277,521)(278,520)(279,522)(280,533)
(281,532)(282,534)(283,536)(284,535)(285,537)(286,539)(287,538)(288,540)
(289,524)(290,523)(291,525)(292,527)(293,526)(294,528)(295,530)(296,529)
(297,531)(298,488)(299,487)(300,489)(301,491)(302,490)(303,492)(304,494)
(305,493)(306,495)(307,506)(308,505)(309,507)(310,509)(311,508)(312,510)
(313,512)(314,511)(315,513)(316,497)(317,496)(318,498)(319,500)(320,499)
(321,501)(322,503)(323,502)(324,504)(325,569)(326,568)(327,570)(328,572)
(329,571)(330,573)(331,575)(332,574)(333,576)(334,587)(335,586)(336,588)
(337,590)(338,589)(339,591)(340,593)(341,592)(342,594)(343,578)(344,577)
(345,579)(346,581)(347,580)(348,582)(349,584)(350,583)(351,585)(352,542)
(353,541)(354,543)(355,545)(356,544)(357,546)(358,548)(359,547)(360,549)
(361,560)(362,559)(363,561)(364,563)(365,562)(366,564)(367,566)(368,565)
(369,567)(370,551)(371,550)(372,552)(373,554)(374,553)(375,555)(376,557)
(377,556)(378,558)(379,623)(380,622)(381,624)(382,626)(383,625)(384,627)
(385,629)(386,628)(387,630)(388,641)(389,640)(390,642)(391,644)(392,643)
(393,645)(394,647)(395,646)(396,648)(397,632)(398,631)(399,633)(400,635)
(401,634)(402,636)(403,638)(404,637)(405,639)(406,596)(407,595)(408,597)
(409,599)(410,598)(411,600)(412,602)(413,601)(414,603)(415,614)(416,613)
(417,615)(418,617)(419,616)(420,618)(421,620)(422,619)(423,621)(424,605)
(425,604)(426,606)(427,608)(428,607)(429,609)(430,611)(431,610)(432,612);;
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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)!( 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)(109,598)(110,599)(111,600)
(112,595)(113,596)(114,597)(115,601)(116,602)(117,603)(118,616)(119,617)
(120,618)(121,613)(122,614)(123,615)(124,619)(125,620)(126,621)(127,607)
(128,608)(129,609)(130,604)(131,605)(132,606)(133,610)(134,611)(135,612)
(136,625)(137,626)(138,627)(139,622)(140,623)(141,624)(142,628)(143,629)
(144,630)(145,643)(146,644)(147,645)(148,640)(149,641)(150,642)(151,646)
(152,647)(153,648)(154,634)(155,635)(156,636)(157,631)(158,632)(159,633)
(160,637)(161,638)(162,639)(163,544)(164,545)(165,546)(166,541)(167,542)
(168,543)(169,547)(170,548)(171,549)(172,562)(173,563)(174,564)(175,559)
(176,560)(177,561)(178,565)(179,566)(180,567)(181,553)(182,554)(183,555)
(184,550)(185,551)(186,552)(187,556)(188,557)(189,558)(190,571)(191,572)
(192,573)(193,568)(194,569)(195,570)(196,574)(197,575)(198,576)(199,589)
(200,590)(201,591)(202,586)(203,587)(204,588)(205,592)(206,593)(207,594)
(208,580)(209,581)(210,582)(211,577)(212,578)(213,579)(214,583)(215,584)
(216,585)(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)(325,841)(326,842)(327,843)
(328,838)(329,839)(330,840)(331,844)(332,845)(333,846)(334,859)(335,860)
(336,861)(337,856)(338,857)(339,858)(340,862)(341,863)(342,864)(343,850)
(344,851)(345,852)(346,847)(347,848)(348,849)(349,853)(350,854)(351,855)
(352,814)(353,815)(354,816)(355,811)(356,812)(357,813)(358,817)(359,818)
(360,819)(361,832)(362,833)(363,834)(364,829)(365,830)(366,831)(367,835)
(368,836)(369,837)(370,823)(371,824)(372,825)(373,820)(374,821)(375,822)
(376,826)(377,827)(378,828)(379,787)(380,788)(381,789)(382,784)(383,785)
(384,786)(385,790)(386,791)(387,792)(388,805)(389,806)(390,807)(391,802)
(392,803)(393,804)(394,808)(395,809)(396,810)(397,796)(398,797)(399,798)
(400,793)(401,794)(402,795)(403,799)(404,800)(405,801)(406,760)(407,761)
(408,762)(409,757)(410,758)(411,759)(412,763)(413,764)(414,765)(415,778)
(416,779)(417,780)(418,775)(419,776)(420,777)(421,781)(422,782)(423,783)
(424,769)(425,770)(426,771)(427,766)(428,767)(429,768)(430,772)(431,773)
(432,774);
s2 := Sym(864)!( 1,766)( 2,768)( 3,767)( 4,769)( 5,771)( 6,770)( 7,772)
( 8,774)( 9,773)( 10,757)( 11,759)( 12,758)( 13,760)( 14,762)( 15,761)
( 16,763)( 17,765)( 18,764)( 19,775)( 20,777)( 21,776)( 22,778)( 23,780)
( 24,779)( 25,781)( 26,783)( 27,782)( 28,793)( 29,795)( 30,794)( 31,796)
( 32,798)( 33,797)( 34,799)( 35,801)( 36,800)( 37,784)( 38,786)( 39,785)
( 40,787)( 41,789)( 42,788)( 43,790)( 44,792)( 45,791)( 46,802)( 47,804)
( 48,803)( 49,805)( 50,807)( 51,806)( 52,808)( 53,810)( 54,809)( 55,820)
( 56,822)( 57,821)( 58,823)( 59,825)( 60,824)( 61,826)( 62,828)( 63,827)
( 64,811)( 65,813)( 66,812)( 67,814)( 68,816)( 69,815)( 70,817)( 71,819)
( 72,818)( 73,829)( 74,831)( 75,830)( 76,832)( 77,834)( 78,833)( 79,835)
( 80,837)( 81,836)( 82,847)( 83,849)( 84,848)( 85,850)( 86,852)( 87,851)
( 88,853)( 89,855)( 90,854)( 91,838)( 92,840)( 93,839)( 94,841)( 95,843)
( 96,842)( 97,844)( 98,846)( 99,845)(100,856)(101,858)(102,857)(103,859)
(104,861)(105,860)(106,862)(107,864)(108,863)(109,658)(110,660)(111,659)
(112,661)(113,663)(114,662)(115,664)(116,666)(117,665)(118,649)(119,651)
(120,650)(121,652)(122,654)(123,653)(124,655)(125,657)(126,656)(127,667)
(128,669)(129,668)(130,670)(131,672)(132,671)(133,673)(134,675)(135,674)
(136,685)(137,687)(138,686)(139,688)(140,690)(141,689)(142,691)(143,693)
(144,692)(145,676)(146,678)(147,677)(148,679)(149,681)(150,680)(151,682)
(152,684)(153,683)(154,694)(155,696)(156,695)(157,697)(158,699)(159,698)
(160,700)(161,702)(162,701)(163,712)(164,714)(165,713)(166,715)(167,717)
(168,716)(169,718)(170,720)(171,719)(172,703)(173,705)(174,704)(175,706)
(176,708)(177,707)(178,709)(179,711)(180,710)(181,721)(182,723)(183,722)
(184,724)(185,726)(186,725)(187,727)(188,729)(189,728)(190,739)(191,741)
(192,740)(193,742)(194,744)(195,743)(196,745)(197,747)(198,746)(199,730)
(200,732)(201,731)(202,733)(203,735)(204,734)(205,736)(206,738)(207,737)
(208,748)(209,750)(210,749)(211,751)(212,753)(213,752)(214,754)(215,756)
(216,755)(217,577)(218,579)(219,578)(220,580)(221,582)(222,581)(223,583)
(224,585)(225,584)(226,568)(227,570)(228,569)(229,571)(230,573)(231,572)
(232,574)(233,576)(234,575)(235,586)(236,588)(237,587)(238,589)(239,591)
(240,590)(241,592)(242,594)(243,593)(244,550)(245,552)(246,551)(247,553)
(248,555)(249,554)(250,556)(251,558)(252,557)(253,541)(254,543)(255,542)
(256,544)(257,546)(258,545)(259,547)(260,549)(261,548)(262,559)(263,561)
(264,560)(265,562)(266,564)(267,563)(268,565)(269,567)(270,566)(271,631)
(272,633)(273,632)(274,634)(275,636)(276,635)(277,637)(278,639)(279,638)
(280,622)(281,624)(282,623)(283,625)(284,627)(285,626)(286,628)(287,630)
(288,629)(289,640)(290,642)(291,641)(292,643)(293,645)(294,644)(295,646)
(296,648)(297,647)(298,604)(299,606)(300,605)(301,607)(302,609)(303,608)
(304,610)(305,612)(306,611)(307,595)(308,597)(309,596)(310,598)(311,600)
(312,599)(313,601)(314,603)(315,602)(316,613)(317,615)(318,614)(319,616)
(320,618)(321,617)(322,619)(323,621)(324,620)(325,469)(326,471)(327,470)
(328,472)(329,474)(330,473)(331,475)(332,477)(333,476)(334,460)(335,462)
(336,461)(337,463)(338,465)(339,464)(340,466)(341,468)(342,467)(343,478)
(344,480)(345,479)(346,481)(347,483)(348,482)(349,484)(350,486)(351,485)
(352,442)(353,444)(354,443)(355,445)(356,447)(357,446)(358,448)(359,450)
(360,449)(361,433)(362,435)(363,434)(364,436)(365,438)(366,437)(367,439)
(368,441)(369,440)(370,451)(371,453)(372,452)(373,454)(374,456)(375,455)
(376,457)(377,459)(378,458)(379,523)(380,525)(381,524)(382,526)(383,528)
(384,527)(385,529)(386,531)(387,530)(388,514)(389,516)(390,515)(391,517)
(392,519)(393,518)(394,520)(395,522)(396,521)(397,532)(398,534)(399,533)
(400,535)(401,537)(402,536)(403,538)(404,540)(405,539)(406,496)(407,498)
(408,497)(409,499)(410,501)(411,500)(412,502)(413,504)(414,503)(415,487)
(416,489)(417,488)(418,490)(419,492)(420,491)(421,493)(422,495)(423,494)
(424,505)(425,507)(426,506)(427,508)(428,510)(429,509)(430,511)(431,513)
(432,512);
s3 := Sym(864)!( 1,650)( 2,649)( 3,651)( 4,653)( 5,652)( 6,654)( 7,656)
( 8,655)( 9,657)( 10,668)( 11,667)( 12,669)( 13,671)( 14,670)( 15,672)
( 16,674)( 17,673)( 18,675)( 19,659)( 20,658)( 21,660)( 22,662)( 23,661)
( 24,663)( 25,665)( 26,664)( 27,666)( 28,677)( 29,676)( 30,678)( 31,680)
( 32,679)( 33,681)( 34,683)( 35,682)( 36,684)( 37,695)( 38,694)( 39,696)
( 40,698)( 41,697)( 42,699)( 43,701)( 44,700)( 45,702)( 46,686)( 47,685)
( 48,687)( 49,689)( 50,688)( 51,690)( 52,692)( 53,691)( 54,693)( 55,704)
( 56,703)( 57,705)( 58,707)( 59,706)( 60,708)( 61,710)( 62,709)( 63,711)
( 64,722)( 65,721)( 66,723)( 67,725)( 68,724)( 69,726)( 70,728)( 71,727)
( 72,729)( 73,713)( 74,712)( 75,714)( 76,716)( 77,715)( 78,717)( 79,719)
( 80,718)( 81,720)( 82,731)( 83,730)( 84,732)( 85,734)( 86,733)( 87,735)
( 88,737)( 89,736)( 90,738)( 91,749)( 92,748)( 93,750)( 94,752)( 95,751)
( 96,753)( 97,755)( 98,754)( 99,756)(100,740)(101,739)(102,741)(103,743)
(104,742)(105,744)(106,746)(107,745)(108,747)(109,758)(110,757)(111,759)
(112,761)(113,760)(114,762)(115,764)(116,763)(117,765)(118,776)(119,775)
(120,777)(121,779)(122,778)(123,780)(124,782)(125,781)(126,783)(127,767)
(128,766)(129,768)(130,770)(131,769)(132,771)(133,773)(134,772)(135,774)
(136,785)(137,784)(138,786)(139,788)(140,787)(141,789)(142,791)(143,790)
(144,792)(145,803)(146,802)(147,804)(148,806)(149,805)(150,807)(151,809)
(152,808)(153,810)(154,794)(155,793)(156,795)(157,797)(158,796)(159,798)
(160,800)(161,799)(162,801)(163,812)(164,811)(165,813)(166,815)(167,814)
(168,816)(169,818)(170,817)(171,819)(172,830)(173,829)(174,831)(175,833)
(176,832)(177,834)(178,836)(179,835)(180,837)(181,821)(182,820)(183,822)
(184,824)(185,823)(186,825)(187,827)(188,826)(189,828)(190,839)(191,838)
(192,840)(193,842)(194,841)(195,843)(196,845)(197,844)(198,846)(199,857)
(200,856)(201,858)(202,860)(203,859)(204,861)(205,863)(206,862)(207,864)
(208,848)(209,847)(210,849)(211,851)(212,850)(213,852)(214,854)(215,853)
(216,855)(217,461)(218,460)(219,462)(220,464)(221,463)(222,465)(223,467)
(224,466)(225,468)(226,479)(227,478)(228,480)(229,482)(230,481)(231,483)
(232,485)(233,484)(234,486)(235,470)(236,469)(237,471)(238,473)(239,472)
(240,474)(241,476)(242,475)(243,477)(244,434)(245,433)(246,435)(247,437)
(248,436)(249,438)(250,440)(251,439)(252,441)(253,452)(254,451)(255,453)
(256,455)(257,454)(258,456)(259,458)(260,457)(261,459)(262,443)(263,442)
(264,444)(265,446)(266,445)(267,447)(268,449)(269,448)(270,450)(271,515)
(272,514)(273,516)(274,518)(275,517)(276,519)(277,521)(278,520)(279,522)
(280,533)(281,532)(282,534)(283,536)(284,535)(285,537)(286,539)(287,538)
(288,540)(289,524)(290,523)(291,525)(292,527)(293,526)(294,528)(295,530)
(296,529)(297,531)(298,488)(299,487)(300,489)(301,491)(302,490)(303,492)
(304,494)(305,493)(306,495)(307,506)(308,505)(309,507)(310,509)(311,508)
(312,510)(313,512)(314,511)(315,513)(316,497)(317,496)(318,498)(319,500)
(320,499)(321,501)(322,503)(323,502)(324,504)(325,569)(326,568)(327,570)
(328,572)(329,571)(330,573)(331,575)(332,574)(333,576)(334,587)(335,586)
(336,588)(337,590)(338,589)(339,591)(340,593)(341,592)(342,594)(343,578)
(344,577)(345,579)(346,581)(347,580)(348,582)(349,584)(350,583)(351,585)
(352,542)(353,541)(354,543)(355,545)(356,544)(357,546)(358,548)(359,547)
(360,549)(361,560)(362,559)(363,561)(364,563)(365,562)(366,564)(367,566)
(368,565)(369,567)(370,551)(371,550)(372,552)(373,554)(374,553)(375,555)
(376,557)(377,556)(378,558)(379,623)(380,622)(381,624)(382,626)(383,625)
(384,627)(385,629)(386,628)(387,630)(388,641)(389,640)(390,642)(391,644)
(392,643)(393,645)(394,647)(395,646)(396,648)(397,632)(398,631)(399,633)
(400,635)(401,634)(402,636)(403,638)(404,637)(405,639)(406,596)(407,595)
(408,597)(409,599)(410,598)(411,600)(412,602)(413,601)(414,603)(415,614)
(416,613)(417,615)(418,617)(419,616)(420,618)(421,620)(422,619)(423,621)
(424,605)(425,604)(426,606)(427,608)(428,607)(429,609)(430,611)(431,610)
(432,612);
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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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