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