Polytope of Type {3,24,6}

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