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Polytope of Type {6,6,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,24}*1728e
if this polytope has a name.
Group : SmallGroup(1728,36607)
Rank : 4
Schlafli Type : {6,6,24}
Number of vertices, edges, etc : 6, 18, 72, 24
Order of s0s1s2s3 : 24
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 : {3,6,24}*864b, {6,6,12}*864e
   3-fold quotients : {6,2,24}*576, {6,6,8}*576c
   4-fold quotients : {3,6,12}*432b, {6,6,6}*432g
   6-fold quotients : {3,2,24}*288, {3,6,8}*288, {6,2,12}*288, {6,6,4}*288c
   8-fold quotients : {3,6,6}*216b
   9-fold quotients : {2,2,24}*192, {6,2,8}*192
   12-fold quotients : {3,2,12}*144, {3,6,4}*144, {6,2,6}*144, {6,6,2}*144c
   18-fold quotients : {3,2,8}*96, {2,2,12}*96, {6,2,4}*96
   24-fold quotients : {3,2,6}*72, {3,6,2}*72, {6,2,3}*72
   27-fold quotients : {2,2,8}*64
   36-fold quotients : {3,2,4}*48, {2,2,6}*48, {6,2,2}*48
   48-fold quotients : {3,2,3}*36
   54-fold quotients : {2,2,4}*32
   72-fold quotients : {2,2,3}*24, {3,2,2}*24
   108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,649)(  2,651)(  3,650)(  4,652)(  5,654)(  6,653)(  7,655)(  8,657)
(  9,656)( 10,667)( 11,669)( 12,668)( 13,670)( 14,672)( 15,671)( 16,673)
( 17,675)( 18,674)( 19,658)( 20,660)( 21,659)( 22,661)( 23,663)( 24,662)
( 25,664)( 26,666)( 27,665)( 28,676)( 29,678)( 30,677)( 31,679)( 32,681)
( 33,680)( 34,682)( 35,684)( 36,683)( 37,694)( 38,696)( 39,695)( 40,697)
( 41,699)( 42,698)( 43,700)( 44,702)( 45,701)( 46,685)( 47,687)( 48,686)
( 49,688)( 50,690)( 51,689)( 52,691)( 53,693)( 54,692)( 55,703)( 56,705)
( 57,704)( 58,706)( 59,708)( 60,707)( 61,709)( 62,711)( 63,710)( 64,721)
( 65,723)( 66,722)( 67,724)( 68,726)( 69,725)( 70,727)( 71,729)( 72,728)
( 73,712)( 74,714)( 75,713)( 76,715)( 77,717)( 78,716)( 79,718)( 80,720)
( 81,719)( 82,730)( 83,732)( 84,731)( 85,733)( 86,735)( 87,734)( 88,736)
( 89,738)( 90,737)( 91,748)( 92,750)( 93,749)( 94,751)( 95,753)( 96,752)
( 97,754)( 98,756)( 99,755)(100,739)(101,741)(102,740)(103,742)(104,744)
(105,743)(106,745)(107,747)(108,746)(109,757)(110,759)(111,758)(112,760)
(113,762)(114,761)(115,763)(116,765)(117,764)(118,775)(119,777)(120,776)
(121,778)(122,780)(123,779)(124,781)(125,783)(126,782)(127,766)(128,768)
(129,767)(130,769)(131,771)(132,770)(133,772)(134,774)(135,773)(136,784)
(137,786)(138,785)(139,787)(140,789)(141,788)(142,790)(143,792)(144,791)
(145,802)(146,804)(147,803)(148,805)(149,807)(150,806)(151,808)(152,810)
(153,809)(154,793)(155,795)(156,794)(157,796)(158,798)(159,797)(160,799)
(161,801)(162,800)(163,811)(164,813)(165,812)(166,814)(167,816)(168,815)
(169,817)(170,819)(171,818)(172,829)(173,831)(174,830)(175,832)(176,834)
(177,833)(178,835)(179,837)(180,836)(181,820)(182,822)(183,821)(184,823)
(185,825)(186,824)(187,826)(188,828)(189,827)(190,838)(191,840)(192,839)
(193,841)(194,843)(195,842)(196,844)(197,846)(198,845)(199,856)(200,858)
(201,857)(202,859)(203,861)(204,860)(205,862)(206,864)(207,863)(208,847)
(209,849)(210,848)(211,850)(212,852)(213,851)(214,853)(215,855)(216,854)
(217,487)(218,489)(219,488)(220,490)(221,492)(222,491)(223,493)(224,495)
(225,494)(226,505)(227,507)(228,506)(229,508)(230,510)(231,509)(232,511)
(233,513)(234,512)(235,496)(236,498)(237,497)(238,499)(239,501)(240,500)
(241,502)(242,504)(243,503)(244,514)(245,516)(246,515)(247,517)(248,519)
(249,518)(250,520)(251,522)(252,521)(253,532)(254,534)(255,533)(256,535)
(257,537)(258,536)(259,538)(260,540)(261,539)(262,523)(263,525)(264,524)
(265,526)(266,528)(267,527)(268,529)(269,531)(270,530)(271,460)(272,462)
(273,461)(274,463)(275,465)(276,464)(277,466)(278,468)(279,467)(280,478)
(281,480)(282,479)(283,481)(284,483)(285,482)(286,484)(287,486)(288,485)
(289,469)(290,471)(291,470)(292,472)(293,474)(294,473)(295,475)(296,477)
(297,476)(298,433)(299,435)(300,434)(301,436)(302,438)(303,437)(304,439)
(305,441)(306,440)(307,451)(308,453)(309,452)(310,454)(311,456)(312,455)
(313,457)(314,459)(315,458)(316,442)(317,444)(318,443)(319,445)(320,447)
(321,446)(322,448)(323,450)(324,449)(325,595)(326,597)(327,596)(328,598)
(329,600)(330,599)(331,601)(332,603)(333,602)(334,613)(335,615)(336,614)
(337,616)(338,618)(339,617)(340,619)(341,621)(342,620)(343,604)(344,606)
(345,605)(346,607)(347,609)(348,608)(349,610)(350,612)(351,611)(352,622)
(353,624)(354,623)(355,625)(356,627)(357,626)(358,628)(359,630)(360,629)
(361,640)(362,642)(363,641)(364,643)(365,645)(366,644)(367,646)(368,648)
(369,647)(370,631)(371,633)(372,632)(373,634)(374,636)(375,635)(376,637)
(377,639)(378,638)(379,568)(380,570)(381,569)(382,571)(383,573)(384,572)
(385,574)(386,576)(387,575)(388,586)(389,588)(390,587)(391,589)(392,591)
(393,590)(394,592)(395,594)(396,593)(397,577)(398,579)(399,578)(400,580)
(401,582)(402,581)(403,583)(404,585)(405,584)(406,541)(407,543)(408,542)
(409,544)(410,546)(411,545)(412,547)(413,549)(414,548)(415,559)(416,561)
(417,560)(418,562)(419,564)(420,563)(421,565)(422,567)(423,566)(424,550)
(425,552)(426,551)(427,553)(428,555)(429,554)(430,556)(431,558)(432,557);;
s1 := (  1,767)(  2,766)(  3,768)(  4,770)(  5,769)(  6,771)(  7,773)(  8,772)
(  9,774)( 10,758)( 11,757)( 12,759)( 13,761)( 14,760)( 15,762)( 16,764)
( 17,763)( 18,765)( 19,776)( 20,775)( 21,777)( 22,779)( 23,778)( 24,780)
( 25,782)( 26,781)( 27,783)( 28,794)( 29,793)( 30,795)( 31,797)( 32,796)
( 33,798)( 34,800)( 35,799)( 36,801)( 37,785)( 38,784)( 39,786)( 40,788)
( 41,787)( 42,789)( 43,791)( 44,790)( 45,792)( 46,803)( 47,802)( 48,804)
( 49,806)( 50,805)( 51,807)( 52,809)( 53,808)( 54,810)( 55,821)( 56,820)
( 57,822)( 58,824)( 59,823)( 60,825)( 61,827)( 62,826)( 63,828)( 64,812)
( 65,811)( 66,813)( 67,815)( 68,814)( 69,816)( 70,818)( 71,817)( 72,819)
( 73,830)( 74,829)( 75,831)( 76,833)( 77,832)( 78,834)( 79,836)( 80,835)
( 81,837)( 82,848)( 83,847)( 84,849)( 85,851)( 86,850)( 87,852)( 88,854)
( 89,853)( 90,855)( 91,839)( 92,838)( 93,840)( 94,842)( 95,841)( 96,843)
( 97,845)( 98,844)( 99,846)(100,857)(101,856)(102,858)(103,860)(104,859)
(105,861)(106,863)(107,862)(108,864)(109,659)(110,658)(111,660)(112,662)
(113,661)(114,663)(115,665)(116,664)(117,666)(118,650)(119,649)(120,651)
(121,653)(122,652)(123,654)(124,656)(125,655)(126,657)(127,668)(128,667)
(129,669)(130,671)(131,670)(132,672)(133,674)(134,673)(135,675)(136,686)
(137,685)(138,687)(139,689)(140,688)(141,690)(142,692)(143,691)(144,693)
(145,677)(146,676)(147,678)(148,680)(149,679)(150,681)(151,683)(152,682)
(153,684)(154,695)(155,694)(156,696)(157,698)(158,697)(159,699)(160,701)
(161,700)(162,702)(163,713)(164,712)(165,714)(166,716)(167,715)(168,717)
(169,719)(170,718)(171,720)(172,704)(173,703)(174,705)(175,707)(176,706)
(177,708)(178,710)(179,709)(180,711)(181,722)(182,721)(183,723)(184,725)
(185,724)(186,726)(187,728)(188,727)(189,729)(190,740)(191,739)(192,741)
(193,743)(194,742)(195,744)(196,746)(197,745)(198,747)(199,731)(200,730)
(201,732)(202,734)(203,733)(204,735)(205,737)(206,736)(207,738)(208,749)
(209,748)(210,750)(211,752)(212,751)(213,753)(214,755)(215,754)(216,756)
(217,605)(218,604)(219,606)(220,608)(221,607)(222,609)(223,611)(224,610)
(225,612)(226,596)(227,595)(228,597)(229,599)(230,598)(231,600)(232,602)
(233,601)(234,603)(235,614)(236,613)(237,615)(238,617)(239,616)(240,618)
(241,620)(242,619)(243,621)(244,632)(245,631)(246,633)(247,635)(248,634)
(249,636)(250,638)(251,637)(252,639)(253,623)(254,622)(255,624)(256,626)
(257,625)(258,627)(259,629)(260,628)(261,630)(262,641)(263,640)(264,642)
(265,644)(266,643)(267,645)(268,647)(269,646)(270,648)(271,578)(272,577)
(273,579)(274,581)(275,580)(276,582)(277,584)(278,583)(279,585)(280,569)
(281,568)(282,570)(283,572)(284,571)(285,573)(286,575)(287,574)(288,576)
(289,587)(290,586)(291,588)(292,590)(293,589)(294,591)(295,593)(296,592)
(297,594)(298,551)(299,550)(300,552)(301,554)(302,553)(303,555)(304,557)
(305,556)(306,558)(307,542)(308,541)(309,543)(310,545)(311,544)(312,546)
(313,548)(314,547)(315,549)(316,560)(317,559)(318,561)(319,563)(320,562)
(321,564)(322,566)(323,565)(324,567)(325,497)(326,496)(327,498)(328,500)
(329,499)(330,501)(331,503)(332,502)(333,504)(334,488)(335,487)(336,489)
(337,491)(338,490)(339,492)(340,494)(341,493)(342,495)(343,506)(344,505)
(345,507)(346,509)(347,508)(348,510)(349,512)(350,511)(351,513)(352,524)
(353,523)(354,525)(355,527)(356,526)(357,528)(358,530)(359,529)(360,531)
(361,515)(362,514)(363,516)(364,518)(365,517)(366,519)(367,521)(368,520)
(369,522)(370,533)(371,532)(372,534)(373,536)(374,535)(375,537)(376,539)
(377,538)(378,540)(379,470)(380,469)(381,471)(382,473)(383,472)(384,474)
(385,476)(386,475)(387,477)(388,461)(389,460)(390,462)(391,464)(392,463)
(393,465)(394,467)(395,466)(396,468)(397,479)(398,478)(399,480)(400,482)
(401,481)(402,483)(403,485)(404,484)(405,486)(406,443)(407,442)(408,444)
(409,446)(410,445)(411,447)(412,449)(413,448)(414,450)(415,434)(416,433)
(417,435)(418,437)(419,436)(420,438)(421,440)(422,439)(423,441)(424,452)
(425,451)(426,453)(427,455)(428,454)(429,456)(430,458)(431,457)(432,459);;
s2 := (  1,433)(  2,434)(  3,435)(  4,439)(  5,440)(  6,441)(  7,436)(  8,437)
(  9,438)( 10,451)( 11,452)( 12,453)( 13,457)( 14,458)( 15,459)( 16,454)
( 17,455)( 18,456)( 19,442)( 20,443)( 21,444)( 22,448)( 23,449)( 24,450)
( 25,445)( 26,446)( 27,447)( 28,460)( 29,461)( 30,462)( 31,466)( 32,467)
( 33,468)( 34,463)( 35,464)( 36,465)( 37,478)( 38,479)( 39,480)( 40,484)
( 41,485)( 42,486)( 43,481)( 44,482)( 45,483)( 46,469)( 47,470)( 48,471)
( 49,475)( 50,476)( 51,477)( 52,472)( 53,473)( 54,474)( 55,514)( 56,515)
( 57,516)( 58,520)( 59,521)( 60,522)( 61,517)( 62,518)( 63,519)( 64,532)
( 65,533)( 66,534)( 67,538)( 68,539)( 69,540)( 70,535)( 71,536)( 72,537)
( 73,523)( 74,524)( 75,525)( 76,529)( 77,530)( 78,531)( 79,526)( 80,527)
( 81,528)( 82,487)( 83,488)( 84,489)( 85,493)( 86,494)( 87,495)( 88,490)
( 89,491)( 90,492)( 91,505)( 92,506)( 93,507)( 94,511)( 95,512)( 96,513)
( 97,508)( 98,509)( 99,510)(100,496)(101,497)(102,498)(103,502)(104,503)
(105,504)(106,499)(107,500)(108,501)(109,541)(110,542)(111,543)(112,547)
(113,548)(114,549)(115,544)(116,545)(117,546)(118,559)(119,560)(120,561)
(121,565)(122,566)(123,567)(124,562)(125,563)(126,564)(127,550)(128,551)
(129,552)(130,556)(131,557)(132,558)(133,553)(134,554)(135,555)(136,568)
(137,569)(138,570)(139,574)(140,575)(141,576)(142,571)(143,572)(144,573)
(145,586)(146,587)(147,588)(148,592)(149,593)(150,594)(151,589)(152,590)
(153,591)(154,577)(155,578)(156,579)(157,583)(158,584)(159,585)(160,580)
(161,581)(162,582)(163,622)(164,623)(165,624)(166,628)(167,629)(168,630)
(169,625)(170,626)(171,627)(172,640)(173,641)(174,642)(175,646)(176,647)
(177,648)(178,643)(179,644)(180,645)(181,631)(182,632)(183,633)(184,637)
(185,638)(186,639)(187,634)(188,635)(189,636)(190,595)(191,596)(192,597)
(193,601)(194,602)(195,603)(196,598)(197,599)(198,600)(199,613)(200,614)
(201,615)(202,619)(203,620)(204,621)(205,616)(206,617)(207,618)(208,604)
(209,605)(210,606)(211,610)(212,611)(213,612)(214,607)(215,608)(216,609)
(217,730)(218,731)(219,732)(220,736)(221,737)(222,738)(223,733)(224,734)
(225,735)(226,748)(227,749)(228,750)(229,754)(230,755)(231,756)(232,751)
(233,752)(234,753)(235,739)(236,740)(237,741)(238,745)(239,746)(240,747)
(241,742)(242,743)(243,744)(244,703)(245,704)(246,705)(247,709)(248,710)
(249,711)(250,706)(251,707)(252,708)(253,721)(254,722)(255,723)(256,727)
(257,728)(258,729)(259,724)(260,725)(261,726)(262,712)(263,713)(264,714)
(265,718)(266,719)(267,720)(268,715)(269,716)(270,717)(271,676)(272,677)
(273,678)(274,682)(275,683)(276,684)(277,679)(278,680)(279,681)(280,694)
(281,695)(282,696)(283,700)(284,701)(285,702)(286,697)(287,698)(288,699)
(289,685)(290,686)(291,687)(292,691)(293,692)(294,693)(295,688)(296,689)
(297,690)(298,649)(299,650)(300,651)(301,655)(302,656)(303,657)(304,652)
(305,653)(306,654)(307,667)(308,668)(309,669)(310,673)(311,674)(312,675)
(313,670)(314,671)(315,672)(316,658)(317,659)(318,660)(319,664)(320,665)
(321,666)(322,661)(323,662)(324,663)(325,838)(326,839)(327,840)(328,844)
(329,845)(330,846)(331,841)(332,842)(333,843)(334,856)(335,857)(336,858)
(337,862)(338,863)(339,864)(340,859)(341,860)(342,861)(343,847)(344,848)
(345,849)(346,853)(347,854)(348,855)(349,850)(350,851)(351,852)(352,811)
(353,812)(354,813)(355,817)(356,818)(357,819)(358,814)(359,815)(360,816)
(361,829)(362,830)(363,831)(364,835)(365,836)(366,837)(367,832)(368,833)
(369,834)(370,820)(371,821)(372,822)(373,826)(374,827)(375,828)(376,823)
(377,824)(378,825)(379,784)(380,785)(381,786)(382,790)(383,791)(384,792)
(385,787)(386,788)(387,789)(388,802)(389,803)(390,804)(391,808)(392,809)
(393,810)(394,805)(395,806)(396,807)(397,793)(398,794)(399,795)(400,799)
(401,800)(402,801)(403,796)(404,797)(405,798)(406,757)(407,758)(408,759)
(409,763)(410,764)(411,765)(412,760)(413,761)(414,762)(415,775)(416,776)
(417,777)(418,781)(419,782)(420,783)(421,778)(422,779)(423,780)(424,766)
(425,767)(426,768)(427,772)(428,773)(429,774)(430,769)(431,770)(432,771);;
s3 := (  1,  4)(  2,  5)(  3,  6)( 10, 13)( 11, 14)( 12, 15)( 19, 22)( 20, 23)
( 21, 24)( 28, 31)( 29, 32)( 30, 33)( 37, 40)( 38, 41)( 39, 42)( 46, 49)
( 47, 50)( 48, 51)( 55, 85)( 56, 86)( 57, 87)( 58, 82)( 59, 83)( 60, 84)
( 61, 88)( 62, 89)( 63, 90)( 64, 94)( 65, 95)( 66, 96)( 67, 91)( 68, 92)
( 69, 93)( 70, 97)( 71, 98)( 72, 99)( 73,103)( 74,104)( 75,105)( 76,100)
( 77,101)( 78,102)( 79,106)( 80,107)( 81,108)(109,112)(110,113)(111,114)
(118,121)(119,122)(120,123)(127,130)(128,131)(129,132)(136,139)(137,140)
(138,141)(145,148)(146,149)(147,150)(154,157)(155,158)(156,159)(163,193)
(164,194)(165,195)(166,190)(167,191)(168,192)(169,196)(170,197)(171,198)
(172,202)(173,203)(174,204)(175,199)(176,200)(177,201)(178,205)(179,206)
(180,207)(181,211)(182,212)(183,213)(184,208)(185,209)(186,210)(187,214)
(188,215)(189,216)(217,301)(218,302)(219,303)(220,298)(221,299)(222,300)
(223,304)(224,305)(225,306)(226,310)(227,311)(228,312)(229,307)(230,308)
(231,309)(232,313)(233,314)(234,315)(235,319)(236,320)(237,321)(238,316)
(239,317)(240,318)(241,322)(242,323)(243,324)(244,274)(245,275)(246,276)
(247,271)(248,272)(249,273)(250,277)(251,278)(252,279)(253,283)(254,284)
(255,285)(256,280)(257,281)(258,282)(259,286)(260,287)(261,288)(262,292)
(263,293)(264,294)(265,289)(266,290)(267,291)(268,295)(269,296)(270,297)
(325,409)(326,410)(327,411)(328,406)(329,407)(330,408)(331,412)(332,413)
(333,414)(334,418)(335,419)(336,420)(337,415)(338,416)(339,417)(340,421)
(341,422)(342,423)(343,427)(344,428)(345,429)(346,424)(347,425)(348,426)
(349,430)(350,431)(351,432)(352,382)(353,383)(354,384)(355,379)(356,380)
(357,381)(358,385)(359,386)(360,387)(361,391)(362,392)(363,393)(364,388)
(365,389)(366,390)(367,394)(368,395)(369,396)(370,400)(371,401)(372,402)
(373,397)(374,398)(375,399)(376,403)(377,404)(378,405)(433,490)(434,491)
(435,492)(436,487)(437,488)(438,489)(439,493)(440,494)(441,495)(442,499)
(443,500)(444,501)(445,496)(446,497)(447,498)(448,502)(449,503)(450,504)
(451,508)(452,509)(453,510)(454,505)(455,506)(456,507)(457,511)(458,512)
(459,513)(460,517)(461,518)(462,519)(463,514)(464,515)(465,516)(466,520)
(467,521)(468,522)(469,526)(470,527)(471,528)(472,523)(473,524)(474,525)
(475,529)(476,530)(477,531)(478,535)(479,536)(480,537)(481,532)(482,533)
(483,534)(484,538)(485,539)(486,540)(541,598)(542,599)(543,600)(544,595)
(545,596)(546,597)(547,601)(548,602)(549,603)(550,607)(551,608)(552,609)
(553,604)(554,605)(555,606)(556,610)(557,611)(558,612)(559,616)(560,617)
(561,618)(562,613)(563,614)(564,615)(565,619)(566,620)(567,621)(568,625)
(569,626)(570,627)(571,622)(572,623)(573,624)(574,628)(575,629)(576,630)
(577,634)(578,635)(579,636)(580,631)(581,632)(582,633)(583,637)(584,638)
(585,639)(586,643)(587,644)(588,645)(589,640)(590,641)(591,642)(592,646)
(593,647)(594,648)(649,652)(650,653)(651,654)(658,661)(659,662)(660,663)
(667,670)(668,671)(669,672)(676,679)(677,680)(678,681)(685,688)(686,689)
(687,690)(694,697)(695,698)(696,699)(703,733)(704,734)(705,735)(706,730)
(707,731)(708,732)(709,736)(710,737)(711,738)(712,742)(713,743)(714,744)
(715,739)(716,740)(717,741)(718,745)(719,746)(720,747)(721,751)(722,752)
(723,753)(724,748)(725,749)(726,750)(727,754)(728,755)(729,756)(757,760)
(758,761)(759,762)(766,769)(767,770)(768,771)(775,778)(776,779)(777,780)
(784,787)(785,788)(786,789)(793,796)(794,797)(795,798)(802,805)(803,806)
(804,807)(811,841)(812,842)(813,843)(814,838)(815,839)(816,840)(817,844)
(818,845)(819,846)(820,850)(821,851)(822,852)(823,847)(824,848)(825,849)
(826,853)(827,854)(828,855)(829,859)(830,860)(831,861)(832,856)(833,857)
(834,858)(835,862)(836,863)(837,864);;
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*s3*s2*s1*s2*s3*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(864)!(  1,649)(  2,651)(  3,650)(  4,652)(  5,654)(  6,653)(  7,655)
(  8,657)(  9,656)( 10,667)( 11,669)( 12,668)( 13,670)( 14,672)( 15,671)
( 16,673)( 17,675)( 18,674)( 19,658)( 20,660)( 21,659)( 22,661)( 23,663)
( 24,662)( 25,664)( 26,666)( 27,665)( 28,676)( 29,678)( 30,677)( 31,679)
( 32,681)( 33,680)( 34,682)( 35,684)( 36,683)( 37,694)( 38,696)( 39,695)
( 40,697)( 41,699)( 42,698)( 43,700)( 44,702)( 45,701)( 46,685)( 47,687)
( 48,686)( 49,688)( 50,690)( 51,689)( 52,691)( 53,693)( 54,692)( 55,703)
( 56,705)( 57,704)( 58,706)( 59,708)( 60,707)( 61,709)( 62,711)( 63,710)
( 64,721)( 65,723)( 66,722)( 67,724)( 68,726)( 69,725)( 70,727)( 71,729)
( 72,728)( 73,712)( 74,714)( 75,713)( 76,715)( 77,717)( 78,716)( 79,718)
( 80,720)( 81,719)( 82,730)( 83,732)( 84,731)( 85,733)( 86,735)( 87,734)
( 88,736)( 89,738)( 90,737)( 91,748)( 92,750)( 93,749)( 94,751)( 95,753)
( 96,752)( 97,754)( 98,756)( 99,755)(100,739)(101,741)(102,740)(103,742)
(104,744)(105,743)(106,745)(107,747)(108,746)(109,757)(110,759)(111,758)
(112,760)(113,762)(114,761)(115,763)(116,765)(117,764)(118,775)(119,777)
(120,776)(121,778)(122,780)(123,779)(124,781)(125,783)(126,782)(127,766)
(128,768)(129,767)(130,769)(131,771)(132,770)(133,772)(134,774)(135,773)
(136,784)(137,786)(138,785)(139,787)(140,789)(141,788)(142,790)(143,792)
(144,791)(145,802)(146,804)(147,803)(148,805)(149,807)(150,806)(151,808)
(152,810)(153,809)(154,793)(155,795)(156,794)(157,796)(158,798)(159,797)
(160,799)(161,801)(162,800)(163,811)(164,813)(165,812)(166,814)(167,816)
(168,815)(169,817)(170,819)(171,818)(172,829)(173,831)(174,830)(175,832)
(176,834)(177,833)(178,835)(179,837)(180,836)(181,820)(182,822)(183,821)
(184,823)(185,825)(186,824)(187,826)(188,828)(189,827)(190,838)(191,840)
(192,839)(193,841)(194,843)(195,842)(196,844)(197,846)(198,845)(199,856)
(200,858)(201,857)(202,859)(203,861)(204,860)(205,862)(206,864)(207,863)
(208,847)(209,849)(210,848)(211,850)(212,852)(213,851)(214,853)(215,855)
(216,854)(217,487)(218,489)(219,488)(220,490)(221,492)(222,491)(223,493)
(224,495)(225,494)(226,505)(227,507)(228,506)(229,508)(230,510)(231,509)
(232,511)(233,513)(234,512)(235,496)(236,498)(237,497)(238,499)(239,501)
(240,500)(241,502)(242,504)(243,503)(244,514)(245,516)(246,515)(247,517)
(248,519)(249,518)(250,520)(251,522)(252,521)(253,532)(254,534)(255,533)
(256,535)(257,537)(258,536)(259,538)(260,540)(261,539)(262,523)(263,525)
(264,524)(265,526)(266,528)(267,527)(268,529)(269,531)(270,530)(271,460)
(272,462)(273,461)(274,463)(275,465)(276,464)(277,466)(278,468)(279,467)
(280,478)(281,480)(282,479)(283,481)(284,483)(285,482)(286,484)(287,486)
(288,485)(289,469)(290,471)(291,470)(292,472)(293,474)(294,473)(295,475)
(296,477)(297,476)(298,433)(299,435)(300,434)(301,436)(302,438)(303,437)
(304,439)(305,441)(306,440)(307,451)(308,453)(309,452)(310,454)(311,456)
(312,455)(313,457)(314,459)(315,458)(316,442)(317,444)(318,443)(319,445)
(320,447)(321,446)(322,448)(323,450)(324,449)(325,595)(326,597)(327,596)
(328,598)(329,600)(330,599)(331,601)(332,603)(333,602)(334,613)(335,615)
(336,614)(337,616)(338,618)(339,617)(340,619)(341,621)(342,620)(343,604)
(344,606)(345,605)(346,607)(347,609)(348,608)(349,610)(350,612)(351,611)
(352,622)(353,624)(354,623)(355,625)(356,627)(357,626)(358,628)(359,630)
(360,629)(361,640)(362,642)(363,641)(364,643)(365,645)(366,644)(367,646)
(368,648)(369,647)(370,631)(371,633)(372,632)(373,634)(374,636)(375,635)
(376,637)(377,639)(378,638)(379,568)(380,570)(381,569)(382,571)(383,573)
(384,572)(385,574)(386,576)(387,575)(388,586)(389,588)(390,587)(391,589)
(392,591)(393,590)(394,592)(395,594)(396,593)(397,577)(398,579)(399,578)
(400,580)(401,582)(402,581)(403,583)(404,585)(405,584)(406,541)(407,543)
(408,542)(409,544)(410,546)(411,545)(412,547)(413,549)(414,548)(415,559)
(416,561)(417,560)(418,562)(419,564)(420,563)(421,565)(422,567)(423,566)
(424,550)(425,552)(426,551)(427,553)(428,555)(429,554)(430,556)(431,558)
(432,557);
s1 := Sym(864)!(  1,767)(  2,766)(  3,768)(  4,770)(  5,769)(  6,771)(  7,773)
(  8,772)(  9,774)( 10,758)( 11,757)( 12,759)( 13,761)( 14,760)( 15,762)
( 16,764)( 17,763)( 18,765)( 19,776)( 20,775)( 21,777)( 22,779)( 23,778)
( 24,780)( 25,782)( 26,781)( 27,783)( 28,794)( 29,793)( 30,795)( 31,797)
( 32,796)( 33,798)( 34,800)( 35,799)( 36,801)( 37,785)( 38,784)( 39,786)
( 40,788)( 41,787)( 42,789)( 43,791)( 44,790)( 45,792)( 46,803)( 47,802)
( 48,804)( 49,806)( 50,805)( 51,807)( 52,809)( 53,808)( 54,810)( 55,821)
( 56,820)( 57,822)( 58,824)( 59,823)( 60,825)( 61,827)( 62,826)( 63,828)
( 64,812)( 65,811)( 66,813)( 67,815)( 68,814)( 69,816)( 70,818)( 71,817)
( 72,819)( 73,830)( 74,829)( 75,831)( 76,833)( 77,832)( 78,834)( 79,836)
( 80,835)( 81,837)( 82,848)( 83,847)( 84,849)( 85,851)( 86,850)( 87,852)
( 88,854)( 89,853)( 90,855)( 91,839)( 92,838)( 93,840)( 94,842)( 95,841)
( 96,843)( 97,845)( 98,844)( 99,846)(100,857)(101,856)(102,858)(103,860)
(104,859)(105,861)(106,863)(107,862)(108,864)(109,659)(110,658)(111,660)
(112,662)(113,661)(114,663)(115,665)(116,664)(117,666)(118,650)(119,649)
(120,651)(121,653)(122,652)(123,654)(124,656)(125,655)(126,657)(127,668)
(128,667)(129,669)(130,671)(131,670)(132,672)(133,674)(134,673)(135,675)
(136,686)(137,685)(138,687)(139,689)(140,688)(141,690)(142,692)(143,691)
(144,693)(145,677)(146,676)(147,678)(148,680)(149,679)(150,681)(151,683)
(152,682)(153,684)(154,695)(155,694)(156,696)(157,698)(158,697)(159,699)
(160,701)(161,700)(162,702)(163,713)(164,712)(165,714)(166,716)(167,715)
(168,717)(169,719)(170,718)(171,720)(172,704)(173,703)(174,705)(175,707)
(176,706)(177,708)(178,710)(179,709)(180,711)(181,722)(182,721)(183,723)
(184,725)(185,724)(186,726)(187,728)(188,727)(189,729)(190,740)(191,739)
(192,741)(193,743)(194,742)(195,744)(196,746)(197,745)(198,747)(199,731)
(200,730)(201,732)(202,734)(203,733)(204,735)(205,737)(206,736)(207,738)
(208,749)(209,748)(210,750)(211,752)(212,751)(213,753)(214,755)(215,754)
(216,756)(217,605)(218,604)(219,606)(220,608)(221,607)(222,609)(223,611)
(224,610)(225,612)(226,596)(227,595)(228,597)(229,599)(230,598)(231,600)
(232,602)(233,601)(234,603)(235,614)(236,613)(237,615)(238,617)(239,616)
(240,618)(241,620)(242,619)(243,621)(244,632)(245,631)(246,633)(247,635)
(248,634)(249,636)(250,638)(251,637)(252,639)(253,623)(254,622)(255,624)
(256,626)(257,625)(258,627)(259,629)(260,628)(261,630)(262,641)(263,640)
(264,642)(265,644)(266,643)(267,645)(268,647)(269,646)(270,648)(271,578)
(272,577)(273,579)(274,581)(275,580)(276,582)(277,584)(278,583)(279,585)
(280,569)(281,568)(282,570)(283,572)(284,571)(285,573)(286,575)(287,574)
(288,576)(289,587)(290,586)(291,588)(292,590)(293,589)(294,591)(295,593)
(296,592)(297,594)(298,551)(299,550)(300,552)(301,554)(302,553)(303,555)
(304,557)(305,556)(306,558)(307,542)(308,541)(309,543)(310,545)(311,544)
(312,546)(313,548)(314,547)(315,549)(316,560)(317,559)(318,561)(319,563)
(320,562)(321,564)(322,566)(323,565)(324,567)(325,497)(326,496)(327,498)
(328,500)(329,499)(330,501)(331,503)(332,502)(333,504)(334,488)(335,487)
(336,489)(337,491)(338,490)(339,492)(340,494)(341,493)(342,495)(343,506)
(344,505)(345,507)(346,509)(347,508)(348,510)(349,512)(350,511)(351,513)
(352,524)(353,523)(354,525)(355,527)(356,526)(357,528)(358,530)(359,529)
(360,531)(361,515)(362,514)(363,516)(364,518)(365,517)(366,519)(367,521)
(368,520)(369,522)(370,533)(371,532)(372,534)(373,536)(374,535)(375,537)
(376,539)(377,538)(378,540)(379,470)(380,469)(381,471)(382,473)(383,472)
(384,474)(385,476)(386,475)(387,477)(388,461)(389,460)(390,462)(391,464)
(392,463)(393,465)(394,467)(395,466)(396,468)(397,479)(398,478)(399,480)
(400,482)(401,481)(402,483)(403,485)(404,484)(405,486)(406,443)(407,442)
(408,444)(409,446)(410,445)(411,447)(412,449)(413,448)(414,450)(415,434)
(416,433)(417,435)(418,437)(419,436)(420,438)(421,440)(422,439)(423,441)
(424,452)(425,451)(426,453)(427,455)(428,454)(429,456)(430,458)(431,457)
(432,459);
s2 := Sym(864)!(  1,433)(  2,434)(  3,435)(  4,439)(  5,440)(  6,441)(  7,436)
(  8,437)(  9,438)( 10,451)( 11,452)( 12,453)( 13,457)( 14,458)( 15,459)
( 16,454)( 17,455)( 18,456)( 19,442)( 20,443)( 21,444)( 22,448)( 23,449)
( 24,450)( 25,445)( 26,446)( 27,447)( 28,460)( 29,461)( 30,462)( 31,466)
( 32,467)( 33,468)( 34,463)( 35,464)( 36,465)( 37,478)( 38,479)( 39,480)
( 40,484)( 41,485)( 42,486)( 43,481)( 44,482)( 45,483)( 46,469)( 47,470)
( 48,471)( 49,475)( 50,476)( 51,477)( 52,472)( 53,473)( 54,474)( 55,514)
( 56,515)( 57,516)( 58,520)( 59,521)( 60,522)( 61,517)( 62,518)( 63,519)
( 64,532)( 65,533)( 66,534)( 67,538)( 68,539)( 69,540)( 70,535)( 71,536)
( 72,537)( 73,523)( 74,524)( 75,525)( 76,529)( 77,530)( 78,531)( 79,526)
( 80,527)( 81,528)( 82,487)( 83,488)( 84,489)( 85,493)( 86,494)( 87,495)
( 88,490)( 89,491)( 90,492)( 91,505)( 92,506)( 93,507)( 94,511)( 95,512)
( 96,513)( 97,508)( 98,509)( 99,510)(100,496)(101,497)(102,498)(103,502)
(104,503)(105,504)(106,499)(107,500)(108,501)(109,541)(110,542)(111,543)
(112,547)(113,548)(114,549)(115,544)(116,545)(117,546)(118,559)(119,560)
(120,561)(121,565)(122,566)(123,567)(124,562)(125,563)(126,564)(127,550)
(128,551)(129,552)(130,556)(131,557)(132,558)(133,553)(134,554)(135,555)
(136,568)(137,569)(138,570)(139,574)(140,575)(141,576)(142,571)(143,572)
(144,573)(145,586)(146,587)(147,588)(148,592)(149,593)(150,594)(151,589)
(152,590)(153,591)(154,577)(155,578)(156,579)(157,583)(158,584)(159,585)
(160,580)(161,581)(162,582)(163,622)(164,623)(165,624)(166,628)(167,629)
(168,630)(169,625)(170,626)(171,627)(172,640)(173,641)(174,642)(175,646)
(176,647)(177,648)(178,643)(179,644)(180,645)(181,631)(182,632)(183,633)
(184,637)(185,638)(186,639)(187,634)(188,635)(189,636)(190,595)(191,596)
(192,597)(193,601)(194,602)(195,603)(196,598)(197,599)(198,600)(199,613)
(200,614)(201,615)(202,619)(203,620)(204,621)(205,616)(206,617)(207,618)
(208,604)(209,605)(210,606)(211,610)(212,611)(213,612)(214,607)(215,608)
(216,609)(217,730)(218,731)(219,732)(220,736)(221,737)(222,738)(223,733)
(224,734)(225,735)(226,748)(227,749)(228,750)(229,754)(230,755)(231,756)
(232,751)(233,752)(234,753)(235,739)(236,740)(237,741)(238,745)(239,746)
(240,747)(241,742)(242,743)(243,744)(244,703)(245,704)(246,705)(247,709)
(248,710)(249,711)(250,706)(251,707)(252,708)(253,721)(254,722)(255,723)
(256,727)(257,728)(258,729)(259,724)(260,725)(261,726)(262,712)(263,713)
(264,714)(265,718)(266,719)(267,720)(268,715)(269,716)(270,717)(271,676)
(272,677)(273,678)(274,682)(275,683)(276,684)(277,679)(278,680)(279,681)
(280,694)(281,695)(282,696)(283,700)(284,701)(285,702)(286,697)(287,698)
(288,699)(289,685)(290,686)(291,687)(292,691)(293,692)(294,693)(295,688)
(296,689)(297,690)(298,649)(299,650)(300,651)(301,655)(302,656)(303,657)
(304,652)(305,653)(306,654)(307,667)(308,668)(309,669)(310,673)(311,674)
(312,675)(313,670)(314,671)(315,672)(316,658)(317,659)(318,660)(319,664)
(320,665)(321,666)(322,661)(323,662)(324,663)(325,838)(326,839)(327,840)
(328,844)(329,845)(330,846)(331,841)(332,842)(333,843)(334,856)(335,857)
(336,858)(337,862)(338,863)(339,864)(340,859)(341,860)(342,861)(343,847)
(344,848)(345,849)(346,853)(347,854)(348,855)(349,850)(350,851)(351,852)
(352,811)(353,812)(354,813)(355,817)(356,818)(357,819)(358,814)(359,815)
(360,816)(361,829)(362,830)(363,831)(364,835)(365,836)(366,837)(367,832)
(368,833)(369,834)(370,820)(371,821)(372,822)(373,826)(374,827)(375,828)
(376,823)(377,824)(378,825)(379,784)(380,785)(381,786)(382,790)(383,791)
(384,792)(385,787)(386,788)(387,789)(388,802)(389,803)(390,804)(391,808)
(392,809)(393,810)(394,805)(395,806)(396,807)(397,793)(398,794)(399,795)
(400,799)(401,800)(402,801)(403,796)(404,797)(405,798)(406,757)(407,758)
(408,759)(409,763)(410,764)(411,765)(412,760)(413,761)(414,762)(415,775)
(416,776)(417,777)(418,781)(419,782)(420,783)(421,778)(422,779)(423,780)
(424,766)(425,767)(426,768)(427,772)(428,773)(429,774)(430,769)(431,770)
(432,771);
s3 := Sym(864)!(  1,  4)(  2,  5)(  3,  6)( 10, 13)( 11, 14)( 12, 15)( 19, 22)
( 20, 23)( 21, 24)( 28, 31)( 29, 32)( 30, 33)( 37, 40)( 38, 41)( 39, 42)
( 46, 49)( 47, 50)( 48, 51)( 55, 85)( 56, 86)( 57, 87)( 58, 82)( 59, 83)
( 60, 84)( 61, 88)( 62, 89)( 63, 90)( 64, 94)( 65, 95)( 66, 96)( 67, 91)
( 68, 92)( 69, 93)( 70, 97)( 71, 98)( 72, 99)( 73,103)( 74,104)( 75,105)
( 76,100)( 77,101)( 78,102)( 79,106)( 80,107)( 81,108)(109,112)(110,113)
(111,114)(118,121)(119,122)(120,123)(127,130)(128,131)(129,132)(136,139)
(137,140)(138,141)(145,148)(146,149)(147,150)(154,157)(155,158)(156,159)
(163,193)(164,194)(165,195)(166,190)(167,191)(168,192)(169,196)(170,197)
(171,198)(172,202)(173,203)(174,204)(175,199)(176,200)(177,201)(178,205)
(179,206)(180,207)(181,211)(182,212)(183,213)(184,208)(185,209)(186,210)
(187,214)(188,215)(189,216)(217,301)(218,302)(219,303)(220,298)(221,299)
(222,300)(223,304)(224,305)(225,306)(226,310)(227,311)(228,312)(229,307)
(230,308)(231,309)(232,313)(233,314)(234,315)(235,319)(236,320)(237,321)
(238,316)(239,317)(240,318)(241,322)(242,323)(243,324)(244,274)(245,275)
(246,276)(247,271)(248,272)(249,273)(250,277)(251,278)(252,279)(253,283)
(254,284)(255,285)(256,280)(257,281)(258,282)(259,286)(260,287)(261,288)
(262,292)(263,293)(264,294)(265,289)(266,290)(267,291)(268,295)(269,296)
(270,297)(325,409)(326,410)(327,411)(328,406)(329,407)(330,408)(331,412)
(332,413)(333,414)(334,418)(335,419)(336,420)(337,415)(338,416)(339,417)
(340,421)(341,422)(342,423)(343,427)(344,428)(345,429)(346,424)(347,425)
(348,426)(349,430)(350,431)(351,432)(352,382)(353,383)(354,384)(355,379)
(356,380)(357,381)(358,385)(359,386)(360,387)(361,391)(362,392)(363,393)
(364,388)(365,389)(366,390)(367,394)(368,395)(369,396)(370,400)(371,401)
(372,402)(373,397)(374,398)(375,399)(376,403)(377,404)(378,405)(433,490)
(434,491)(435,492)(436,487)(437,488)(438,489)(439,493)(440,494)(441,495)
(442,499)(443,500)(444,501)(445,496)(446,497)(447,498)(448,502)(449,503)
(450,504)(451,508)(452,509)(453,510)(454,505)(455,506)(456,507)(457,511)
(458,512)(459,513)(460,517)(461,518)(462,519)(463,514)(464,515)(465,516)
(466,520)(467,521)(468,522)(469,526)(470,527)(471,528)(472,523)(473,524)
(474,525)(475,529)(476,530)(477,531)(478,535)(479,536)(480,537)(481,532)
(482,533)(483,534)(484,538)(485,539)(486,540)(541,598)(542,599)(543,600)
(544,595)(545,596)(546,597)(547,601)(548,602)(549,603)(550,607)(551,608)
(552,609)(553,604)(554,605)(555,606)(556,610)(557,611)(558,612)(559,616)
(560,617)(561,618)(562,613)(563,614)(564,615)(565,619)(566,620)(567,621)
(568,625)(569,626)(570,627)(571,622)(572,623)(573,624)(574,628)(575,629)
(576,630)(577,634)(578,635)(579,636)(580,631)(581,632)(582,633)(583,637)
(584,638)(585,639)(586,643)(587,644)(588,645)(589,640)(590,641)(591,642)
(592,646)(593,647)(594,648)(649,652)(650,653)(651,654)(658,661)(659,662)
(660,663)(667,670)(668,671)(669,672)(676,679)(677,680)(678,681)(685,688)
(686,689)(687,690)(694,697)(695,698)(696,699)(703,733)(704,734)(705,735)
(706,730)(707,731)(708,732)(709,736)(710,737)(711,738)(712,742)(713,743)
(714,744)(715,739)(716,740)(717,741)(718,745)(719,746)(720,747)(721,751)
(722,752)(723,753)(724,748)(725,749)(726,750)(727,754)(728,755)(729,756)
(757,760)(758,761)(759,762)(766,769)(767,770)(768,771)(775,778)(776,779)
(777,780)(784,787)(785,788)(786,789)(793,796)(794,797)(795,798)(802,805)
(803,806)(804,807)(811,841)(812,842)(813,843)(814,838)(815,839)(816,840)
(817,844)(818,845)(819,846)(820,850)(821,851)(822,852)(823,847)(824,848)
(825,849)(826,853)(827,854)(828,855)(829,859)(830,860)(831,861)(832,856)
(833,857)(834,858)(835,862)(836,863)(837,864);
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*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope