Polytope of Type {6,24,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,24,3}*1728b
if this polytope has a name.
Group : SmallGroup(1728,46303)
Rank : 4
Schlafli Type : {6,24,3}
Number of vertices, edges, etc : 6, 144, 72, 6
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,12,3}*864b
3-fold quotients : {2,24,3}*576, {6,8,3}*576
6-fold quotients : {6,4,3}*288, {2,12,3}*288
8-fold quotients : {6,6,3}*216b
9-fold quotients : {2,8,3}*192
18-fold quotients : {2,4,3}*96
24-fold quotients : {2,6,3}*72, {6,2,3}*72
36-fold quotients : {2,4,3}*48
48-fold quotients : {3,2,3}*36
72-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 25, 49)( 26, 50)( 27, 51)( 28, 52)( 29, 53)( 30, 54)( 31, 55)( 32, 56)
( 33, 57)( 34, 58)( 35, 59)( 36, 60)( 37, 61)( 38, 62)( 39, 63)( 40, 64)
( 41, 65)( 42, 66)( 43, 67)( 44, 68)( 45, 69)( 46, 70)( 47, 71)( 48, 72)
( 97,121)( 98,122)( 99,123)(100,124)(101,125)(102,126)(103,127)(104,128)
(105,129)(106,130)(107,131)(108,132)(109,133)(110,134)(111,135)(112,136)
(113,137)(114,138)(115,139)(116,140)(117,141)(118,142)(119,143)(120,144)
(169,193)(170,194)(171,195)(172,196)(173,197)(174,198)(175,199)(176,200)
(177,201)(178,202)(179,203)(180,204)(181,205)(182,206)(183,207)(184,208)
(185,209)(186,210)(187,211)(188,212)(189,213)(190,214)(191,215)(192,216)
(241,265)(242,266)(243,267)(244,268)(245,269)(246,270)(247,271)(248,272)
(249,273)(250,274)(251,275)(252,276)(253,277)(254,278)(255,279)(256,280)
(257,281)(258,282)(259,283)(260,284)(261,285)(262,286)(263,287)(264,288)
(313,337)(314,338)(315,339)(316,340)(317,341)(318,342)(319,343)(320,344)
(321,345)(322,346)(323,347)(324,348)(325,349)(326,350)(327,351)(328,352)
(329,353)(330,354)(331,355)(332,356)(333,357)(334,358)(335,359)(336,360)
(385,409)(386,410)(387,411)(388,412)(389,413)(390,414)(391,415)(392,416)
(393,417)(394,418)(395,419)(396,420)(397,421)(398,422)(399,423)(400,424)
(401,425)(402,426)(403,427)(404,428)(405,429)(406,430)(407,431)(408,432)
(457,481)(458,482)(459,483)(460,484)(461,485)(462,486)(463,487)(464,488)
(465,489)(466,490)(467,491)(468,492)(469,493)(470,494)(471,495)(472,496)
(473,497)(474,498)(475,499)(476,500)(477,501)(478,502)(479,503)(480,504)
(529,553)(530,554)(531,555)(532,556)(533,557)(534,558)(535,559)(536,560)
(537,561)(538,562)(539,563)(540,564)(541,565)(542,566)(543,567)(544,568)
(545,569)(546,570)(547,571)(548,572)(549,573)(550,574)(551,575)(552,576)
(601,625)(602,626)(603,627)(604,628)(605,629)(606,630)(607,631)(608,632)
(609,633)(610,634)(611,635)(612,636)(613,637)(614,638)(615,639)(616,640)
(617,641)(618,642)(619,643)(620,644)(621,645)(622,646)(623,647)(624,648)
(673,697)(674,698)(675,699)(676,700)(677,701)(678,702)(679,703)(680,704)
(681,705)(682,706)(683,707)(684,708)(685,709)(686,710)(687,711)(688,712)
(689,713)(690,714)(691,715)(692,716)(693,717)(694,718)(695,719)(696,720)
(745,769)(746,770)(747,771)(748,772)(749,773)(750,774)(751,775)(752,776)
(753,777)(754,778)(755,779)(756,780)(757,781)(758,782)(759,783)(760,784)
(761,785)(762,786)(763,787)(764,788)(765,789)(766,790)(767,791)(768,792)
(817,841)(818,842)(819,843)(820,844)(821,845)(822,846)(823,847)(824,848)
(825,849)(826,850)(827,851)(828,852)(829,853)(830,854)(831,855)(832,856)
(833,857)(834,858)(835,859)(836,860)(837,861)(838,862)(839,863)(840,864);;
s1 := ( 1,461)( 2,462)( 3,464)( 4,463)( 5,458)( 6,457)( 7,459)( 8,460)
( 9,477)( 10,478)( 11,480)( 12,479)( 13,474)( 14,473)( 15,475)( 16,476)
( 17,469)( 18,470)( 19,472)( 20,471)( 21,466)( 22,465)( 23,467)( 24,468)
( 25,437)( 26,438)( 27,440)( 28,439)( 29,434)( 30,433)( 31,435)( 32,436)
( 33,453)( 34,454)( 35,456)( 36,455)( 37,450)( 38,449)( 39,451)( 40,452)
( 41,445)( 42,446)( 43,448)( 44,447)( 45,442)( 46,441)( 47,443)( 48,444)
( 49,485)( 50,486)( 51,488)( 52,487)( 53,482)( 54,481)( 55,483)( 56,484)
( 57,501)( 58,502)( 59,504)( 60,503)( 61,498)( 62,497)( 63,499)( 64,500)
( 65,493)( 66,494)( 67,496)( 68,495)( 69,490)( 70,489)( 71,491)( 72,492)
( 73,533)( 74,534)( 75,536)( 76,535)( 77,530)( 78,529)( 79,531)( 80,532)
( 81,549)( 82,550)( 83,552)( 84,551)( 85,546)( 86,545)( 87,547)( 88,548)
( 89,541)( 90,542)( 91,544)( 92,543)( 93,538)( 94,537)( 95,539)( 96,540)
( 97,509)( 98,510)( 99,512)(100,511)(101,506)(102,505)(103,507)(104,508)
(105,525)(106,526)(107,528)(108,527)(109,522)(110,521)(111,523)(112,524)
(113,517)(114,518)(115,520)(116,519)(117,514)(118,513)(119,515)(120,516)
(121,557)(122,558)(123,560)(124,559)(125,554)(126,553)(127,555)(128,556)
(129,573)(130,574)(131,576)(132,575)(133,570)(134,569)(135,571)(136,572)
(137,565)(138,566)(139,568)(140,567)(141,562)(142,561)(143,563)(144,564)
(145,605)(146,606)(147,608)(148,607)(149,602)(150,601)(151,603)(152,604)
(153,621)(154,622)(155,624)(156,623)(157,618)(158,617)(159,619)(160,620)
(161,613)(162,614)(163,616)(164,615)(165,610)(166,609)(167,611)(168,612)
(169,581)(170,582)(171,584)(172,583)(173,578)(174,577)(175,579)(176,580)
(177,597)(178,598)(179,600)(180,599)(181,594)(182,593)(183,595)(184,596)
(185,589)(186,590)(187,592)(188,591)(189,586)(190,585)(191,587)(192,588)
(193,629)(194,630)(195,632)(196,631)(197,626)(198,625)(199,627)(200,628)
(201,645)(202,646)(203,648)(204,647)(205,642)(206,641)(207,643)(208,644)
(209,637)(210,638)(211,640)(212,639)(213,634)(214,633)(215,635)(216,636)
(217,678)(218,677)(219,679)(220,680)(221,673)(222,674)(223,676)(224,675)
(225,694)(226,693)(227,695)(228,696)(229,689)(230,690)(231,692)(232,691)
(233,686)(234,685)(235,687)(236,688)(237,681)(238,682)(239,684)(240,683)
(241,654)(242,653)(243,655)(244,656)(245,649)(246,650)(247,652)(248,651)
(249,670)(250,669)(251,671)(252,672)(253,665)(254,666)(255,668)(256,667)
(257,662)(258,661)(259,663)(260,664)(261,657)(262,658)(263,660)(264,659)
(265,702)(266,701)(267,703)(268,704)(269,697)(270,698)(271,700)(272,699)
(273,718)(274,717)(275,719)(276,720)(277,713)(278,714)(279,716)(280,715)
(281,710)(282,709)(283,711)(284,712)(285,705)(286,706)(287,708)(288,707)
(289,750)(290,749)(291,751)(292,752)(293,745)(294,746)(295,748)(296,747)
(297,766)(298,765)(299,767)(300,768)(301,761)(302,762)(303,764)(304,763)
(305,758)(306,757)(307,759)(308,760)(309,753)(310,754)(311,756)(312,755)
(313,726)(314,725)(315,727)(316,728)(317,721)(318,722)(319,724)(320,723)
(321,742)(322,741)(323,743)(324,744)(325,737)(326,738)(327,740)(328,739)
(329,734)(330,733)(331,735)(332,736)(333,729)(334,730)(335,732)(336,731)
(337,774)(338,773)(339,775)(340,776)(341,769)(342,770)(343,772)(344,771)
(345,790)(346,789)(347,791)(348,792)(349,785)(350,786)(351,788)(352,787)
(353,782)(354,781)(355,783)(356,784)(357,777)(358,778)(359,780)(360,779)
(361,822)(362,821)(363,823)(364,824)(365,817)(366,818)(367,820)(368,819)
(369,838)(370,837)(371,839)(372,840)(373,833)(374,834)(375,836)(376,835)
(377,830)(378,829)(379,831)(380,832)(381,825)(382,826)(383,828)(384,827)
(385,798)(386,797)(387,799)(388,800)(389,793)(390,794)(391,796)(392,795)
(393,814)(394,813)(395,815)(396,816)(397,809)(398,810)(399,812)(400,811)
(401,806)(402,805)(403,807)(404,808)(405,801)(406,802)(407,804)(408,803)
(409,846)(410,845)(411,847)(412,848)(413,841)(414,842)(415,844)(416,843)
(417,862)(418,861)(419,863)(420,864)(421,857)(422,858)(423,860)(424,859)
(425,854)(426,853)(427,855)(428,856)(429,849)(430,850)(431,852)(432,851);;
s2 := ( 1,657)( 2,658)( 3,660)( 4,659)( 5,663)( 6,664)( 7,661)( 8,662)
( 9,649)( 10,650)( 11,652)( 12,651)( 13,655)( 14,656)( 15,653)( 16,654)
( 17,665)( 18,666)( 19,668)( 20,667)( 21,671)( 22,672)( 23,669)( 24,670)
( 25,681)( 26,682)( 27,684)( 28,683)( 29,687)( 30,688)( 31,685)( 32,686)
( 33,673)( 34,674)( 35,676)( 36,675)( 37,679)( 38,680)( 39,677)( 40,678)
( 41,689)( 42,690)( 43,692)( 44,691)( 45,695)( 46,696)( 47,693)( 48,694)
( 49,705)( 50,706)( 51,708)( 52,707)( 53,711)( 54,712)( 55,709)( 56,710)
( 57,697)( 58,698)( 59,700)( 60,699)( 61,703)( 62,704)( 63,701)( 64,702)
( 65,713)( 66,714)( 67,716)( 68,715)( 69,719)( 70,720)( 71,717)( 72,718)
( 73,801)( 74,802)( 75,804)( 76,803)( 77,807)( 78,808)( 79,805)( 80,806)
( 81,793)( 82,794)( 83,796)( 84,795)( 85,799)( 86,800)( 87,797)( 88,798)
( 89,809)( 90,810)( 91,812)( 92,811)( 93,815)( 94,816)( 95,813)( 96,814)
( 97,825)( 98,826)( 99,828)(100,827)(101,831)(102,832)(103,829)(104,830)
(105,817)(106,818)(107,820)(108,819)(109,823)(110,824)(111,821)(112,822)
(113,833)(114,834)(115,836)(116,835)(117,839)(118,840)(119,837)(120,838)
(121,849)(122,850)(123,852)(124,851)(125,855)(126,856)(127,853)(128,854)
(129,841)(130,842)(131,844)(132,843)(133,847)(134,848)(135,845)(136,846)
(137,857)(138,858)(139,860)(140,859)(141,863)(142,864)(143,861)(144,862)
(145,729)(146,730)(147,732)(148,731)(149,735)(150,736)(151,733)(152,734)
(153,721)(154,722)(155,724)(156,723)(157,727)(158,728)(159,725)(160,726)
(161,737)(162,738)(163,740)(164,739)(165,743)(166,744)(167,741)(168,742)
(169,753)(170,754)(171,756)(172,755)(173,759)(174,760)(175,757)(176,758)
(177,745)(178,746)(179,748)(180,747)(181,751)(182,752)(183,749)(184,750)
(185,761)(186,762)(187,764)(188,763)(189,767)(190,768)(191,765)(192,766)
(193,777)(194,778)(195,780)(196,779)(197,783)(198,784)(199,781)(200,782)
(201,769)(202,770)(203,772)(204,771)(205,775)(206,776)(207,773)(208,774)
(209,785)(210,786)(211,788)(212,787)(213,791)(214,792)(215,789)(216,790)
(217,442)(218,441)(219,443)(220,444)(221,448)(222,447)(223,446)(224,445)
(225,434)(226,433)(227,435)(228,436)(229,440)(230,439)(231,438)(232,437)
(233,450)(234,449)(235,451)(236,452)(237,456)(238,455)(239,454)(240,453)
(241,466)(242,465)(243,467)(244,468)(245,472)(246,471)(247,470)(248,469)
(249,458)(250,457)(251,459)(252,460)(253,464)(254,463)(255,462)(256,461)
(257,474)(258,473)(259,475)(260,476)(261,480)(262,479)(263,478)(264,477)
(265,490)(266,489)(267,491)(268,492)(269,496)(270,495)(271,494)(272,493)
(273,482)(274,481)(275,483)(276,484)(277,488)(278,487)(279,486)(280,485)
(281,498)(282,497)(283,499)(284,500)(285,504)(286,503)(287,502)(288,501)
(289,586)(290,585)(291,587)(292,588)(293,592)(294,591)(295,590)(296,589)
(297,578)(298,577)(299,579)(300,580)(301,584)(302,583)(303,582)(304,581)
(305,594)(306,593)(307,595)(308,596)(309,600)(310,599)(311,598)(312,597)
(313,610)(314,609)(315,611)(316,612)(317,616)(318,615)(319,614)(320,613)
(321,602)(322,601)(323,603)(324,604)(325,608)(326,607)(327,606)(328,605)
(329,618)(330,617)(331,619)(332,620)(333,624)(334,623)(335,622)(336,621)
(337,634)(338,633)(339,635)(340,636)(341,640)(342,639)(343,638)(344,637)
(345,626)(346,625)(347,627)(348,628)(349,632)(350,631)(351,630)(352,629)
(353,642)(354,641)(355,643)(356,644)(357,648)(358,647)(359,646)(360,645)
(361,514)(362,513)(363,515)(364,516)(365,520)(366,519)(367,518)(368,517)
(369,506)(370,505)(371,507)(372,508)(373,512)(374,511)(375,510)(376,509)
(377,522)(378,521)(379,523)(380,524)(381,528)(382,527)(383,526)(384,525)
(385,538)(386,537)(387,539)(388,540)(389,544)(390,543)(391,542)(392,541)
(393,530)(394,529)(395,531)(396,532)(397,536)(398,535)(399,534)(400,533)
(401,546)(402,545)(403,547)(404,548)(405,552)(406,551)(407,550)(408,549)
(409,562)(410,561)(411,563)(412,564)(413,568)(414,567)(415,566)(416,565)
(417,554)(418,553)(419,555)(420,556)(421,560)(422,559)(423,558)(424,557)
(425,570)(426,569)(427,571)(428,572)(429,576)(430,575)(431,574)(432,573);;
s3 := ( 1,721)( 2,722)( 3,727)( 4,728)( 5,726)( 6,725)( 7,723)( 8,724)
( 9,737)( 10,738)( 11,743)( 12,744)( 13,742)( 14,741)( 15,739)( 16,740)
( 17,729)( 18,730)( 19,735)( 20,736)( 21,734)( 22,733)( 23,731)( 24,732)
( 25,745)( 26,746)( 27,751)( 28,752)( 29,750)( 30,749)( 31,747)( 32,748)
( 33,761)( 34,762)( 35,767)( 36,768)( 37,766)( 38,765)( 39,763)( 40,764)
( 41,753)( 42,754)( 43,759)( 44,760)( 45,758)( 46,757)( 47,755)( 48,756)
( 49,769)( 50,770)( 51,775)( 52,776)( 53,774)( 54,773)( 55,771)( 56,772)
( 57,785)( 58,786)( 59,791)( 60,792)( 61,790)( 62,789)( 63,787)( 64,788)
( 65,777)( 66,778)( 67,783)( 68,784)( 69,782)( 70,781)( 71,779)( 72,780)
( 73,649)( 74,650)( 75,655)( 76,656)( 77,654)( 78,653)( 79,651)( 80,652)
( 81,665)( 82,666)( 83,671)( 84,672)( 85,670)( 86,669)( 87,667)( 88,668)
( 89,657)( 90,658)( 91,663)( 92,664)( 93,662)( 94,661)( 95,659)( 96,660)
( 97,673)( 98,674)( 99,679)(100,680)(101,678)(102,677)(103,675)(104,676)
(105,689)(106,690)(107,695)(108,696)(109,694)(110,693)(111,691)(112,692)
(113,681)(114,682)(115,687)(116,688)(117,686)(118,685)(119,683)(120,684)
(121,697)(122,698)(123,703)(124,704)(125,702)(126,701)(127,699)(128,700)
(129,713)(130,714)(131,719)(132,720)(133,718)(134,717)(135,715)(136,716)
(137,705)(138,706)(139,711)(140,712)(141,710)(142,709)(143,707)(144,708)
(145,793)(146,794)(147,799)(148,800)(149,798)(150,797)(151,795)(152,796)
(153,809)(154,810)(155,815)(156,816)(157,814)(158,813)(159,811)(160,812)
(161,801)(162,802)(163,807)(164,808)(165,806)(166,805)(167,803)(168,804)
(169,817)(170,818)(171,823)(172,824)(173,822)(174,821)(175,819)(176,820)
(177,833)(178,834)(179,839)(180,840)(181,838)(182,837)(183,835)(184,836)
(185,825)(186,826)(187,831)(188,832)(189,830)(190,829)(191,827)(192,828)
(193,841)(194,842)(195,847)(196,848)(197,846)(198,845)(199,843)(200,844)
(201,857)(202,858)(203,863)(204,864)(205,862)(206,861)(207,859)(208,860)
(209,849)(210,850)(211,855)(212,856)(213,854)(214,853)(215,851)(216,852)
(217,506)(218,505)(219,512)(220,511)(221,509)(222,510)(223,508)(224,507)
(225,522)(226,521)(227,528)(228,527)(229,525)(230,526)(231,524)(232,523)
(233,514)(234,513)(235,520)(236,519)(237,517)(238,518)(239,516)(240,515)
(241,530)(242,529)(243,536)(244,535)(245,533)(246,534)(247,532)(248,531)
(249,546)(250,545)(251,552)(252,551)(253,549)(254,550)(255,548)(256,547)
(257,538)(258,537)(259,544)(260,543)(261,541)(262,542)(263,540)(264,539)
(265,554)(266,553)(267,560)(268,559)(269,557)(270,558)(271,556)(272,555)
(273,570)(274,569)(275,576)(276,575)(277,573)(278,574)(279,572)(280,571)
(281,562)(282,561)(283,568)(284,567)(285,565)(286,566)(287,564)(288,563)
(289,434)(290,433)(291,440)(292,439)(293,437)(294,438)(295,436)(296,435)
(297,450)(298,449)(299,456)(300,455)(301,453)(302,454)(303,452)(304,451)
(305,442)(306,441)(307,448)(308,447)(309,445)(310,446)(311,444)(312,443)
(313,458)(314,457)(315,464)(316,463)(317,461)(318,462)(319,460)(320,459)
(321,474)(322,473)(323,480)(324,479)(325,477)(326,478)(327,476)(328,475)
(329,466)(330,465)(331,472)(332,471)(333,469)(334,470)(335,468)(336,467)
(337,482)(338,481)(339,488)(340,487)(341,485)(342,486)(343,484)(344,483)
(345,498)(346,497)(347,504)(348,503)(349,501)(350,502)(351,500)(352,499)
(353,490)(354,489)(355,496)(356,495)(357,493)(358,494)(359,492)(360,491)
(361,578)(362,577)(363,584)(364,583)(365,581)(366,582)(367,580)(368,579)
(369,594)(370,593)(371,600)(372,599)(373,597)(374,598)(375,596)(376,595)
(377,586)(378,585)(379,592)(380,591)(381,589)(382,590)(383,588)(384,587)
(385,602)(386,601)(387,608)(388,607)(389,605)(390,606)(391,604)(392,603)
(393,618)(394,617)(395,624)(396,623)(397,621)(398,622)(399,620)(400,619)
(401,610)(402,609)(403,616)(404,615)(405,613)(406,614)(407,612)(408,611)
(409,626)(410,625)(411,632)(412,631)(413,629)(414,630)(415,628)(416,627)
(417,642)(418,641)(419,648)(420,647)(421,645)(422,646)(423,644)(424,643)
(425,634)(426,633)(427,640)(428,639)(429,637)(430,638)(431,636)(432,635);;
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,
s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 25, 49)( 26, 50)( 27, 51)( 28, 52)( 29, 53)( 30, 54)( 31, 55)
( 32, 56)( 33, 57)( 34, 58)( 35, 59)( 36, 60)( 37, 61)( 38, 62)( 39, 63)
( 40, 64)( 41, 65)( 42, 66)( 43, 67)( 44, 68)( 45, 69)( 46, 70)( 47, 71)
( 48, 72)( 97,121)( 98,122)( 99,123)(100,124)(101,125)(102,126)(103,127)
(104,128)(105,129)(106,130)(107,131)(108,132)(109,133)(110,134)(111,135)
(112,136)(113,137)(114,138)(115,139)(116,140)(117,141)(118,142)(119,143)
(120,144)(169,193)(170,194)(171,195)(172,196)(173,197)(174,198)(175,199)
(176,200)(177,201)(178,202)(179,203)(180,204)(181,205)(182,206)(183,207)
(184,208)(185,209)(186,210)(187,211)(188,212)(189,213)(190,214)(191,215)
(192,216)(241,265)(242,266)(243,267)(244,268)(245,269)(246,270)(247,271)
(248,272)(249,273)(250,274)(251,275)(252,276)(253,277)(254,278)(255,279)
(256,280)(257,281)(258,282)(259,283)(260,284)(261,285)(262,286)(263,287)
(264,288)(313,337)(314,338)(315,339)(316,340)(317,341)(318,342)(319,343)
(320,344)(321,345)(322,346)(323,347)(324,348)(325,349)(326,350)(327,351)
(328,352)(329,353)(330,354)(331,355)(332,356)(333,357)(334,358)(335,359)
(336,360)(385,409)(386,410)(387,411)(388,412)(389,413)(390,414)(391,415)
(392,416)(393,417)(394,418)(395,419)(396,420)(397,421)(398,422)(399,423)
(400,424)(401,425)(402,426)(403,427)(404,428)(405,429)(406,430)(407,431)
(408,432)(457,481)(458,482)(459,483)(460,484)(461,485)(462,486)(463,487)
(464,488)(465,489)(466,490)(467,491)(468,492)(469,493)(470,494)(471,495)
(472,496)(473,497)(474,498)(475,499)(476,500)(477,501)(478,502)(479,503)
(480,504)(529,553)(530,554)(531,555)(532,556)(533,557)(534,558)(535,559)
(536,560)(537,561)(538,562)(539,563)(540,564)(541,565)(542,566)(543,567)
(544,568)(545,569)(546,570)(547,571)(548,572)(549,573)(550,574)(551,575)
(552,576)(601,625)(602,626)(603,627)(604,628)(605,629)(606,630)(607,631)
(608,632)(609,633)(610,634)(611,635)(612,636)(613,637)(614,638)(615,639)
(616,640)(617,641)(618,642)(619,643)(620,644)(621,645)(622,646)(623,647)
(624,648)(673,697)(674,698)(675,699)(676,700)(677,701)(678,702)(679,703)
(680,704)(681,705)(682,706)(683,707)(684,708)(685,709)(686,710)(687,711)
(688,712)(689,713)(690,714)(691,715)(692,716)(693,717)(694,718)(695,719)
(696,720)(745,769)(746,770)(747,771)(748,772)(749,773)(750,774)(751,775)
(752,776)(753,777)(754,778)(755,779)(756,780)(757,781)(758,782)(759,783)
(760,784)(761,785)(762,786)(763,787)(764,788)(765,789)(766,790)(767,791)
(768,792)(817,841)(818,842)(819,843)(820,844)(821,845)(822,846)(823,847)
(824,848)(825,849)(826,850)(827,851)(828,852)(829,853)(830,854)(831,855)
(832,856)(833,857)(834,858)(835,859)(836,860)(837,861)(838,862)(839,863)
(840,864);
s1 := Sym(864)!( 1,461)( 2,462)( 3,464)( 4,463)( 5,458)( 6,457)( 7,459)
( 8,460)( 9,477)( 10,478)( 11,480)( 12,479)( 13,474)( 14,473)( 15,475)
( 16,476)( 17,469)( 18,470)( 19,472)( 20,471)( 21,466)( 22,465)( 23,467)
( 24,468)( 25,437)( 26,438)( 27,440)( 28,439)( 29,434)( 30,433)( 31,435)
( 32,436)( 33,453)( 34,454)( 35,456)( 36,455)( 37,450)( 38,449)( 39,451)
( 40,452)( 41,445)( 42,446)( 43,448)( 44,447)( 45,442)( 46,441)( 47,443)
( 48,444)( 49,485)( 50,486)( 51,488)( 52,487)( 53,482)( 54,481)( 55,483)
( 56,484)( 57,501)( 58,502)( 59,504)( 60,503)( 61,498)( 62,497)( 63,499)
( 64,500)( 65,493)( 66,494)( 67,496)( 68,495)( 69,490)( 70,489)( 71,491)
( 72,492)( 73,533)( 74,534)( 75,536)( 76,535)( 77,530)( 78,529)( 79,531)
( 80,532)( 81,549)( 82,550)( 83,552)( 84,551)( 85,546)( 86,545)( 87,547)
( 88,548)( 89,541)( 90,542)( 91,544)( 92,543)( 93,538)( 94,537)( 95,539)
( 96,540)( 97,509)( 98,510)( 99,512)(100,511)(101,506)(102,505)(103,507)
(104,508)(105,525)(106,526)(107,528)(108,527)(109,522)(110,521)(111,523)
(112,524)(113,517)(114,518)(115,520)(116,519)(117,514)(118,513)(119,515)
(120,516)(121,557)(122,558)(123,560)(124,559)(125,554)(126,553)(127,555)
(128,556)(129,573)(130,574)(131,576)(132,575)(133,570)(134,569)(135,571)
(136,572)(137,565)(138,566)(139,568)(140,567)(141,562)(142,561)(143,563)
(144,564)(145,605)(146,606)(147,608)(148,607)(149,602)(150,601)(151,603)
(152,604)(153,621)(154,622)(155,624)(156,623)(157,618)(158,617)(159,619)
(160,620)(161,613)(162,614)(163,616)(164,615)(165,610)(166,609)(167,611)
(168,612)(169,581)(170,582)(171,584)(172,583)(173,578)(174,577)(175,579)
(176,580)(177,597)(178,598)(179,600)(180,599)(181,594)(182,593)(183,595)
(184,596)(185,589)(186,590)(187,592)(188,591)(189,586)(190,585)(191,587)
(192,588)(193,629)(194,630)(195,632)(196,631)(197,626)(198,625)(199,627)
(200,628)(201,645)(202,646)(203,648)(204,647)(205,642)(206,641)(207,643)
(208,644)(209,637)(210,638)(211,640)(212,639)(213,634)(214,633)(215,635)
(216,636)(217,678)(218,677)(219,679)(220,680)(221,673)(222,674)(223,676)
(224,675)(225,694)(226,693)(227,695)(228,696)(229,689)(230,690)(231,692)
(232,691)(233,686)(234,685)(235,687)(236,688)(237,681)(238,682)(239,684)
(240,683)(241,654)(242,653)(243,655)(244,656)(245,649)(246,650)(247,652)
(248,651)(249,670)(250,669)(251,671)(252,672)(253,665)(254,666)(255,668)
(256,667)(257,662)(258,661)(259,663)(260,664)(261,657)(262,658)(263,660)
(264,659)(265,702)(266,701)(267,703)(268,704)(269,697)(270,698)(271,700)
(272,699)(273,718)(274,717)(275,719)(276,720)(277,713)(278,714)(279,716)
(280,715)(281,710)(282,709)(283,711)(284,712)(285,705)(286,706)(287,708)
(288,707)(289,750)(290,749)(291,751)(292,752)(293,745)(294,746)(295,748)
(296,747)(297,766)(298,765)(299,767)(300,768)(301,761)(302,762)(303,764)
(304,763)(305,758)(306,757)(307,759)(308,760)(309,753)(310,754)(311,756)
(312,755)(313,726)(314,725)(315,727)(316,728)(317,721)(318,722)(319,724)
(320,723)(321,742)(322,741)(323,743)(324,744)(325,737)(326,738)(327,740)
(328,739)(329,734)(330,733)(331,735)(332,736)(333,729)(334,730)(335,732)
(336,731)(337,774)(338,773)(339,775)(340,776)(341,769)(342,770)(343,772)
(344,771)(345,790)(346,789)(347,791)(348,792)(349,785)(350,786)(351,788)
(352,787)(353,782)(354,781)(355,783)(356,784)(357,777)(358,778)(359,780)
(360,779)(361,822)(362,821)(363,823)(364,824)(365,817)(366,818)(367,820)
(368,819)(369,838)(370,837)(371,839)(372,840)(373,833)(374,834)(375,836)
(376,835)(377,830)(378,829)(379,831)(380,832)(381,825)(382,826)(383,828)
(384,827)(385,798)(386,797)(387,799)(388,800)(389,793)(390,794)(391,796)
(392,795)(393,814)(394,813)(395,815)(396,816)(397,809)(398,810)(399,812)
(400,811)(401,806)(402,805)(403,807)(404,808)(405,801)(406,802)(407,804)
(408,803)(409,846)(410,845)(411,847)(412,848)(413,841)(414,842)(415,844)
(416,843)(417,862)(418,861)(419,863)(420,864)(421,857)(422,858)(423,860)
(424,859)(425,854)(426,853)(427,855)(428,856)(429,849)(430,850)(431,852)
(432,851);
s2 := Sym(864)!( 1,657)( 2,658)( 3,660)( 4,659)( 5,663)( 6,664)( 7,661)
( 8,662)( 9,649)( 10,650)( 11,652)( 12,651)( 13,655)( 14,656)( 15,653)
( 16,654)( 17,665)( 18,666)( 19,668)( 20,667)( 21,671)( 22,672)( 23,669)
( 24,670)( 25,681)( 26,682)( 27,684)( 28,683)( 29,687)( 30,688)( 31,685)
( 32,686)( 33,673)( 34,674)( 35,676)( 36,675)( 37,679)( 38,680)( 39,677)
( 40,678)( 41,689)( 42,690)( 43,692)( 44,691)( 45,695)( 46,696)( 47,693)
( 48,694)( 49,705)( 50,706)( 51,708)( 52,707)( 53,711)( 54,712)( 55,709)
( 56,710)( 57,697)( 58,698)( 59,700)( 60,699)( 61,703)( 62,704)( 63,701)
( 64,702)( 65,713)( 66,714)( 67,716)( 68,715)( 69,719)( 70,720)( 71,717)
( 72,718)( 73,801)( 74,802)( 75,804)( 76,803)( 77,807)( 78,808)( 79,805)
( 80,806)( 81,793)( 82,794)( 83,796)( 84,795)( 85,799)( 86,800)( 87,797)
( 88,798)( 89,809)( 90,810)( 91,812)( 92,811)( 93,815)( 94,816)( 95,813)
( 96,814)( 97,825)( 98,826)( 99,828)(100,827)(101,831)(102,832)(103,829)
(104,830)(105,817)(106,818)(107,820)(108,819)(109,823)(110,824)(111,821)
(112,822)(113,833)(114,834)(115,836)(116,835)(117,839)(118,840)(119,837)
(120,838)(121,849)(122,850)(123,852)(124,851)(125,855)(126,856)(127,853)
(128,854)(129,841)(130,842)(131,844)(132,843)(133,847)(134,848)(135,845)
(136,846)(137,857)(138,858)(139,860)(140,859)(141,863)(142,864)(143,861)
(144,862)(145,729)(146,730)(147,732)(148,731)(149,735)(150,736)(151,733)
(152,734)(153,721)(154,722)(155,724)(156,723)(157,727)(158,728)(159,725)
(160,726)(161,737)(162,738)(163,740)(164,739)(165,743)(166,744)(167,741)
(168,742)(169,753)(170,754)(171,756)(172,755)(173,759)(174,760)(175,757)
(176,758)(177,745)(178,746)(179,748)(180,747)(181,751)(182,752)(183,749)
(184,750)(185,761)(186,762)(187,764)(188,763)(189,767)(190,768)(191,765)
(192,766)(193,777)(194,778)(195,780)(196,779)(197,783)(198,784)(199,781)
(200,782)(201,769)(202,770)(203,772)(204,771)(205,775)(206,776)(207,773)
(208,774)(209,785)(210,786)(211,788)(212,787)(213,791)(214,792)(215,789)
(216,790)(217,442)(218,441)(219,443)(220,444)(221,448)(222,447)(223,446)
(224,445)(225,434)(226,433)(227,435)(228,436)(229,440)(230,439)(231,438)
(232,437)(233,450)(234,449)(235,451)(236,452)(237,456)(238,455)(239,454)
(240,453)(241,466)(242,465)(243,467)(244,468)(245,472)(246,471)(247,470)
(248,469)(249,458)(250,457)(251,459)(252,460)(253,464)(254,463)(255,462)
(256,461)(257,474)(258,473)(259,475)(260,476)(261,480)(262,479)(263,478)
(264,477)(265,490)(266,489)(267,491)(268,492)(269,496)(270,495)(271,494)
(272,493)(273,482)(274,481)(275,483)(276,484)(277,488)(278,487)(279,486)
(280,485)(281,498)(282,497)(283,499)(284,500)(285,504)(286,503)(287,502)
(288,501)(289,586)(290,585)(291,587)(292,588)(293,592)(294,591)(295,590)
(296,589)(297,578)(298,577)(299,579)(300,580)(301,584)(302,583)(303,582)
(304,581)(305,594)(306,593)(307,595)(308,596)(309,600)(310,599)(311,598)
(312,597)(313,610)(314,609)(315,611)(316,612)(317,616)(318,615)(319,614)
(320,613)(321,602)(322,601)(323,603)(324,604)(325,608)(326,607)(327,606)
(328,605)(329,618)(330,617)(331,619)(332,620)(333,624)(334,623)(335,622)
(336,621)(337,634)(338,633)(339,635)(340,636)(341,640)(342,639)(343,638)
(344,637)(345,626)(346,625)(347,627)(348,628)(349,632)(350,631)(351,630)
(352,629)(353,642)(354,641)(355,643)(356,644)(357,648)(358,647)(359,646)
(360,645)(361,514)(362,513)(363,515)(364,516)(365,520)(366,519)(367,518)
(368,517)(369,506)(370,505)(371,507)(372,508)(373,512)(374,511)(375,510)
(376,509)(377,522)(378,521)(379,523)(380,524)(381,528)(382,527)(383,526)
(384,525)(385,538)(386,537)(387,539)(388,540)(389,544)(390,543)(391,542)
(392,541)(393,530)(394,529)(395,531)(396,532)(397,536)(398,535)(399,534)
(400,533)(401,546)(402,545)(403,547)(404,548)(405,552)(406,551)(407,550)
(408,549)(409,562)(410,561)(411,563)(412,564)(413,568)(414,567)(415,566)
(416,565)(417,554)(418,553)(419,555)(420,556)(421,560)(422,559)(423,558)
(424,557)(425,570)(426,569)(427,571)(428,572)(429,576)(430,575)(431,574)
(432,573);
s3 := Sym(864)!( 1,721)( 2,722)( 3,727)( 4,728)( 5,726)( 6,725)( 7,723)
( 8,724)( 9,737)( 10,738)( 11,743)( 12,744)( 13,742)( 14,741)( 15,739)
( 16,740)( 17,729)( 18,730)( 19,735)( 20,736)( 21,734)( 22,733)( 23,731)
( 24,732)( 25,745)( 26,746)( 27,751)( 28,752)( 29,750)( 30,749)( 31,747)
( 32,748)( 33,761)( 34,762)( 35,767)( 36,768)( 37,766)( 38,765)( 39,763)
( 40,764)( 41,753)( 42,754)( 43,759)( 44,760)( 45,758)( 46,757)( 47,755)
( 48,756)( 49,769)( 50,770)( 51,775)( 52,776)( 53,774)( 54,773)( 55,771)
( 56,772)( 57,785)( 58,786)( 59,791)( 60,792)( 61,790)( 62,789)( 63,787)
( 64,788)( 65,777)( 66,778)( 67,783)( 68,784)( 69,782)( 70,781)( 71,779)
( 72,780)( 73,649)( 74,650)( 75,655)( 76,656)( 77,654)( 78,653)( 79,651)
( 80,652)( 81,665)( 82,666)( 83,671)( 84,672)( 85,670)( 86,669)( 87,667)
( 88,668)( 89,657)( 90,658)( 91,663)( 92,664)( 93,662)( 94,661)( 95,659)
( 96,660)( 97,673)( 98,674)( 99,679)(100,680)(101,678)(102,677)(103,675)
(104,676)(105,689)(106,690)(107,695)(108,696)(109,694)(110,693)(111,691)
(112,692)(113,681)(114,682)(115,687)(116,688)(117,686)(118,685)(119,683)
(120,684)(121,697)(122,698)(123,703)(124,704)(125,702)(126,701)(127,699)
(128,700)(129,713)(130,714)(131,719)(132,720)(133,718)(134,717)(135,715)
(136,716)(137,705)(138,706)(139,711)(140,712)(141,710)(142,709)(143,707)
(144,708)(145,793)(146,794)(147,799)(148,800)(149,798)(150,797)(151,795)
(152,796)(153,809)(154,810)(155,815)(156,816)(157,814)(158,813)(159,811)
(160,812)(161,801)(162,802)(163,807)(164,808)(165,806)(166,805)(167,803)
(168,804)(169,817)(170,818)(171,823)(172,824)(173,822)(174,821)(175,819)
(176,820)(177,833)(178,834)(179,839)(180,840)(181,838)(182,837)(183,835)
(184,836)(185,825)(186,826)(187,831)(188,832)(189,830)(190,829)(191,827)
(192,828)(193,841)(194,842)(195,847)(196,848)(197,846)(198,845)(199,843)
(200,844)(201,857)(202,858)(203,863)(204,864)(205,862)(206,861)(207,859)
(208,860)(209,849)(210,850)(211,855)(212,856)(213,854)(214,853)(215,851)
(216,852)(217,506)(218,505)(219,512)(220,511)(221,509)(222,510)(223,508)
(224,507)(225,522)(226,521)(227,528)(228,527)(229,525)(230,526)(231,524)
(232,523)(233,514)(234,513)(235,520)(236,519)(237,517)(238,518)(239,516)
(240,515)(241,530)(242,529)(243,536)(244,535)(245,533)(246,534)(247,532)
(248,531)(249,546)(250,545)(251,552)(252,551)(253,549)(254,550)(255,548)
(256,547)(257,538)(258,537)(259,544)(260,543)(261,541)(262,542)(263,540)
(264,539)(265,554)(266,553)(267,560)(268,559)(269,557)(270,558)(271,556)
(272,555)(273,570)(274,569)(275,576)(276,575)(277,573)(278,574)(279,572)
(280,571)(281,562)(282,561)(283,568)(284,567)(285,565)(286,566)(287,564)
(288,563)(289,434)(290,433)(291,440)(292,439)(293,437)(294,438)(295,436)
(296,435)(297,450)(298,449)(299,456)(300,455)(301,453)(302,454)(303,452)
(304,451)(305,442)(306,441)(307,448)(308,447)(309,445)(310,446)(311,444)
(312,443)(313,458)(314,457)(315,464)(316,463)(317,461)(318,462)(319,460)
(320,459)(321,474)(322,473)(323,480)(324,479)(325,477)(326,478)(327,476)
(328,475)(329,466)(330,465)(331,472)(332,471)(333,469)(334,470)(335,468)
(336,467)(337,482)(338,481)(339,488)(340,487)(341,485)(342,486)(343,484)
(344,483)(345,498)(346,497)(347,504)(348,503)(349,501)(350,502)(351,500)
(352,499)(353,490)(354,489)(355,496)(356,495)(357,493)(358,494)(359,492)
(360,491)(361,578)(362,577)(363,584)(364,583)(365,581)(366,582)(367,580)
(368,579)(369,594)(370,593)(371,600)(372,599)(373,597)(374,598)(375,596)
(376,595)(377,586)(378,585)(379,592)(380,591)(381,589)(382,590)(383,588)
(384,587)(385,602)(386,601)(387,608)(388,607)(389,605)(390,606)(391,604)
(392,603)(393,618)(394,617)(395,624)(396,623)(397,621)(398,622)(399,620)
(400,619)(401,610)(402,609)(403,616)(404,615)(405,613)(406,614)(407,612)
(408,611)(409,626)(410,625)(411,632)(412,631)(413,629)(414,630)(415,628)
(416,627)(417,642)(418,641)(419,648)(420,647)(421,645)(422,646)(423,644)
(424,643)(425,634)(426,633)(427,640)(428,639)(429,637)(430,638)(431,636)
(432,635);
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, s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope