Polytope of Type {12,6,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,4}*1728j
if this polytope has a name.
Group : SmallGroup(1728,46356)
Rank : 4
Schlafli Type : {12,6,4}
Number of vertices, edges, etc : 36, 108, 36, 4
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-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 : {6,6,4}*864i
3-fold quotients : {12,6,4}*576d, {12,6,4}*576e
6-fold quotients : {6,6,4}*288d, {6,6,4}*288e
9-fold quotients : {4,6,4}*192b
12-fold quotients : {6,3,4}*144
18-fold quotients : {2,6,4}*96c
36-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,433)( 2,434)( 3,435)( 4,436)( 5,441)( 6,442)( 7,443)( 8,444)
( 9,437)( 10,438)( 11,439)( 12,440)( 13,457)( 14,458)( 15,459)( 16,460)
( 17,465)( 18,466)( 19,467)( 20,468)( 21,461)( 22,462)( 23,463)( 24,464)
( 25,445)( 26,446)( 27,447)( 28,448)( 29,453)( 30,454)( 31,455)( 32,456)
( 33,449)( 34,450)( 35,451)( 36,452)( 37,469)( 38,470)( 39,471)( 40,472)
( 41,477)( 42,478)( 43,479)( 44,480)( 45,473)( 46,474)( 47,475)( 48,476)
( 49,493)( 50,494)( 51,495)( 52,496)( 53,501)( 54,502)( 55,503)( 56,504)
( 57,497)( 58,498)( 59,499)( 60,500)( 61,481)( 62,482)( 63,483)( 64,484)
( 65,489)( 66,490)( 67,491)( 68,492)( 69,485)( 70,486)( 71,487)( 72,488)
( 73,505)( 74,506)( 75,507)( 76,508)( 77,513)( 78,514)( 79,515)( 80,516)
( 81,509)( 82,510)( 83,511)( 84,512)( 85,529)( 86,530)( 87,531)( 88,532)
( 89,537)( 90,538)( 91,539)( 92,540)( 93,533)( 94,534)( 95,535)( 96,536)
( 97,517)( 98,518)( 99,519)(100,520)(101,525)(102,526)(103,527)(104,528)
(105,521)(106,522)(107,523)(108,524)(109,541)(110,542)(111,543)(112,544)
(113,549)(114,550)(115,551)(116,552)(117,545)(118,546)(119,547)(120,548)
(121,565)(122,566)(123,567)(124,568)(125,573)(126,574)(127,575)(128,576)
(129,569)(130,570)(131,571)(132,572)(133,553)(134,554)(135,555)(136,556)
(137,561)(138,562)(139,563)(140,564)(141,557)(142,558)(143,559)(144,560)
(145,577)(146,578)(147,579)(148,580)(149,585)(150,586)(151,587)(152,588)
(153,581)(154,582)(155,583)(156,584)(157,601)(158,602)(159,603)(160,604)
(161,609)(162,610)(163,611)(164,612)(165,605)(166,606)(167,607)(168,608)
(169,589)(170,590)(171,591)(172,592)(173,597)(174,598)(175,599)(176,600)
(177,593)(178,594)(179,595)(180,596)(181,613)(182,614)(183,615)(184,616)
(185,621)(186,622)(187,623)(188,624)(189,617)(190,618)(191,619)(192,620)
(193,637)(194,638)(195,639)(196,640)(197,645)(198,646)(199,647)(200,648)
(201,641)(202,642)(203,643)(204,644)(205,625)(206,626)(207,627)(208,628)
(209,633)(210,634)(211,635)(212,636)(213,629)(214,630)(215,631)(216,632)
(217,757)(218,758)(219,759)(220,760)(221,765)(222,766)(223,767)(224,768)
(225,761)(226,762)(227,763)(228,764)(229,781)(230,782)(231,783)(232,784)
(233,789)(234,790)(235,791)(236,792)(237,785)(238,786)(239,787)(240,788)
(241,769)(242,770)(243,771)(244,772)(245,777)(246,778)(247,779)(248,780)
(249,773)(250,774)(251,775)(252,776)(253,793)(254,794)(255,795)(256,796)
(257,801)(258,802)(259,803)(260,804)(261,797)(262,798)(263,799)(264,800)
(265,817)(266,818)(267,819)(268,820)(269,825)(270,826)(271,827)(272,828)
(273,821)(274,822)(275,823)(276,824)(277,805)(278,806)(279,807)(280,808)
(281,813)(282,814)(283,815)(284,816)(285,809)(286,810)(287,811)(288,812)
(289,829)(290,830)(291,831)(292,832)(293,837)(294,838)(295,839)(296,840)
(297,833)(298,834)(299,835)(300,836)(301,853)(302,854)(303,855)(304,856)
(305,861)(306,862)(307,863)(308,864)(309,857)(310,858)(311,859)(312,860)
(313,841)(314,842)(315,843)(316,844)(317,849)(318,850)(319,851)(320,852)
(321,845)(322,846)(323,847)(324,848)(325,649)(326,650)(327,651)(328,652)
(329,657)(330,658)(331,659)(332,660)(333,653)(334,654)(335,655)(336,656)
(337,673)(338,674)(339,675)(340,676)(341,681)(342,682)(343,683)(344,684)
(345,677)(346,678)(347,679)(348,680)(349,661)(350,662)(351,663)(352,664)
(353,669)(354,670)(355,671)(356,672)(357,665)(358,666)(359,667)(360,668)
(361,685)(362,686)(363,687)(364,688)(365,693)(366,694)(367,695)(368,696)
(369,689)(370,690)(371,691)(372,692)(373,709)(374,710)(375,711)(376,712)
(377,717)(378,718)(379,719)(380,720)(381,713)(382,714)(383,715)(384,716)
(385,697)(386,698)(387,699)(388,700)(389,705)(390,706)(391,707)(392,708)
(393,701)(394,702)(395,703)(396,704)(397,721)(398,722)(399,723)(400,724)
(401,729)(402,730)(403,731)(404,732)(405,725)(406,726)(407,727)(408,728)
(409,745)(410,746)(411,747)(412,748)(413,753)(414,754)(415,755)(416,756)
(417,749)(418,750)(419,751)(420,752)(421,733)(422,734)(423,735)(424,736)
(425,741)(426,742)(427,743)(428,744)(429,737)(430,738)(431,739)(432,740);;
s1 := ( 1,665)( 2,666)( 3,668)( 4,667)( 5,661)( 6,662)( 7,664)( 8,663)
( 9,669)( 10,670)( 11,672)( 12,671)( 13,653)( 14,654)( 15,656)( 16,655)
( 17,649)( 18,650)( 19,652)( 20,651)( 21,657)( 22,658)( 23,660)( 24,659)
( 25,677)( 26,678)( 27,680)( 28,679)( 29,673)( 30,674)( 31,676)( 32,675)
( 33,681)( 34,682)( 35,684)( 36,683)( 37,737)( 38,738)( 39,740)( 40,739)
( 41,733)( 42,734)( 43,736)( 44,735)( 45,741)( 46,742)( 47,744)( 48,743)
( 49,725)( 50,726)( 51,728)( 52,727)( 53,721)( 54,722)( 55,724)( 56,723)
( 57,729)( 58,730)( 59,732)( 60,731)( 61,749)( 62,750)( 63,752)( 64,751)
( 65,745)( 66,746)( 67,748)( 68,747)( 69,753)( 70,754)( 71,756)( 72,755)
( 73,701)( 74,702)( 75,704)( 76,703)( 77,697)( 78,698)( 79,700)( 80,699)
( 81,705)( 82,706)( 83,708)( 84,707)( 85,689)( 86,690)( 87,692)( 88,691)
( 89,685)( 90,686)( 91,688)( 92,687)( 93,693)( 94,694)( 95,696)( 96,695)
( 97,713)( 98,714)( 99,716)(100,715)(101,709)(102,710)(103,712)(104,711)
(105,717)(106,718)(107,720)(108,719)(109,773)(110,774)(111,776)(112,775)
(113,769)(114,770)(115,772)(116,771)(117,777)(118,778)(119,780)(120,779)
(121,761)(122,762)(123,764)(124,763)(125,757)(126,758)(127,760)(128,759)
(129,765)(130,766)(131,768)(132,767)(133,785)(134,786)(135,788)(136,787)
(137,781)(138,782)(139,784)(140,783)(141,789)(142,790)(143,792)(144,791)
(145,845)(146,846)(147,848)(148,847)(149,841)(150,842)(151,844)(152,843)
(153,849)(154,850)(155,852)(156,851)(157,833)(158,834)(159,836)(160,835)
(161,829)(162,830)(163,832)(164,831)(165,837)(166,838)(167,840)(168,839)
(169,857)(170,858)(171,860)(172,859)(173,853)(174,854)(175,856)(176,855)
(177,861)(178,862)(179,864)(180,863)(181,809)(182,810)(183,812)(184,811)
(185,805)(186,806)(187,808)(188,807)(189,813)(190,814)(191,816)(192,815)
(193,797)(194,798)(195,800)(196,799)(197,793)(198,794)(199,796)(200,795)
(201,801)(202,802)(203,804)(204,803)(205,821)(206,822)(207,824)(208,823)
(209,817)(210,818)(211,820)(212,819)(213,825)(214,826)(215,828)(216,827)
(217,449)(218,450)(219,452)(220,451)(221,445)(222,446)(223,448)(224,447)
(225,453)(226,454)(227,456)(228,455)(229,437)(230,438)(231,440)(232,439)
(233,433)(234,434)(235,436)(236,435)(237,441)(238,442)(239,444)(240,443)
(241,461)(242,462)(243,464)(244,463)(245,457)(246,458)(247,460)(248,459)
(249,465)(250,466)(251,468)(252,467)(253,521)(254,522)(255,524)(256,523)
(257,517)(258,518)(259,520)(260,519)(261,525)(262,526)(263,528)(264,527)
(265,509)(266,510)(267,512)(268,511)(269,505)(270,506)(271,508)(272,507)
(273,513)(274,514)(275,516)(276,515)(277,533)(278,534)(279,536)(280,535)
(281,529)(282,530)(283,532)(284,531)(285,537)(286,538)(287,540)(288,539)
(289,485)(290,486)(291,488)(292,487)(293,481)(294,482)(295,484)(296,483)
(297,489)(298,490)(299,492)(300,491)(301,473)(302,474)(303,476)(304,475)
(305,469)(306,470)(307,472)(308,471)(309,477)(310,478)(311,480)(312,479)
(313,497)(314,498)(315,500)(316,499)(317,493)(318,494)(319,496)(320,495)
(321,501)(322,502)(323,504)(324,503)(325,557)(326,558)(327,560)(328,559)
(329,553)(330,554)(331,556)(332,555)(333,561)(334,562)(335,564)(336,563)
(337,545)(338,546)(339,548)(340,547)(341,541)(342,542)(343,544)(344,543)
(345,549)(346,550)(347,552)(348,551)(349,569)(350,570)(351,572)(352,571)
(353,565)(354,566)(355,568)(356,567)(357,573)(358,574)(359,576)(360,575)
(361,629)(362,630)(363,632)(364,631)(365,625)(366,626)(367,628)(368,627)
(369,633)(370,634)(371,636)(372,635)(373,617)(374,618)(375,620)(376,619)
(377,613)(378,614)(379,616)(380,615)(381,621)(382,622)(383,624)(384,623)
(385,641)(386,642)(387,644)(388,643)(389,637)(390,638)(391,640)(392,639)
(393,645)(394,646)(395,648)(396,647)(397,593)(398,594)(399,596)(400,595)
(401,589)(402,590)(403,592)(404,591)(405,597)(406,598)(407,600)(408,599)
(409,581)(410,582)(411,584)(412,583)(413,577)(414,578)(415,580)(416,579)
(417,585)(418,586)(419,588)(420,587)(421,605)(422,606)(423,608)(424,607)
(425,601)(426,602)(427,604)(428,603)(429,609)(430,610)(431,612)(432,611);;
s2 := ( 1,685)( 2,688)( 3,687)( 4,686)( 5,693)( 6,696)( 7,695)( 8,694)
( 9,689)( 10,692)( 11,691)( 12,690)( 13,697)( 14,700)( 15,699)( 16,698)
( 17,705)( 18,708)( 19,707)( 20,706)( 21,701)( 22,704)( 23,703)( 24,702)
( 25,709)( 26,712)( 27,711)( 28,710)( 29,717)( 30,720)( 31,719)( 32,718)
( 33,713)( 34,716)( 35,715)( 36,714)( 37,649)( 38,652)( 39,651)( 40,650)
( 41,657)( 42,660)( 43,659)( 44,658)( 45,653)( 46,656)( 47,655)( 48,654)
( 49,661)( 50,664)( 51,663)( 52,662)( 53,669)( 54,672)( 55,671)( 56,670)
( 57,665)( 58,668)( 59,667)( 60,666)( 61,673)( 62,676)( 63,675)( 64,674)
( 65,681)( 66,684)( 67,683)( 68,682)( 69,677)( 70,680)( 71,679)( 72,678)
( 73,721)( 74,724)( 75,723)( 76,722)( 77,729)( 78,732)( 79,731)( 80,730)
( 81,725)( 82,728)( 83,727)( 84,726)( 85,733)( 86,736)( 87,735)( 88,734)
( 89,741)( 90,744)( 91,743)( 92,742)( 93,737)( 94,740)( 95,739)( 96,738)
( 97,745)( 98,748)( 99,747)(100,746)(101,753)(102,756)(103,755)(104,754)
(105,749)(106,752)(107,751)(108,750)(109,793)(110,796)(111,795)(112,794)
(113,801)(114,804)(115,803)(116,802)(117,797)(118,800)(119,799)(120,798)
(121,805)(122,808)(123,807)(124,806)(125,813)(126,816)(127,815)(128,814)
(129,809)(130,812)(131,811)(132,810)(133,817)(134,820)(135,819)(136,818)
(137,825)(138,828)(139,827)(140,826)(141,821)(142,824)(143,823)(144,822)
(145,757)(146,760)(147,759)(148,758)(149,765)(150,768)(151,767)(152,766)
(153,761)(154,764)(155,763)(156,762)(157,769)(158,772)(159,771)(160,770)
(161,777)(162,780)(163,779)(164,778)(165,773)(166,776)(167,775)(168,774)
(169,781)(170,784)(171,783)(172,782)(173,789)(174,792)(175,791)(176,790)
(177,785)(178,788)(179,787)(180,786)(181,829)(182,832)(183,831)(184,830)
(185,837)(186,840)(187,839)(188,838)(189,833)(190,836)(191,835)(192,834)
(193,841)(194,844)(195,843)(196,842)(197,849)(198,852)(199,851)(200,850)
(201,845)(202,848)(203,847)(204,846)(205,853)(206,856)(207,855)(208,854)
(209,861)(210,864)(211,863)(212,862)(213,857)(214,860)(215,859)(216,858)
(217,577)(218,580)(219,579)(220,578)(221,585)(222,588)(223,587)(224,586)
(225,581)(226,584)(227,583)(228,582)(229,589)(230,592)(231,591)(232,590)
(233,597)(234,600)(235,599)(236,598)(237,593)(238,596)(239,595)(240,594)
(241,601)(242,604)(243,603)(244,602)(245,609)(246,612)(247,611)(248,610)
(249,605)(250,608)(251,607)(252,606)(253,541)(254,544)(255,543)(256,542)
(257,549)(258,552)(259,551)(260,550)(261,545)(262,548)(263,547)(264,546)
(265,553)(266,556)(267,555)(268,554)(269,561)(270,564)(271,563)(272,562)
(273,557)(274,560)(275,559)(276,558)(277,565)(278,568)(279,567)(280,566)
(281,573)(282,576)(283,575)(284,574)(285,569)(286,572)(287,571)(288,570)
(289,613)(290,616)(291,615)(292,614)(293,621)(294,624)(295,623)(296,622)
(297,617)(298,620)(299,619)(300,618)(301,625)(302,628)(303,627)(304,626)
(305,633)(306,636)(307,635)(308,634)(309,629)(310,632)(311,631)(312,630)
(313,637)(314,640)(315,639)(316,638)(317,645)(318,648)(319,647)(320,646)
(321,641)(322,644)(323,643)(324,642)(325,469)(326,472)(327,471)(328,470)
(329,477)(330,480)(331,479)(332,478)(333,473)(334,476)(335,475)(336,474)
(337,481)(338,484)(339,483)(340,482)(341,489)(342,492)(343,491)(344,490)
(345,485)(346,488)(347,487)(348,486)(349,493)(350,496)(351,495)(352,494)
(353,501)(354,504)(355,503)(356,502)(357,497)(358,500)(359,499)(360,498)
(361,433)(362,436)(363,435)(364,434)(365,441)(366,444)(367,443)(368,442)
(369,437)(370,440)(371,439)(372,438)(373,445)(374,448)(375,447)(376,446)
(377,453)(378,456)(379,455)(380,454)(381,449)(382,452)(383,451)(384,450)
(385,457)(386,460)(387,459)(388,458)(389,465)(390,468)(391,467)(392,466)
(393,461)(394,464)(395,463)(396,462)(397,505)(398,508)(399,507)(400,506)
(401,513)(402,516)(403,515)(404,514)(405,509)(406,512)(407,511)(408,510)
(409,517)(410,520)(411,519)(412,518)(413,525)(414,528)(415,527)(416,526)
(417,521)(418,524)(419,523)(420,522)(421,529)(422,532)(423,531)(424,530)
(425,537)(426,540)(427,539)(428,538)(429,533)(430,536)(431,535)(432,534);;
s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)
(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)
(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)
(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)
(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)
(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)
(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)
(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)(367,368)
(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)
(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)(399,400)
(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)
(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)(431,432)
(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)(447,448)
(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)(463,464)
(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)(479,480)
(481,482)(483,484)(485,486)(487,488)(489,490)(491,492)(493,494)(495,496)
(497,498)(499,500)(501,502)(503,504)(505,506)(507,508)(509,510)(511,512)
(513,514)(515,516)(517,518)(519,520)(521,522)(523,524)(525,526)(527,528)
(529,530)(531,532)(533,534)(535,536)(537,538)(539,540)(541,542)(543,544)
(545,546)(547,548)(549,550)(551,552)(553,554)(555,556)(557,558)(559,560)
(561,562)(563,564)(565,566)(567,568)(569,570)(571,572)(573,574)(575,576)
(577,578)(579,580)(581,582)(583,584)(585,586)(587,588)(589,590)(591,592)
(593,594)(595,596)(597,598)(599,600)(601,602)(603,604)(605,606)(607,608)
(609,610)(611,612)(613,614)(615,616)(617,618)(619,620)(621,622)(623,624)
(625,626)(627,628)(629,630)(631,632)(633,634)(635,636)(637,638)(639,640)
(641,642)(643,644)(645,646)(647,648)(649,650)(651,652)(653,654)(655,656)
(657,658)(659,660)(661,662)(663,664)(665,666)(667,668)(669,670)(671,672)
(673,674)(675,676)(677,678)(679,680)(681,682)(683,684)(685,686)(687,688)
(689,690)(691,692)(693,694)(695,696)(697,698)(699,700)(701,702)(703,704)
(705,706)(707,708)(709,710)(711,712)(713,714)(715,716)(717,718)(719,720)
(721,722)(723,724)(725,726)(727,728)(729,730)(731,732)(733,734)(735,736)
(737,738)(739,740)(741,742)(743,744)(745,746)(747,748)(749,750)(751,752)
(753,754)(755,756)(757,758)(759,760)(761,762)(763,764)(765,766)(767,768)
(769,770)(771,772)(773,774)(775,776)(777,778)(779,780)(781,782)(783,784)
(785,786)(787,788)(789,790)(791,792)(793,794)(795,796)(797,798)(799,800)
(801,802)(803,804)(805,806)(807,808)(809,810)(811,812)(813,814)(815,816)
(817,818)(819,820)(821,822)(823,824)(825,826)(827,828)(829,830)(831,832)
(833,834)(835,836)(837,838)(839,840)(841,842)(843,844)(845,846)(847,848)
(849,850)(851,852)(853,854)(855,856)(857,858)(859,860)(861,862)(863,864);;
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, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s2*s1*s3*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s0*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 1,433)( 2,434)( 3,435)( 4,436)( 5,441)( 6,442)( 7,443)
( 8,444)( 9,437)( 10,438)( 11,439)( 12,440)( 13,457)( 14,458)( 15,459)
( 16,460)( 17,465)( 18,466)( 19,467)( 20,468)( 21,461)( 22,462)( 23,463)
( 24,464)( 25,445)( 26,446)( 27,447)( 28,448)( 29,453)( 30,454)( 31,455)
( 32,456)( 33,449)( 34,450)( 35,451)( 36,452)( 37,469)( 38,470)( 39,471)
( 40,472)( 41,477)( 42,478)( 43,479)( 44,480)( 45,473)( 46,474)( 47,475)
( 48,476)( 49,493)( 50,494)( 51,495)( 52,496)( 53,501)( 54,502)( 55,503)
( 56,504)( 57,497)( 58,498)( 59,499)( 60,500)( 61,481)( 62,482)( 63,483)
( 64,484)( 65,489)( 66,490)( 67,491)( 68,492)( 69,485)( 70,486)( 71,487)
( 72,488)( 73,505)( 74,506)( 75,507)( 76,508)( 77,513)( 78,514)( 79,515)
( 80,516)( 81,509)( 82,510)( 83,511)( 84,512)( 85,529)( 86,530)( 87,531)
( 88,532)( 89,537)( 90,538)( 91,539)( 92,540)( 93,533)( 94,534)( 95,535)
( 96,536)( 97,517)( 98,518)( 99,519)(100,520)(101,525)(102,526)(103,527)
(104,528)(105,521)(106,522)(107,523)(108,524)(109,541)(110,542)(111,543)
(112,544)(113,549)(114,550)(115,551)(116,552)(117,545)(118,546)(119,547)
(120,548)(121,565)(122,566)(123,567)(124,568)(125,573)(126,574)(127,575)
(128,576)(129,569)(130,570)(131,571)(132,572)(133,553)(134,554)(135,555)
(136,556)(137,561)(138,562)(139,563)(140,564)(141,557)(142,558)(143,559)
(144,560)(145,577)(146,578)(147,579)(148,580)(149,585)(150,586)(151,587)
(152,588)(153,581)(154,582)(155,583)(156,584)(157,601)(158,602)(159,603)
(160,604)(161,609)(162,610)(163,611)(164,612)(165,605)(166,606)(167,607)
(168,608)(169,589)(170,590)(171,591)(172,592)(173,597)(174,598)(175,599)
(176,600)(177,593)(178,594)(179,595)(180,596)(181,613)(182,614)(183,615)
(184,616)(185,621)(186,622)(187,623)(188,624)(189,617)(190,618)(191,619)
(192,620)(193,637)(194,638)(195,639)(196,640)(197,645)(198,646)(199,647)
(200,648)(201,641)(202,642)(203,643)(204,644)(205,625)(206,626)(207,627)
(208,628)(209,633)(210,634)(211,635)(212,636)(213,629)(214,630)(215,631)
(216,632)(217,757)(218,758)(219,759)(220,760)(221,765)(222,766)(223,767)
(224,768)(225,761)(226,762)(227,763)(228,764)(229,781)(230,782)(231,783)
(232,784)(233,789)(234,790)(235,791)(236,792)(237,785)(238,786)(239,787)
(240,788)(241,769)(242,770)(243,771)(244,772)(245,777)(246,778)(247,779)
(248,780)(249,773)(250,774)(251,775)(252,776)(253,793)(254,794)(255,795)
(256,796)(257,801)(258,802)(259,803)(260,804)(261,797)(262,798)(263,799)
(264,800)(265,817)(266,818)(267,819)(268,820)(269,825)(270,826)(271,827)
(272,828)(273,821)(274,822)(275,823)(276,824)(277,805)(278,806)(279,807)
(280,808)(281,813)(282,814)(283,815)(284,816)(285,809)(286,810)(287,811)
(288,812)(289,829)(290,830)(291,831)(292,832)(293,837)(294,838)(295,839)
(296,840)(297,833)(298,834)(299,835)(300,836)(301,853)(302,854)(303,855)
(304,856)(305,861)(306,862)(307,863)(308,864)(309,857)(310,858)(311,859)
(312,860)(313,841)(314,842)(315,843)(316,844)(317,849)(318,850)(319,851)
(320,852)(321,845)(322,846)(323,847)(324,848)(325,649)(326,650)(327,651)
(328,652)(329,657)(330,658)(331,659)(332,660)(333,653)(334,654)(335,655)
(336,656)(337,673)(338,674)(339,675)(340,676)(341,681)(342,682)(343,683)
(344,684)(345,677)(346,678)(347,679)(348,680)(349,661)(350,662)(351,663)
(352,664)(353,669)(354,670)(355,671)(356,672)(357,665)(358,666)(359,667)
(360,668)(361,685)(362,686)(363,687)(364,688)(365,693)(366,694)(367,695)
(368,696)(369,689)(370,690)(371,691)(372,692)(373,709)(374,710)(375,711)
(376,712)(377,717)(378,718)(379,719)(380,720)(381,713)(382,714)(383,715)
(384,716)(385,697)(386,698)(387,699)(388,700)(389,705)(390,706)(391,707)
(392,708)(393,701)(394,702)(395,703)(396,704)(397,721)(398,722)(399,723)
(400,724)(401,729)(402,730)(403,731)(404,732)(405,725)(406,726)(407,727)
(408,728)(409,745)(410,746)(411,747)(412,748)(413,753)(414,754)(415,755)
(416,756)(417,749)(418,750)(419,751)(420,752)(421,733)(422,734)(423,735)
(424,736)(425,741)(426,742)(427,743)(428,744)(429,737)(430,738)(431,739)
(432,740);
s1 := Sym(864)!( 1,665)( 2,666)( 3,668)( 4,667)( 5,661)( 6,662)( 7,664)
( 8,663)( 9,669)( 10,670)( 11,672)( 12,671)( 13,653)( 14,654)( 15,656)
( 16,655)( 17,649)( 18,650)( 19,652)( 20,651)( 21,657)( 22,658)( 23,660)
( 24,659)( 25,677)( 26,678)( 27,680)( 28,679)( 29,673)( 30,674)( 31,676)
( 32,675)( 33,681)( 34,682)( 35,684)( 36,683)( 37,737)( 38,738)( 39,740)
( 40,739)( 41,733)( 42,734)( 43,736)( 44,735)( 45,741)( 46,742)( 47,744)
( 48,743)( 49,725)( 50,726)( 51,728)( 52,727)( 53,721)( 54,722)( 55,724)
( 56,723)( 57,729)( 58,730)( 59,732)( 60,731)( 61,749)( 62,750)( 63,752)
( 64,751)( 65,745)( 66,746)( 67,748)( 68,747)( 69,753)( 70,754)( 71,756)
( 72,755)( 73,701)( 74,702)( 75,704)( 76,703)( 77,697)( 78,698)( 79,700)
( 80,699)( 81,705)( 82,706)( 83,708)( 84,707)( 85,689)( 86,690)( 87,692)
( 88,691)( 89,685)( 90,686)( 91,688)( 92,687)( 93,693)( 94,694)( 95,696)
( 96,695)( 97,713)( 98,714)( 99,716)(100,715)(101,709)(102,710)(103,712)
(104,711)(105,717)(106,718)(107,720)(108,719)(109,773)(110,774)(111,776)
(112,775)(113,769)(114,770)(115,772)(116,771)(117,777)(118,778)(119,780)
(120,779)(121,761)(122,762)(123,764)(124,763)(125,757)(126,758)(127,760)
(128,759)(129,765)(130,766)(131,768)(132,767)(133,785)(134,786)(135,788)
(136,787)(137,781)(138,782)(139,784)(140,783)(141,789)(142,790)(143,792)
(144,791)(145,845)(146,846)(147,848)(148,847)(149,841)(150,842)(151,844)
(152,843)(153,849)(154,850)(155,852)(156,851)(157,833)(158,834)(159,836)
(160,835)(161,829)(162,830)(163,832)(164,831)(165,837)(166,838)(167,840)
(168,839)(169,857)(170,858)(171,860)(172,859)(173,853)(174,854)(175,856)
(176,855)(177,861)(178,862)(179,864)(180,863)(181,809)(182,810)(183,812)
(184,811)(185,805)(186,806)(187,808)(188,807)(189,813)(190,814)(191,816)
(192,815)(193,797)(194,798)(195,800)(196,799)(197,793)(198,794)(199,796)
(200,795)(201,801)(202,802)(203,804)(204,803)(205,821)(206,822)(207,824)
(208,823)(209,817)(210,818)(211,820)(212,819)(213,825)(214,826)(215,828)
(216,827)(217,449)(218,450)(219,452)(220,451)(221,445)(222,446)(223,448)
(224,447)(225,453)(226,454)(227,456)(228,455)(229,437)(230,438)(231,440)
(232,439)(233,433)(234,434)(235,436)(236,435)(237,441)(238,442)(239,444)
(240,443)(241,461)(242,462)(243,464)(244,463)(245,457)(246,458)(247,460)
(248,459)(249,465)(250,466)(251,468)(252,467)(253,521)(254,522)(255,524)
(256,523)(257,517)(258,518)(259,520)(260,519)(261,525)(262,526)(263,528)
(264,527)(265,509)(266,510)(267,512)(268,511)(269,505)(270,506)(271,508)
(272,507)(273,513)(274,514)(275,516)(276,515)(277,533)(278,534)(279,536)
(280,535)(281,529)(282,530)(283,532)(284,531)(285,537)(286,538)(287,540)
(288,539)(289,485)(290,486)(291,488)(292,487)(293,481)(294,482)(295,484)
(296,483)(297,489)(298,490)(299,492)(300,491)(301,473)(302,474)(303,476)
(304,475)(305,469)(306,470)(307,472)(308,471)(309,477)(310,478)(311,480)
(312,479)(313,497)(314,498)(315,500)(316,499)(317,493)(318,494)(319,496)
(320,495)(321,501)(322,502)(323,504)(324,503)(325,557)(326,558)(327,560)
(328,559)(329,553)(330,554)(331,556)(332,555)(333,561)(334,562)(335,564)
(336,563)(337,545)(338,546)(339,548)(340,547)(341,541)(342,542)(343,544)
(344,543)(345,549)(346,550)(347,552)(348,551)(349,569)(350,570)(351,572)
(352,571)(353,565)(354,566)(355,568)(356,567)(357,573)(358,574)(359,576)
(360,575)(361,629)(362,630)(363,632)(364,631)(365,625)(366,626)(367,628)
(368,627)(369,633)(370,634)(371,636)(372,635)(373,617)(374,618)(375,620)
(376,619)(377,613)(378,614)(379,616)(380,615)(381,621)(382,622)(383,624)
(384,623)(385,641)(386,642)(387,644)(388,643)(389,637)(390,638)(391,640)
(392,639)(393,645)(394,646)(395,648)(396,647)(397,593)(398,594)(399,596)
(400,595)(401,589)(402,590)(403,592)(404,591)(405,597)(406,598)(407,600)
(408,599)(409,581)(410,582)(411,584)(412,583)(413,577)(414,578)(415,580)
(416,579)(417,585)(418,586)(419,588)(420,587)(421,605)(422,606)(423,608)
(424,607)(425,601)(426,602)(427,604)(428,603)(429,609)(430,610)(431,612)
(432,611);
s2 := Sym(864)!( 1,685)( 2,688)( 3,687)( 4,686)( 5,693)( 6,696)( 7,695)
( 8,694)( 9,689)( 10,692)( 11,691)( 12,690)( 13,697)( 14,700)( 15,699)
( 16,698)( 17,705)( 18,708)( 19,707)( 20,706)( 21,701)( 22,704)( 23,703)
( 24,702)( 25,709)( 26,712)( 27,711)( 28,710)( 29,717)( 30,720)( 31,719)
( 32,718)( 33,713)( 34,716)( 35,715)( 36,714)( 37,649)( 38,652)( 39,651)
( 40,650)( 41,657)( 42,660)( 43,659)( 44,658)( 45,653)( 46,656)( 47,655)
( 48,654)( 49,661)( 50,664)( 51,663)( 52,662)( 53,669)( 54,672)( 55,671)
( 56,670)( 57,665)( 58,668)( 59,667)( 60,666)( 61,673)( 62,676)( 63,675)
( 64,674)( 65,681)( 66,684)( 67,683)( 68,682)( 69,677)( 70,680)( 71,679)
( 72,678)( 73,721)( 74,724)( 75,723)( 76,722)( 77,729)( 78,732)( 79,731)
( 80,730)( 81,725)( 82,728)( 83,727)( 84,726)( 85,733)( 86,736)( 87,735)
( 88,734)( 89,741)( 90,744)( 91,743)( 92,742)( 93,737)( 94,740)( 95,739)
( 96,738)( 97,745)( 98,748)( 99,747)(100,746)(101,753)(102,756)(103,755)
(104,754)(105,749)(106,752)(107,751)(108,750)(109,793)(110,796)(111,795)
(112,794)(113,801)(114,804)(115,803)(116,802)(117,797)(118,800)(119,799)
(120,798)(121,805)(122,808)(123,807)(124,806)(125,813)(126,816)(127,815)
(128,814)(129,809)(130,812)(131,811)(132,810)(133,817)(134,820)(135,819)
(136,818)(137,825)(138,828)(139,827)(140,826)(141,821)(142,824)(143,823)
(144,822)(145,757)(146,760)(147,759)(148,758)(149,765)(150,768)(151,767)
(152,766)(153,761)(154,764)(155,763)(156,762)(157,769)(158,772)(159,771)
(160,770)(161,777)(162,780)(163,779)(164,778)(165,773)(166,776)(167,775)
(168,774)(169,781)(170,784)(171,783)(172,782)(173,789)(174,792)(175,791)
(176,790)(177,785)(178,788)(179,787)(180,786)(181,829)(182,832)(183,831)
(184,830)(185,837)(186,840)(187,839)(188,838)(189,833)(190,836)(191,835)
(192,834)(193,841)(194,844)(195,843)(196,842)(197,849)(198,852)(199,851)
(200,850)(201,845)(202,848)(203,847)(204,846)(205,853)(206,856)(207,855)
(208,854)(209,861)(210,864)(211,863)(212,862)(213,857)(214,860)(215,859)
(216,858)(217,577)(218,580)(219,579)(220,578)(221,585)(222,588)(223,587)
(224,586)(225,581)(226,584)(227,583)(228,582)(229,589)(230,592)(231,591)
(232,590)(233,597)(234,600)(235,599)(236,598)(237,593)(238,596)(239,595)
(240,594)(241,601)(242,604)(243,603)(244,602)(245,609)(246,612)(247,611)
(248,610)(249,605)(250,608)(251,607)(252,606)(253,541)(254,544)(255,543)
(256,542)(257,549)(258,552)(259,551)(260,550)(261,545)(262,548)(263,547)
(264,546)(265,553)(266,556)(267,555)(268,554)(269,561)(270,564)(271,563)
(272,562)(273,557)(274,560)(275,559)(276,558)(277,565)(278,568)(279,567)
(280,566)(281,573)(282,576)(283,575)(284,574)(285,569)(286,572)(287,571)
(288,570)(289,613)(290,616)(291,615)(292,614)(293,621)(294,624)(295,623)
(296,622)(297,617)(298,620)(299,619)(300,618)(301,625)(302,628)(303,627)
(304,626)(305,633)(306,636)(307,635)(308,634)(309,629)(310,632)(311,631)
(312,630)(313,637)(314,640)(315,639)(316,638)(317,645)(318,648)(319,647)
(320,646)(321,641)(322,644)(323,643)(324,642)(325,469)(326,472)(327,471)
(328,470)(329,477)(330,480)(331,479)(332,478)(333,473)(334,476)(335,475)
(336,474)(337,481)(338,484)(339,483)(340,482)(341,489)(342,492)(343,491)
(344,490)(345,485)(346,488)(347,487)(348,486)(349,493)(350,496)(351,495)
(352,494)(353,501)(354,504)(355,503)(356,502)(357,497)(358,500)(359,499)
(360,498)(361,433)(362,436)(363,435)(364,434)(365,441)(366,444)(367,443)
(368,442)(369,437)(370,440)(371,439)(372,438)(373,445)(374,448)(375,447)
(376,446)(377,453)(378,456)(379,455)(380,454)(381,449)(382,452)(383,451)
(384,450)(385,457)(386,460)(387,459)(388,458)(389,465)(390,468)(391,467)
(392,466)(393,461)(394,464)(395,463)(396,462)(397,505)(398,508)(399,507)
(400,506)(401,513)(402,516)(403,515)(404,514)(405,509)(406,512)(407,511)
(408,510)(409,517)(410,520)(411,519)(412,518)(413,525)(414,528)(415,527)
(416,526)(417,521)(418,524)(419,523)(420,522)(421,529)(422,532)(423,531)
(424,530)(425,537)(426,540)(427,539)(428,538)(429,533)(430,536)(431,535)
(432,534);
s3 := Sym(864)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)
(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)
(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)
(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)
(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)
(319,320)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)
(335,336)(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)
(351,352)(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)
(367,368)(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)
(383,384)(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)
(399,400)(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)
(415,416)(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)
(431,432)(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)
(447,448)(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)
(463,464)(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)
(479,480)(481,482)(483,484)(485,486)(487,488)(489,490)(491,492)(493,494)
(495,496)(497,498)(499,500)(501,502)(503,504)(505,506)(507,508)(509,510)
(511,512)(513,514)(515,516)(517,518)(519,520)(521,522)(523,524)(525,526)
(527,528)(529,530)(531,532)(533,534)(535,536)(537,538)(539,540)(541,542)
(543,544)(545,546)(547,548)(549,550)(551,552)(553,554)(555,556)(557,558)
(559,560)(561,562)(563,564)(565,566)(567,568)(569,570)(571,572)(573,574)
(575,576)(577,578)(579,580)(581,582)(583,584)(585,586)(587,588)(589,590)
(591,592)(593,594)(595,596)(597,598)(599,600)(601,602)(603,604)(605,606)
(607,608)(609,610)(611,612)(613,614)(615,616)(617,618)(619,620)(621,622)
(623,624)(625,626)(627,628)(629,630)(631,632)(633,634)(635,636)(637,638)
(639,640)(641,642)(643,644)(645,646)(647,648)(649,650)(651,652)(653,654)
(655,656)(657,658)(659,660)(661,662)(663,664)(665,666)(667,668)(669,670)
(671,672)(673,674)(675,676)(677,678)(679,680)(681,682)(683,684)(685,686)
(687,688)(689,690)(691,692)(693,694)(695,696)(697,698)(699,700)(701,702)
(703,704)(705,706)(707,708)(709,710)(711,712)(713,714)(715,716)(717,718)
(719,720)(721,722)(723,724)(725,726)(727,728)(729,730)(731,732)(733,734)
(735,736)(737,738)(739,740)(741,742)(743,744)(745,746)(747,748)(749,750)
(751,752)(753,754)(755,756)(757,758)(759,760)(761,762)(763,764)(765,766)
(767,768)(769,770)(771,772)(773,774)(775,776)(777,778)(779,780)(781,782)
(783,784)(785,786)(787,788)(789,790)(791,792)(793,794)(795,796)(797,798)
(799,800)(801,802)(803,804)(805,806)(807,808)(809,810)(811,812)(813,814)
(815,816)(817,818)(819,820)(821,822)(823,824)(825,826)(827,828)(829,830)
(831,832)(833,834)(835,836)(837,838)(839,840)(841,842)(843,844)(845,846)
(847,848)(849,850)(851,852)(853,854)(855,856)(857,858)(859,860)(861,862)
(863,864);
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,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s0*s1*s2*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 >;
References : None.
to this polytope