Polytope of Type {3,6,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,12,4}*1728d
if this polytope has a name.
Group : SmallGroup(1728,38805)
Rank : 5
Schlafli Type : {3,6,12,4}
Number of vertices, edges, etc : 3, 9, 36, 24, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 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 : {3,6,12,2}*864b, {3,6,6,4}*864d
3-fold quotients : {3,2,12,4}*576a, {3,6,4,4}*576
4-fold quotients : {3,6,6,2}*432b
6-fold quotients : {3,2,12,2}*288, {3,2,6,4}*288a, {3,6,2,4}*288, {3,6,4,2}*288
9-fold quotients : {3,2,4,4}*192
12-fold quotients : {3,2,6,2}*144, {3,6,2,2}*144
18-fold quotients : {3,2,2,4}*96, {3,2,4,2}*96
24-fold quotients : {3,2,3,2}*72
36-fold quotients : {3,2,2,2}*48
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)
(217,460)(218,462)(219,461)(220,463)(221,465)(222,464)(223,466)(224,468)
(225,467)(226,478)(227,480)(228,479)(229,481)(230,483)(231,482)(232,484)
(233,486)(234,485)(235,469)(236,471)(237,470)(238,472)(239,474)(240,473)
(241,475)(242,477)(243,476)(244,433)(245,435)(246,434)(247,436)(248,438)
(249,437)(250,439)(251,441)(252,440)(253,451)(254,453)(255,452)(256,454)
(257,456)(258,455)(259,457)(260,459)(261,458)(262,442)(263,444)(264,443)
(265,445)(266,447)(267,446)(268,448)(269,450)(270,449)(271,514)(272,516)
(273,515)(274,517)(275,519)(276,518)(277,520)(278,522)(279,521)(280,532)
(281,534)(282,533)(283,535)(284,537)(285,536)(286,538)(287,540)(288,539)
(289,523)(290,525)(291,524)(292,526)(293,528)(294,527)(295,529)(296,531)
(297,530)(298,487)(299,489)(300,488)(301,490)(302,492)(303,491)(304,493)
(305,495)(306,494)(307,505)(308,507)(309,506)(310,508)(311,510)(312,509)
(313,511)(314,513)(315,512)(316,496)(317,498)(318,497)(319,499)(320,501)
(321,500)(322,502)(323,504)(324,503)(325,568)(326,570)(327,569)(328,571)
(329,573)(330,572)(331,574)(332,576)(333,575)(334,586)(335,588)(336,587)
(337,589)(338,591)(339,590)(340,592)(341,594)(342,593)(343,577)(344,579)
(345,578)(346,580)(347,582)(348,581)(349,583)(350,585)(351,584)(352,541)
(353,543)(354,542)(355,544)(356,546)(357,545)(358,547)(359,549)(360,548)
(361,559)(362,561)(363,560)(364,562)(365,564)(366,563)(367,565)(368,567)
(369,566)(370,550)(371,552)(372,551)(373,553)(374,555)(375,554)(376,556)
(377,558)(378,557)(379,622)(380,624)(381,623)(382,625)(383,627)(384,626)
(385,628)(386,630)(387,629)(388,640)(389,642)(390,641)(391,643)(392,645)
(393,644)(394,646)(395,648)(396,647)(397,631)(398,633)(399,632)(400,634)
(401,636)(402,635)(403,637)(404,639)(405,638)(406,595)(407,597)(408,596)
(409,598)(410,600)(411,599)(412,601)(413,603)(414,602)(415,613)(416,615)
(417,614)(418,616)(419,618)(420,617)(421,619)(422,621)(423,620)(424,604)
(425,606)(426,605)(427,607)(428,609)(429,608)(430,610)(431,612)(432,611);;
s1 := ( 1,659)( 2,658)( 3,660)( 4,662)( 5,661)( 6,663)( 7,665)( 8,664)
( 9,666)( 10,650)( 11,649)( 12,651)( 13,653)( 14,652)( 15,654)( 16,656)
( 17,655)( 18,657)( 19,668)( 20,667)( 21,669)( 22,671)( 23,670)( 24,672)
( 25,674)( 26,673)( 27,675)( 28,686)( 29,685)( 30,687)( 31,689)( 32,688)
( 33,690)( 34,692)( 35,691)( 36,693)( 37,677)( 38,676)( 39,678)( 40,680)
( 41,679)( 42,681)( 43,683)( 44,682)( 45,684)( 46,695)( 47,694)( 48,696)
( 49,698)( 50,697)( 51,699)( 52,701)( 53,700)( 54,702)( 55,713)( 56,712)
( 57,714)( 58,716)( 59,715)( 60,717)( 61,719)( 62,718)( 63,720)( 64,704)
( 65,703)( 66,705)( 67,707)( 68,706)( 69,708)( 70,710)( 71,709)( 72,711)
( 73,722)( 74,721)( 75,723)( 76,725)( 77,724)( 78,726)( 79,728)( 80,727)
( 81,729)( 82,740)( 83,739)( 84,741)( 85,743)( 86,742)( 87,744)( 88,746)
( 89,745)( 90,747)( 91,731)( 92,730)( 93,732)( 94,734)( 95,733)( 96,735)
( 97,737)( 98,736)( 99,738)(100,749)(101,748)(102,750)(103,752)(104,751)
(105,753)(106,755)(107,754)(108,756)(109,767)(110,766)(111,768)(112,770)
(113,769)(114,771)(115,773)(116,772)(117,774)(118,758)(119,757)(120,759)
(121,761)(122,760)(123,762)(124,764)(125,763)(126,765)(127,776)(128,775)
(129,777)(130,779)(131,778)(132,780)(133,782)(134,781)(135,783)(136,794)
(137,793)(138,795)(139,797)(140,796)(141,798)(142,800)(143,799)(144,801)
(145,785)(146,784)(147,786)(148,788)(149,787)(150,789)(151,791)(152,790)
(153,792)(154,803)(155,802)(156,804)(157,806)(158,805)(159,807)(160,809)
(161,808)(162,810)(163,821)(164,820)(165,822)(166,824)(167,823)(168,825)
(169,827)(170,826)(171,828)(172,812)(173,811)(174,813)(175,815)(176,814)
(177,816)(178,818)(179,817)(180,819)(181,830)(182,829)(183,831)(184,833)
(185,832)(186,834)(187,836)(188,835)(189,837)(190,848)(191,847)(192,849)
(193,851)(194,850)(195,852)(196,854)(197,853)(198,855)(199,839)(200,838)
(201,840)(202,842)(203,841)(204,843)(205,845)(206,844)(207,846)(208,857)
(209,856)(210,858)(211,860)(212,859)(213,861)(214,863)(215,862)(216,864)
(217,470)(218,469)(219,471)(220,473)(221,472)(222,474)(223,476)(224,475)
(225,477)(226,461)(227,460)(228,462)(229,464)(230,463)(231,465)(232,467)
(233,466)(234,468)(235,479)(236,478)(237,480)(238,482)(239,481)(240,483)
(241,485)(242,484)(243,486)(244,443)(245,442)(246,444)(247,446)(248,445)
(249,447)(250,449)(251,448)(252,450)(253,434)(254,433)(255,435)(256,437)
(257,436)(258,438)(259,440)(260,439)(261,441)(262,452)(263,451)(264,453)
(265,455)(266,454)(267,456)(268,458)(269,457)(270,459)(271,524)(272,523)
(273,525)(274,527)(275,526)(276,528)(277,530)(278,529)(279,531)(280,515)
(281,514)(282,516)(283,518)(284,517)(285,519)(286,521)(287,520)(288,522)
(289,533)(290,532)(291,534)(292,536)(293,535)(294,537)(295,539)(296,538)
(297,540)(298,497)(299,496)(300,498)(301,500)(302,499)(303,501)(304,503)
(305,502)(306,504)(307,488)(308,487)(309,489)(310,491)(311,490)(312,492)
(313,494)(314,493)(315,495)(316,506)(317,505)(318,507)(319,509)(320,508)
(321,510)(322,512)(323,511)(324,513)(325,578)(326,577)(327,579)(328,581)
(329,580)(330,582)(331,584)(332,583)(333,585)(334,569)(335,568)(336,570)
(337,572)(338,571)(339,573)(340,575)(341,574)(342,576)(343,587)(344,586)
(345,588)(346,590)(347,589)(348,591)(349,593)(350,592)(351,594)(352,551)
(353,550)(354,552)(355,554)(356,553)(357,555)(358,557)(359,556)(360,558)
(361,542)(362,541)(363,543)(364,545)(365,544)(366,546)(367,548)(368,547)
(369,549)(370,560)(371,559)(372,561)(373,563)(374,562)(375,564)(376,566)
(377,565)(378,567)(379,632)(380,631)(381,633)(382,635)(383,634)(384,636)
(385,638)(386,637)(387,639)(388,623)(389,622)(390,624)(391,626)(392,625)
(393,627)(394,629)(395,628)(396,630)(397,641)(398,640)(399,642)(400,644)
(401,643)(402,645)(403,647)(404,646)(405,648)(406,605)(407,604)(408,606)
(409,608)(410,607)(411,609)(412,611)(413,610)(414,612)(415,596)(416,595)
(417,597)(418,599)(419,598)(420,600)(421,602)(422,601)(423,603)(424,614)
(425,613)(426,615)(427,617)(428,616)(429,618)(430,620)(431,619)(432,621);;
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)( 55,487)( 56,488)
( 57,489)( 58,493)( 59,494)( 60,495)( 61,490)( 62,491)( 63,492)( 64,505)
( 65,506)( 66,507)( 67,511)( 68,512)( 69,513)( 70,508)( 71,509)( 72,510)
( 73,496)( 74,497)( 75,498)( 76,502)( 77,503)( 78,504)( 79,499)( 80,500)
( 81,501)( 82,514)( 83,515)( 84,516)( 85,520)( 86,521)( 87,522)( 88,517)
( 89,518)( 90,519)( 91,532)( 92,533)( 93,534)( 94,538)( 95,539)( 96,540)
( 97,535)( 98,536)( 99,537)(100,523)(101,524)(102,525)(103,529)(104,530)
(105,531)(106,526)(107,527)(108,528)(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)(163,595)(164,596)(165,597)(166,601)(167,602)(168,603)
(169,598)(170,599)(171,600)(172,613)(173,614)(174,615)(175,619)(176,620)
(177,621)(178,616)(179,617)(180,618)(181,604)(182,605)(183,606)(184,610)
(185,611)(186,612)(187,607)(188,608)(189,609)(190,622)(191,623)(192,624)
(193,628)(194,629)(195,630)(196,625)(197,626)(198,627)(199,640)(200,641)
(201,642)(202,646)(203,647)(204,648)(205,643)(206,644)(207,645)(208,631)
(209,632)(210,633)(211,637)(212,638)(213,639)(214,634)(215,635)(216,636)
(217,676)(218,677)(219,678)(220,682)(221,683)(222,684)(223,679)(224,680)
(225,681)(226,694)(227,695)(228,696)(229,700)(230,701)(231,702)(232,697)
(233,698)(234,699)(235,685)(236,686)(237,687)(238,691)(239,692)(240,693)
(241,688)(242,689)(243,690)(244,649)(245,650)(246,651)(247,655)(248,656)
(249,657)(250,652)(251,653)(252,654)(253,667)(254,668)(255,669)(256,673)
(257,674)(258,675)(259,670)(260,671)(261,672)(262,658)(263,659)(264,660)
(265,664)(266,665)(267,666)(268,661)(269,662)(270,663)(271,730)(272,731)
(273,732)(274,736)(275,737)(276,738)(277,733)(278,734)(279,735)(280,748)
(281,749)(282,750)(283,754)(284,755)(285,756)(286,751)(287,752)(288,753)
(289,739)(290,740)(291,741)(292,745)(293,746)(294,747)(295,742)(296,743)
(297,744)(298,703)(299,704)(300,705)(301,709)(302,710)(303,711)(304,706)
(305,707)(306,708)(307,721)(308,722)(309,723)(310,727)(311,728)(312,729)
(313,724)(314,725)(315,726)(316,712)(317,713)(318,714)(319,718)(320,719)
(321,720)(322,715)(323,716)(324,717)(325,784)(326,785)(327,786)(328,790)
(329,791)(330,792)(331,787)(332,788)(333,789)(334,802)(335,803)(336,804)
(337,808)(338,809)(339,810)(340,805)(341,806)(342,807)(343,793)(344,794)
(345,795)(346,799)(347,800)(348,801)(349,796)(350,797)(351,798)(352,757)
(353,758)(354,759)(355,763)(356,764)(357,765)(358,760)(359,761)(360,762)
(361,775)(362,776)(363,777)(364,781)(365,782)(366,783)(367,778)(368,779)
(369,780)(370,766)(371,767)(372,768)(373,772)(374,773)(375,774)(376,769)
(377,770)(378,771)(379,838)(380,839)(381,840)(382,844)(383,845)(384,846)
(385,841)(386,842)(387,843)(388,856)(389,857)(390,858)(391,862)(392,863)
(393,864)(394,859)(395,860)(396,861)(397,847)(398,848)(399,849)(400,853)
(401,854)(402,855)(403,850)(404,851)(405,852)(406,811)(407,812)(408,813)
(409,817)(410,818)(411,819)(412,814)(413,815)(414,816)(415,829)(416,830)
(417,831)(418,835)(419,836)(420,837)(421,832)(422,833)(423,834)(424,820)
(425,821)(426,822)(427,826)(428,827)(429,828)(430,823)(431,824)(432,825);;
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, 58)( 56, 59)( 57, 60)( 64, 67)( 65, 68)( 66, 69)
( 73, 76)( 74, 77)( 75, 78)( 82, 85)( 83, 86)( 84, 87)( 91, 94)( 92, 95)
( 93, 96)(100,103)(101,104)(102,105)(109,166)(110,167)(111,168)(112,163)
(113,164)(114,165)(115,169)(116,170)(117,171)(118,175)(119,176)(120,177)
(121,172)(122,173)(123,174)(124,178)(125,179)(126,180)(127,184)(128,185)
(129,186)(130,181)(131,182)(132,183)(133,187)(134,188)(135,189)(136,193)
(137,194)(138,195)(139,190)(140,191)(141,192)(142,196)(143,197)(144,198)
(145,202)(146,203)(147,204)(148,199)(149,200)(150,201)(151,205)(152,206)
(153,207)(154,211)(155,212)(156,213)(157,208)(158,209)(159,210)(160,214)
(161,215)(162,216)(217,247)(218,248)(219,249)(220,244)(221,245)(222,246)
(223,250)(224,251)(225,252)(226,256)(227,257)(228,258)(229,253)(230,254)
(231,255)(232,259)(233,260)(234,261)(235,265)(236,266)(237,267)(238,262)
(239,263)(240,264)(241,268)(242,269)(243,270)(271,301)(272,302)(273,303)
(274,298)(275,299)(276,300)(277,304)(278,305)(279,306)(280,310)(281,311)
(282,312)(283,307)(284,308)(285,309)(286,313)(287,314)(288,315)(289,319)
(290,320)(291,321)(292,316)(293,317)(294,318)(295,322)(296,323)(297,324)
(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)(433,463)(434,464)
(435,465)(436,460)(437,461)(438,462)(439,466)(440,467)(441,468)(442,472)
(443,473)(444,474)(445,469)(446,470)(447,471)(448,475)(449,476)(450,477)
(451,481)(452,482)(453,483)(454,478)(455,479)(456,480)(457,484)(458,485)
(459,486)(487,517)(488,518)(489,519)(490,514)(491,515)(492,516)(493,520)
(494,521)(495,522)(496,526)(497,527)(498,528)(499,523)(500,524)(501,525)
(502,529)(503,530)(504,531)(505,535)(506,536)(507,537)(508,532)(509,533)
(510,534)(511,538)(512,539)(513,540)(541,625)(542,626)(543,627)(544,622)
(545,623)(546,624)(547,628)(548,629)(549,630)(550,634)(551,635)(552,636)
(553,631)(554,632)(555,633)(556,637)(557,638)(558,639)(559,643)(560,644)
(561,645)(562,640)(563,641)(564,642)(565,646)(566,647)(567,648)(568,598)
(569,599)(570,600)(571,595)(572,596)(573,597)(574,601)(575,602)(576,603)
(577,607)(578,608)(579,609)(580,604)(581,605)(582,606)(583,610)(584,611)
(585,612)(586,616)(587,617)(588,618)(589,613)(590,614)(591,615)(592,619)
(593,620)(594,621)(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)(703,706)(704,707)(705,708)(712,715)
(713,716)(714,717)(721,724)(722,725)(723,726)(730,733)(731,734)(732,735)
(739,742)(740,743)(741,744)(748,751)(749,752)(750,753)(757,814)(758,815)
(759,816)(760,811)(761,812)(762,813)(763,817)(764,818)(765,819)(766,823)
(767,824)(768,825)(769,820)(770,821)(771,822)(772,826)(773,827)(774,828)
(775,832)(776,833)(777,834)(778,829)(779,830)(780,831)(781,835)(782,836)
(783,837)(784,841)(785,842)(786,843)(787,838)(788,839)(789,840)(790,844)
(791,845)(792,846)(793,850)(794,851)(795,852)(796,847)(797,848)(798,849)
(799,853)(800,854)(801,855)(802,859)(803,860)(804,861)(805,856)(806,857)
(807,858)(808,862)(809,863)(810,864);;
s4 := ( 1,109)( 2,110)( 3,111)( 4,112)( 5,113)( 6,114)( 7,115)( 8,116)
( 9,117)( 10,118)( 11,119)( 12,120)( 13,121)( 14,122)( 15,123)( 16,124)
( 17,125)( 18,126)( 19,127)( 20,128)( 21,129)( 22,130)( 23,131)( 24,132)
( 25,133)( 26,134)( 27,135)( 28,136)( 29,137)( 30,138)( 31,139)( 32,140)
( 33,141)( 34,142)( 35,143)( 36,144)( 37,145)( 38,146)( 39,147)( 40,148)
( 41,149)( 42,150)( 43,151)( 44,152)( 45,153)( 46,154)( 47,155)( 48,156)
( 49,157)( 50,158)( 51,159)( 52,160)( 53,161)( 54,162)( 55,163)( 56,164)
( 57,165)( 58,166)( 59,167)( 60,168)( 61,169)( 62,170)( 63,171)( 64,172)
( 65,173)( 66,174)( 67,175)( 68,176)( 69,177)( 70,178)( 71,179)( 72,180)
( 73,181)( 74,182)( 75,183)( 76,184)( 77,185)( 78,186)( 79,187)( 80,188)
( 81,189)( 82,190)( 83,191)( 84,192)( 85,193)( 86,194)( 87,195)( 88,196)
( 89,197)( 90,198)( 91,199)( 92,200)( 93,201)( 94,202)( 95,203)( 96,204)
( 97,205)( 98,206)( 99,207)(100,208)(101,209)(102,210)(103,211)(104,212)
(105,213)(106,214)(107,215)(108,216)(217,325)(218,326)(219,327)(220,328)
(221,329)(222,330)(223,331)(224,332)(225,333)(226,334)(227,335)(228,336)
(229,337)(230,338)(231,339)(232,340)(233,341)(234,342)(235,343)(236,344)
(237,345)(238,346)(239,347)(240,348)(241,349)(242,350)(243,351)(244,352)
(245,353)(246,354)(247,355)(248,356)(249,357)(250,358)(251,359)(252,360)
(253,361)(254,362)(255,363)(256,364)(257,365)(258,366)(259,367)(260,368)
(261,369)(262,370)(263,371)(264,372)(265,373)(266,374)(267,375)(268,376)
(269,377)(270,378)(271,379)(272,380)(273,381)(274,382)(275,383)(276,384)
(277,385)(278,386)(279,387)(280,388)(281,389)(282,390)(283,391)(284,392)
(285,393)(286,394)(287,395)(288,396)(289,397)(290,398)(291,399)(292,400)
(293,401)(294,402)(295,403)(296,404)(297,405)(298,406)(299,407)(300,408)
(301,409)(302,410)(303,411)(304,412)(305,413)(306,414)(307,415)(308,416)
(309,417)(310,418)(311,419)(312,420)(313,421)(314,422)(315,423)(316,424)
(317,425)(318,426)(319,427)(320,428)(321,429)(322,430)(323,431)(324,432)
(433,541)(434,542)(435,543)(436,544)(437,545)(438,546)(439,547)(440,548)
(441,549)(442,550)(443,551)(444,552)(445,553)(446,554)(447,555)(448,556)
(449,557)(450,558)(451,559)(452,560)(453,561)(454,562)(455,563)(456,564)
(457,565)(458,566)(459,567)(460,568)(461,569)(462,570)(463,571)(464,572)
(465,573)(466,574)(467,575)(468,576)(469,577)(470,578)(471,579)(472,580)
(473,581)(474,582)(475,583)(476,584)(477,585)(478,586)(479,587)(480,588)
(481,589)(482,590)(483,591)(484,592)(485,593)(486,594)(487,595)(488,596)
(489,597)(490,598)(491,599)(492,600)(493,601)(494,602)(495,603)(496,604)
(497,605)(498,606)(499,607)(500,608)(501,609)(502,610)(503,611)(504,612)
(505,613)(506,614)(507,615)(508,616)(509,617)(510,618)(511,619)(512,620)
(513,621)(514,622)(515,623)(516,624)(517,625)(518,626)(519,627)(520,628)
(521,629)(522,630)(523,631)(524,632)(525,633)(526,634)(527,635)(528,636)
(529,637)(530,638)(531,639)(532,640)(533,641)(534,642)(535,643)(536,644)
(537,645)(538,646)(539,647)(540,648)(649,757)(650,758)(651,759)(652,760)
(653,761)(654,762)(655,763)(656,764)(657,765)(658,766)(659,767)(660,768)
(661,769)(662,770)(663,771)(664,772)(665,773)(666,774)(667,775)(668,776)
(669,777)(670,778)(671,779)(672,780)(673,781)(674,782)(675,783)(676,784)
(677,785)(678,786)(679,787)(680,788)(681,789)(682,790)(683,791)(684,792)
(685,793)(686,794)(687,795)(688,796)(689,797)(690,798)(691,799)(692,800)
(693,801)(694,802)(695,803)(696,804)(697,805)(698,806)(699,807)(700,808)
(701,809)(702,810)(703,811)(704,812)(705,813)(706,814)(707,815)(708,816)
(709,817)(710,818)(711,819)(712,820)(713,821)(714,822)(715,823)(716,824)
(717,825)(718,826)(719,827)(720,828)(721,829)(722,830)(723,831)(724,832)
(725,833)(726,834)(727,835)(728,836)(729,837)(730,838)(731,839)(732,840)
(733,841)(734,842)(735,843)(736,844)(737,845)(738,846)(739,847)(740,848)
(741,849)(742,850)(743,851)(744,852)(745,853)(746,854)(747,855)(748,856)
(749,857)(750,858)(751,859)(752,860)(753,861)(754,862)(755,863)(756,864);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s0*s1*s2*s1*s2*s0*s1*s2*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 ];;
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)(217,460)(218,462)(219,461)(220,463)(221,465)(222,464)(223,466)
(224,468)(225,467)(226,478)(227,480)(228,479)(229,481)(230,483)(231,482)
(232,484)(233,486)(234,485)(235,469)(236,471)(237,470)(238,472)(239,474)
(240,473)(241,475)(242,477)(243,476)(244,433)(245,435)(246,434)(247,436)
(248,438)(249,437)(250,439)(251,441)(252,440)(253,451)(254,453)(255,452)
(256,454)(257,456)(258,455)(259,457)(260,459)(261,458)(262,442)(263,444)
(264,443)(265,445)(266,447)(267,446)(268,448)(269,450)(270,449)(271,514)
(272,516)(273,515)(274,517)(275,519)(276,518)(277,520)(278,522)(279,521)
(280,532)(281,534)(282,533)(283,535)(284,537)(285,536)(286,538)(287,540)
(288,539)(289,523)(290,525)(291,524)(292,526)(293,528)(294,527)(295,529)
(296,531)(297,530)(298,487)(299,489)(300,488)(301,490)(302,492)(303,491)
(304,493)(305,495)(306,494)(307,505)(308,507)(309,506)(310,508)(311,510)
(312,509)(313,511)(314,513)(315,512)(316,496)(317,498)(318,497)(319,499)
(320,501)(321,500)(322,502)(323,504)(324,503)(325,568)(326,570)(327,569)
(328,571)(329,573)(330,572)(331,574)(332,576)(333,575)(334,586)(335,588)
(336,587)(337,589)(338,591)(339,590)(340,592)(341,594)(342,593)(343,577)
(344,579)(345,578)(346,580)(347,582)(348,581)(349,583)(350,585)(351,584)
(352,541)(353,543)(354,542)(355,544)(356,546)(357,545)(358,547)(359,549)
(360,548)(361,559)(362,561)(363,560)(364,562)(365,564)(366,563)(367,565)
(368,567)(369,566)(370,550)(371,552)(372,551)(373,553)(374,555)(375,554)
(376,556)(377,558)(378,557)(379,622)(380,624)(381,623)(382,625)(383,627)
(384,626)(385,628)(386,630)(387,629)(388,640)(389,642)(390,641)(391,643)
(392,645)(393,644)(394,646)(395,648)(396,647)(397,631)(398,633)(399,632)
(400,634)(401,636)(402,635)(403,637)(404,639)(405,638)(406,595)(407,597)
(408,596)(409,598)(410,600)(411,599)(412,601)(413,603)(414,602)(415,613)
(416,615)(417,614)(418,616)(419,618)(420,617)(421,619)(422,621)(423,620)
(424,604)(425,606)(426,605)(427,607)(428,609)(429,608)(430,610)(431,612)
(432,611);
s1 := Sym(864)!( 1,659)( 2,658)( 3,660)( 4,662)( 5,661)( 6,663)( 7,665)
( 8,664)( 9,666)( 10,650)( 11,649)( 12,651)( 13,653)( 14,652)( 15,654)
( 16,656)( 17,655)( 18,657)( 19,668)( 20,667)( 21,669)( 22,671)( 23,670)
( 24,672)( 25,674)( 26,673)( 27,675)( 28,686)( 29,685)( 30,687)( 31,689)
( 32,688)( 33,690)( 34,692)( 35,691)( 36,693)( 37,677)( 38,676)( 39,678)
( 40,680)( 41,679)( 42,681)( 43,683)( 44,682)( 45,684)( 46,695)( 47,694)
( 48,696)( 49,698)( 50,697)( 51,699)( 52,701)( 53,700)( 54,702)( 55,713)
( 56,712)( 57,714)( 58,716)( 59,715)( 60,717)( 61,719)( 62,718)( 63,720)
( 64,704)( 65,703)( 66,705)( 67,707)( 68,706)( 69,708)( 70,710)( 71,709)
( 72,711)( 73,722)( 74,721)( 75,723)( 76,725)( 77,724)( 78,726)( 79,728)
( 80,727)( 81,729)( 82,740)( 83,739)( 84,741)( 85,743)( 86,742)( 87,744)
( 88,746)( 89,745)( 90,747)( 91,731)( 92,730)( 93,732)( 94,734)( 95,733)
( 96,735)( 97,737)( 98,736)( 99,738)(100,749)(101,748)(102,750)(103,752)
(104,751)(105,753)(106,755)(107,754)(108,756)(109,767)(110,766)(111,768)
(112,770)(113,769)(114,771)(115,773)(116,772)(117,774)(118,758)(119,757)
(120,759)(121,761)(122,760)(123,762)(124,764)(125,763)(126,765)(127,776)
(128,775)(129,777)(130,779)(131,778)(132,780)(133,782)(134,781)(135,783)
(136,794)(137,793)(138,795)(139,797)(140,796)(141,798)(142,800)(143,799)
(144,801)(145,785)(146,784)(147,786)(148,788)(149,787)(150,789)(151,791)
(152,790)(153,792)(154,803)(155,802)(156,804)(157,806)(158,805)(159,807)
(160,809)(161,808)(162,810)(163,821)(164,820)(165,822)(166,824)(167,823)
(168,825)(169,827)(170,826)(171,828)(172,812)(173,811)(174,813)(175,815)
(176,814)(177,816)(178,818)(179,817)(180,819)(181,830)(182,829)(183,831)
(184,833)(185,832)(186,834)(187,836)(188,835)(189,837)(190,848)(191,847)
(192,849)(193,851)(194,850)(195,852)(196,854)(197,853)(198,855)(199,839)
(200,838)(201,840)(202,842)(203,841)(204,843)(205,845)(206,844)(207,846)
(208,857)(209,856)(210,858)(211,860)(212,859)(213,861)(214,863)(215,862)
(216,864)(217,470)(218,469)(219,471)(220,473)(221,472)(222,474)(223,476)
(224,475)(225,477)(226,461)(227,460)(228,462)(229,464)(230,463)(231,465)
(232,467)(233,466)(234,468)(235,479)(236,478)(237,480)(238,482)(239,481)
(240,483)(241,485)(242,484)(243,486)(244,443)(245,442)(246,444)(247,446)
(248,445)(249,447)(250,449)(251,448)(252,450)(253,434)(254,433)(255,435)
(256,437)(257,436)(258,438)(259,440)(260,439)(261,441)(262,452)(263,451)
(264,453)(265,455)(266,454)(267,456)(268,458)(269,457)(270,459)(271,524)
(272,523)(273,525)(274,527)(275,526)(276,528)(277,530)(278,529)(279,531)
(280,515)(281,514)(282,516)(283,518)(284,517)(285,519)(286,521)(287,520)
(288,522)(289,533)(290,532)(291,534)(292,536)(293,535)(294,537)(295,539)
(296,538)(297,540)(298,497)(299,496)(300,498)(301,500)(302,499)(303,501)
(304,503)(305,502)(306,504)(307,488)(308,487)(309,489)(310,491)(311,490)
(312,492)(313,494)(314,493)(315,495)(316,506)(317,505)(318,507)(319,509)
(320,508)(321,510)(322,512)(323,511)(324,513)(325,578)(326,577)(327,579)
(328,581)(329,580)(330,582)(331,584)(332,583)(333,585)(334,569)(335,568)
(336,570)(337,572)(338,571)(339,573)(340,575)(341,574)(342,576)(343,587)
(344,586)(345,588)(346,590)(347,589)(348,591)(349,593)(350,592)(351,594)
(352,551)(353,550)(354,552)(355,554)(356,553)(357,555)(358,557)(359,556)
(360,558)(361,542)(362,541)(363,543)(364,545)(365,544)(366,546)(367,548)
(368,547)(369,549)(370,560)(371,559)(372,561)(373,563)(374,562)(375,564)
(376,566)(377,565)(378,567)(379,632)(380,631)(381,633)(382,635)(383,634)
(384,636)(385,638)(386,637)(387,639)(388,623)(389,622)(390,624)(391,626)
(392,625)(393,627)(394,629)(395,628)(396,630)(397,641)(398,640)(399,642)
(400,644)(401,643)(402,645)(403,647)(404,646)(405,648)(406,605)(407,604)
(408,606)(409,608)(410,607)(411,609)(412,611)(413,610)(414,612)(415,596)
(416,595)(417,597)(418,599)(419,598)(420,600)(421,602)(422,601)(423,603)
(424,614)(425,613)(426,615)(427,617)(428,616)(429,618)(430,620)(431,619)
(432,621);
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)( 55,487)
( 56,488)( 57,489)( 58,493)( 59,494)( 60,495)( 61,490)( 62,491)( 63,492)
( 64,505)( 65,506)( 66,507)( 67,511)( 68,512)( 69,513)( 70,508)( 71,509)
( 72,510)( 73,496)( 74,497)( 75,498)( 76,502)( 77,503)( 78,504)( 79,499)
( 80,500)( 81,501)( 82,514)( 83,515)( 84,516)( 85,520)( 86,521)( 87,522)
( 88,517)( 89,518)( 90,519)( 91,532)( 92,533)( 93,534)( 94,538)( 95,539)
( 96,540)( 97,535)( 98,536)( 99,537)(100,523)(101,524)(102,525)(103,529)
(104,530)(105,531)(106,526)(107,527)(108,528)(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)(163,595)(164,596)(165,597)(166,601)(167,602)
(168,603)(169,598)(170,599)(171,600)(172,613)(173,614)(174,615)(175,619)
(176,620)(177,621)(178,616)(179,617)(180,618)(181,604)(182,605)(183,606)
(184,610)(185,611)(186,612)(187,607)(188,608)(189,609)(190,622)(191,623)
(192,624)(193,628)(194,629)(195,630)(196,625)(197,626)(198,627)(199,640)
(200,641)(201,642)(202,646)(203,647)(204,648)(205,643)(206,644)(207,645)
(208,631)(209,632)(210,633)(211,637)(212,638)(213,639)(214,634)(215,635)
(216,636)(217,676)(218,677)(219,678)(220,682)(221,683)(222,684)(223,679)
(224,680)(225,681)(226,694)(227,695)(228,696)(229,700)(230,701)(231,702)
(232,697)(233,698)(234,699)(235,685)(236,686)(237,687)(238,691)(239,692)
(240,693)(241,688)(242,689)(243,690)(244,649)(245,650)(246,651)(247,655)
(248,656)(249,657)(250,652)(251,653)(252,654)(253,667)(254,668)(255,669)
(256,673)(257,674)(258,675)(259,670)(260,671)(261,672)(262,658)(263,659)
(264,660)(265,664)(266,665)(267,666)(268,661)(269,662)(270,663)(271,730)
(272,731)(273,732)(274,736)(275,737)(276,738)(277,733)(278,734)(279,735)
(280,748)(281,749)(282,750)(283,754)(284,755)(285,756)(286,751)(287,752)
(288,753)(289,739)(290,740)(291,741)(292,745)(293,746)(294,747)(295,742)
(296,743)(297,744)(298,703)(299,704)(300,705)(301,709)(302,710)(303,711)
(304,706)(305,707)(306,708)(307,721)(308,722)(309,723)(310,727)(311,728)
(312,729)(313,724)(314,725)(315,726)(316,712)(317,713)(318,714)(319,718)
(320,719)(321,720)(322,715)(323,716)(324,717)(325,784)(326,785)(327,786)
(328,790)(329,791)(330,792)(331,787)(332,788)(333,789)(334,802)(335,803)
(336,804)(337,808)(338,809)(339,810)(340,805)(341,806)(342,807)(343,793)
(344,794)(345,795)(346,799)(347,800)(348,801)(349,796)(350,797)(351,798)
(352,757)(353,758)(354,759)(355,763)(356,764)(357,765)(358,760)(359,761)
(360,762)(361,775)(362,776)(363,777)(364,781)(365,782)(366,783)(367,778)
(368,779)(369,780)(370,766)(371,767)(372,768)(373,772)(374,773)(375,774)
(376,769)(377,770)(378,771)(379,838)(380,839)(381,840)(382,844)(383,845)
(384,846)(385,841)(386,842)(387,843)(388,856)(389,857)(390,858)(391,862)
(392,863)(393,864)(394,859)(395,860)(396,861)(397,847)(398,848)(399,849)
(400,853)(401,854)(402,855)(403,850)(404,851)(405,852)(406,811)(407,812)
(408,813)(409,817)(410,818)(411,819)(412,814)(413,815)(414,816)(415,829)
(416,830)(417,831)(418,835)(419,836)(420,837)(421,832)(422,833)(423,834)
(424,820)(425,821)(426,822)(427,826)(428,827)(429,828)(430,823)(431,824)
(432,825);
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, 58)( 56, 59)( 57, 60)( 64, 67)( 65, 68)
( 66, 69)( 73, 76)( 74, 77)( 75, 78)( 82, 85)( 83, 86)( 84, 87)( 91, 94)
( 92, 95)( 93, 96)(100,103)(101,104)(102,105)(109,166)(110,167)(111,168)
(112,163)(113,164)(114,165)(115,169)(116,170)(117,171)(118,175)(119,176)
(120,177)(121,172)(122,173)(123,174)(124,178)(125,179)(126,180)(127,184)
(128,185)(129,186)(130,181)(131,182)(132,183)(133,187)(134,188)(135,189)
(136,193)(137,194)(138,195)(139,190)(140,191)(141,192)(142,196)(143,197)
(144,198)(145,202)(146,203)(147,204)(148,199)(149,200)(150,201)(151,205)
(152,206)(153,207)(154,211)(155,212)(156,213)(157,208)(158,209)(159,210)
(160,214)(161,215)(162,216)(217,247)(218,248)(219,249)(220,244)(221,245)
(222,246)(223,250)(224,251)(225,252)(226,256)(227,257)(228,258)(229,253)
(230,254)(231,255)(232,259)(233,260)(234,261)(235,265)(236,266)(237,267)
(238,262)(239,263)(240,264)(241,268)(242,269)(243,270)(271,301)(272,302)
(273,303)(274,298)(275,299)(276,300)(277,304)(278,305)(279,306)(280,310)
(281,311)(282,312)(283,307)(284,308)(285,309)(286,313)(287,314)(288,315)
(289,319)(290,320)(291,321)(292,316)(293,317)(294,318)(295,322)(296,323)
(297,324)(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)(433,463)
(434,464)(435,465)(436,460)(437,461)(438,462)(439,466)(440,467)(441,468)
(442,472)(443,473)(444,474)(445,469)(446,470)(447,471)(448,475)(449,476)
(450,477)(451,481)(452,482)(453,483)(454,478)(455,479)(456,480)(457,484)
(458,485)(459,486)(487,517)(488,518)(489,519)(490,514)(491,515)(492,516)
(493,520)(494,521)(495,522)(496,526)(497,527)(498,528)(499,523)(500,524)
(501,525)(502,529)(503,530)(504,531)(505,535)(506,536)(507,537)(508,532)
(509,533)(510,534)(511,538)(512,539)(513,540)(541,625)(542,626)(543,627)
(544,622)(545,623)(546,624)(547,628)(548,629)(549,630)(550,634)(551,635)
(552,636)(553,631)(554,632)(555,633)(556,637)(557,638)(558,639)(559,643)
(560,644)(561,645)(562,640)(563,641)(564,642)(565,646)(566,647)(567,648)
(568,598)(569,599)(570,600)(571,595)(572,596)(573,597)(574,601)(575,602)
(576,603)(577,607)(578,608)(579,609)(580,604)(581,605)(582,606)(583,610)
(584,611)(585,612)(586,616)(587,617)(588,618)(589,613)(590,614)(591,615)
(592,619)(593,620)(594,621)(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)(703,706)(704,707)(705,708)
(712,715)(713,716)(714,717)(721,724)(722,725)(723,726)(730,733)(731,734)
(732,735)(739,742)(740,743)(741,744)(748,751)(749,752)(750,753)(757,814)
(758,815)(759,816)(760,811)(761,812)(762,813)(763,817)(764,818)(765,819)
(766,823)(767,824)(768,825)(769,820)(770,821)(771,822)(772,826)(773,827)
(774,828)(775,832)(776,833)(777,834)(778,829)(779,830)(780,831)(781,835)
(782,836)(783,837)(784,841)(785,842)(786,843)(787,838)(788,839)(789,840)
(790,844)(791,845)(792,846)(793,850)(794,851)(795,852)(796,847)(797,848)
(798,849)(799,853)(800,854)(801,855)(802,859)(803,860)(804,861)(805,856)
(806,857)(807,858)(808,862)(809,863)(810,864);
s4 := Sym(864)!( 1,109)( 2,110)( 3,111)( 4,112)( 5,113)( 6,114)( 7,115)
( 8,116)( 9,117)( 10,118)( 11,119)( 12,120)( 13,121)( 14,122)( 15,123)
( 16,124)( 17,125)( 18,126)( 19,127)( 20,128)( 21,129)( 22,130)( 23,131)
( 24,132)( 25,133)( 26,134)( 27,135)( 28,136)( 29,137)( 30,138)( 31,139)
( 32,140)( 33,141)( 34,142)( 35,143)( 36,144)( 37,145)( 38,146)( 39,147)
( 40,148)( 41,149)( 42,150)( 43,151)( 44,152)( 45,153)( 46,154)( 47,155)
( 48,156)( 49,157)( 50,158)( 51,159)( 52,160)( 53,161)( 54,162)( 55,163)
( 56,164)( 57,165)( 58,166)( 59,167)( 60,168)( 61,169)( 62,170)( 63,171)
( 64,172)( 65,173)( 66,174)( 67,175)( 68,176)( 69,177)( 70,178)( 71,179)
( 72,180)( 73,181)( 74,182)( 75,183)( 76,184)( 77,185)( 78,186)( 79,187)
( 80,188)( 81,189)( 82,190)( 83,191)( 84,192)( 85,193)( 86,194)( 87,195)
( 88,196)( 89,197)( 90,198)( 91,199)( 92,200)( 93,201)( 94,202)( 95,203)
( 96,204)( 97,205)( 98,206)( 99,207)(100,208)(101,209)(102,210)(103,211)
(104,212)(105,213)(106,214)(107,215)(108,216)(217,325)(218,326)(219,327)
(220,328)(221,329)(222,330)(223,331)(224,332)(225,333)(226,334)(227,335)
(228,336)(229,337)(230,338)(231,339)(232,340)(233,341)(234,342)(235,343)
(236,344)(237,345)(238,346)(239,347)(240,348)(241,349)(242,350)(243,351)
(244,352)(245,353)(246,354)(247,355)(248,356)(249,357)(250,358)(251,359)
(252,360)(253,361)(254,362)(255,363)(256,364)(257,365)(258,366)(259,367)
(260,368)(261,369)(262,370)(263,371)(264,372)(265,373)(266,374)(267,375)
(268,376)(269,377)(270,378)(271,379)(272,380)(273,381)(274,382)(275,383)
(276,384)(277,385)(278,386)(279,387)(280,388)(281,389)(282,390)(283,391)
(284,392)(285,393)(286,394)(287,395)(288,396)(289,397)(290,398)(291,399)
(292,400)(293,401)(294,402)(295,403)(296,404)(297,405)(298,406)(299,407)
(300,408)(301,409)(302,410)(303,411)(304,412)(305,413)(306,414)(307,415)
(308,416)(309,417)(310,418)(311,419)(312,420)(313,421)(314,422)(315,423)
(316,424)(317,425)(318,426)(319,427)(320,428)(321,429)(322,430)(323,431)
(324,432)(433,541)(434,542)(435,543)(436,544)(437,545)(438,546)(439,547)
(440,548)(441,549)(442,550)(443,551)(444,552)(445,553)(446,554)(447,555)
(448,556)(449,557)(450,558)(451,559)(452,560)(453,561)(454,562)(455,563)
(456,564)(457,565)(458,566)(459,567)(460,568)(461,569)(462,570)(463,571)
(464,572)(465,573)(466,574)(467,575)(468,576)(469,577)(470,578)(471,579)
(472,580)(473,581)(474,582)(475,583)(476,584)(477,585)(478,586)(479,587)
(480,588)(481,589)(482,590)(483,591)(484,592)(485,593)(486,594)(487,595)
(488,596)(489,597)(490,598)(491,599)(492,600)(493,601)(494,602)(495,603)
(496,604)(497,605)(498,606)(499,607)(500,608)(501,609)(502,610)(503,611)
(504,612)(505,613)(506,614)(507,615)(508,616)(509,617)(510,618)(511,619)
(512,620)(513,621)(514,622)(515,623)(516,624)(517,625)(518,626)(519,627)
(520,628)(521,629)(522,630)(523,631)(524,632)(525,633)(526,634)(527,635)
(528,636)(529,637)(530,638)(531,639)(532,640)(533,641)(534,642)(535,643)
(536,644)(537,645)(538,646)(539,647)(540,648)(649,757)(650,758)(651,759)
(652,760)(653,761)(654,762)(655,763)(656,764)(657,765)(658,766)(659,767)
(660,768)(661,769)(662,770)(663,771)(664,772)(665,773)(666,774)(667,775)
(668,776)(669,777)(670,778)(671,779)(672,780)(673,781)(674,782)(675,783)
(676,784)(677,785)(678,786)(679,787)(680,788)(681,789)(682,790)(683,791)
(684,792)(685,793)(686,794)(687,795)(688,796)(689,797)(690,798)(691,799)
(692,800)(693,801)(694,802)(695,803)(696,804)(697,805)(698,806)(699,807)
(700,808)(701,809)(702,810)(703,811)(704,812)(705,813)(706,814)(707,815)
(708,816)(709,817)(710,818)(711,819)(712,820)(713,821)(714,822)(715,823)
(716,824)(717,825)(718,826)(719,827)(720,828)(721,829)(722,830)(723,831)
(724,832)(725,833)(726,834)(727,835)(728,836)(729,837)(730,838)(731,839)
(732,840)(733,841)(734,842)(735,843)(736,844)(737,845)(738,846)(739,847)
(740,848)(741,849)(742,850)(743,851)(744,852)(745,853)(746,854)(747,855)
(748,856)(749,857)(750,858)(751,859)(752,860)(753,861)(754,862)(755,863)
(756,864);
poly := sub<Sym(864)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s0*s1*s2*s1*s2*s0*s1*s2*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 >;
References : None.
to this polytope