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