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Polytope of Type {24,3,6}

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