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