Polytope of Type {4,3,6,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,3,6,12}*1728b
if this polytope has a name.
Group : SmallGroup(1728,46356)
Rank : 5
Schlafli Type : {4,3,6,12}
Number of vertices, edges, etc : 4, 6, 9, 36, 12
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Universal
Non-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 : {4,3,6,6}*864b
3-fold quotients : {4,3,2,12}*576, {4,3,6,4}*576
6-fold quotients : {4,3,2,6}*288, {4,3,6,2}*288
9-fold quotients : {4,3,2,4}*192
12-fold quotients : {4,3,2,3}*144
18-fold quotients : {4,3,2,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)
( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)
( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)
(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)
(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)
(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)
(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)
(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)
(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)
(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)
(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)
(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)
(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)
(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)
(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)
(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)
(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)
(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)(350,352)
(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)(366,368)
(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)(382,384)
(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)(398,400)
(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)(414,416)
(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)(430,432)
(433,435)(434,436)(437,439)(438,440)(441,443)(442,444)(445,447)(446,448)
(449,451)(450,452)(453,455)(454,456)(457,459)(458,460)(461,463)(462,464)
(465,467)(466,468)(469,471)(470,472)(473,475)(474,476)(477,479)(478,480)
(481,483)(482,484)(485,487)(486,488)(489,491)(490,492)(493,495)(494,496)
(497,499)(498,500)(501,503)(502,504)(505,507)(506,508)(509,511)(510,512)
(513,515)(514,516)(517,519)(518,520)(521,523)(522,524)(525,527)(526,528)
(529,531)(530,532)(533,535)(534,536)(537,539)(538,540)(541,543)(542,544)
(545,547)(546,548)(549,551)(550,552)(553,555)(554,556)(557,559)(558,560)
(561,563)(562,564)(565,567)(566,568)(569,571)(570,572)(573,575)(574,576)
(577,579)(578,580)(581,583)(582,584)(585,587)(586,588)(589,591)(590,592)
(593,595)(594,596)(597,599)(598,600)(601,603)(602,604)(605,607)(606,608)
(609,611)(610,612)(613,615)(614,616)(617,619)(618,620)(621,623)(622,624)
(625,627)(626,628)(629,631)(630,632)(633,635)(634,636)(637,639)(638,640)
(641,643)(642,644)(645,647)(646,648)(649,651)(650,652)(653,655)(654,656)
(657,659)(658,660)(661,663)(662,664)(665,667)(666,668)(669,671)(670,672)
(673,675)(674,676)(677,679)(678,680)(681,683)(682,684)(685,687)(686,688)
(689,691)(690,692)(693,695)(694,696)(697,699)(698,700)(701,703)(702,704)
(705,707)(706,708)(709,711)(710,712)(713,715)(714,716)(717,719)(718,720)
(721,723)(722,724)(725,727)(726,728)(729,731)(730,732)(733,735)(734,736)
(737,739)(738,740)(741,743)(742,744)(745,747)(746,748)(749,751)(750,752)
(753,755)(754,756)(757,759)(758,760)(761,763)(762,764)(765,767)(766,768)
(769,771)(770,772)(773,775)(774,776)(777,779)(778,780)(781,783)(782,784)
(785,787)(786,788)(789,791)(790,792)(793,795)(794,796)(797,799)(798,800)
(801,803)(802,804)(805,807)(806,808)(809,811)(810,812)(813,815)(814,816)
(817,819)(818,820)(821,823)(822,824)(825,827)(826,828)(829,831)(830,832)
(833,835)(834,836)(837,839)(838,840)(841,843)(842,844)(845,847)(846,848)
(849,851)(850,852)(853,855)(854,856)(857,859)(858,860)(861,863)(862,864);;
s1 := ( 1,649)( 2,650)( 3,652)( 4,651)( 5,657)( 6,658)( 7,660)( 8,659)
( 9,653)( 10,654)( 11,656)( 12,655)( 13,661)( 14,662)( 15,664)( 16,663)
( 17,669)( 18,670)( 19,672)( 20,671)( 21,665)( 22,666)( 23,668)( 24,667)
( 25,673)( 26,674)( 27,676)( 28,675)( 29,681)( 30,682)( 31,684)( 32,683)
( 33,677)( 34,678)( 35,680)( 36,679)( 37,721)( 38,722)( 39,724)( 40,723)
( 41,729)( 42,730)( 43,732)( 44,731)( 45,725)( 46,726)( 47,728)( 48,727)
( 49,733)( 50,734)( 51,736)( 52,735)( 53,741)( 54,742)( 55,744)( 56,743)
( 57,737)( 58,738)( 59,740)( 60,739)( 61,745)( 62,746)( 63,748)( 64,747)
( 65,753)( 66,754)( 67,756)( 68,755)( 69,749)( 70,750)( 71,752)( 72,751)
( 73,685)( 74,686)( 75,688)( 76,687)( 77,693)( 78,694)( 79,696)( 80,695)
( 81,689)( 82,690)( 83,692)( 84,691)( 85,697)( 86,698)( 87,700)( 88,699)
( 89,705)( 90,706)( 91,708)( 92,707)( 93,701)( 94,702)( 95,704)( 96,703)
( 97,709)( 98,710)( 99,712)(100,711)(101,717)(102,718)(103,720)(104,719)
(105,713)(106,714)(107,716)(108,715)(109,757)(110,758)(111,760)(112,759)
(113,765)(114,766)(115,768)(116,767)(117,761)(118,762)(119,764)(120,763)
(121,769)(122,770)(123,772)(124,771)(125,777)(126,778)(127,780)(128,779)
(129,773)(130,774)(131,776)(132,775)(133,781)(134,782)(135,784)(136,783)
(137,789)(138,790)(139,792)(140,791)(141,785)(142,786)(143,788)(144,787)
(145,829)(146,830)(147,832)(148,831)(149,837)(150,838)(151,840)(152,839)
(153,833)(154,834)(155,836)(156,835)(157,841)(158,842)(159,844)(160,843)
(161,849)(162,850)(163,852)(164,851)(165,845)(166,846)(167,848)(168,847)
(169,853)(170,854)(171,856)(172,855)(173,861)(174,862)(175,864)(176,863)
(177,857)(178,858)(179,860)(180,859)(181,793)(182,794)(183,796)(184,795)
(185,801)(186,802)(187,804)(188,803)(189,797)(190,798)(191,800)(192,799)
(193,805)(194,806)(195,808)(196,807)(197,813)(198,814)(199,816)(200,815)
(201,809)(202,810)(203,812)(204,811)(205,817)(206,818)(207,820)(208,819)
(209,825)(210,826)(211,828)(212,827)(213,821)(214,822)(215,824)(216,823)
(217,541)(218,542)(219,544)(220,543)(221,549)(222,550)(223,552)(224,551)
(225,545)(226,546)(227,548)(228,547)(229,553)(230,554)(231,556)(232,555)
(233,561)(234,562)(235,564)(236,563)(237,557)(238,558)(239,560)(240,559)
(241,565)(242,566)(243,568)(244,567)(245,573)(246,574)(247,576)(248,575)
(249,569)(250,570)(251,572)(252,571)(253,613)(254,614)(255,616)(256,615)
(257,621)(258,622)(259,624)(260,623)(261,617)(262,618)(263,620)(264,619)
(265,625)(266,626)(267,628)(268,627)(269,633)(270,634)(271,636)(272,635)
(273,629)(274,630)(275,632)(276,631)(277,637)(278,638)(279,640)(280,639)
(281,645)(282,646)(283,648)(284,647)(285,641)(286,642)(287,644)(288,643)
(289,577)(290,578)(291,580)(292,579)(293,585)(294,586)(295,588)(296,587)
(297,581)(298,582)(299,584)(300,583)(301,589)(302,590)(303,592)(304,591)
(305,597)(306,598)(307,600)(308,599)(309,593)(310,594)(311,596)(312,595)
(313,601)(314,602)(315,604)(316,603)(317,609)(318,610)(319,612)(320,611)
(321,605)(322,606)(323,608)(324,607)(325,433)(326,434)(327,436)(328,435)
(329,441)(330,442)(331,444)(332,443)(333,437)(334,438)(335,440)(336,439)
(337,445)(338,446)(339,448)(340,447)(341,453)(342,454)(343,456)(344,455)
(345,449)(346,450)(347,452)(348,451)(349,457)(350,458)(351,460)(352,459)
(353,465)(354,466)(355,468)(356,467)(357,461)(358,462)(359,464)(360,463)
(361,505)(362,506)(363,508)(364,507)(365,513)(366,514)(367,516)(368,515)
(369,509)(370,510)(371,512)(372,511)(373,517)(374,518)(375,520)(376,519)
(377,525)(378,526)(379,528)(380,527)(381,521)(382,522)(383,524)(384,523)
(385,529)(386,530)(387,532)(388,531)(389,537)(390,538)(391,540)(392,539)
(393,533)(394,534)(395,536)(396,535)(397,469)(398,470)(399,472)(400,471)
(401,477)(402,478)(403,480)(404,479)(405,473)(406,474)(407,476)(408,475)
(409,481)(410,482)(411,484)(412,483)(413,489)(414,490)(415,492)(416,491)
(417,485)(418,486)(419,488)(420,487)(421,493)(422,494)(423,496)(424,495)
(425,501)(426,502)(427,504)(428,503)(429,497)(430,498)(431,500)(432,499);;
s2 := ( 1,689)( 2,692)( 3,691)( 4,690)( 5,685)( 6,688)( 7,687)( 8,686)
( 9,693)( 10,696)( 11,695)( 12,694)( 13,701)( 14,704)( 15,703)( 16,702)
( 17,697)( 18,700)( 19,699)( 20,698)( 21,705)( 22,708)( 23,707)( 24,706)
( 25,713)( 26,716)( 27,715)( 28,714)( 29,709)( 30,712)( 31,711)( 32,710)
( 33,717)( 34,720)( 35,719)( 36,718)( 37,653)( 38,656)( 39,655)( 40,654)
( 41,649)( 42,652)( 43,651)( 44,650)( 45,657)( 46,660)( 47,659)( 48,658)
( 49,665)( 50,668)( 51,667)( 52,666)( 53,661)( 54,664)( 55,663)( 56,662)
( 57,669)( 58,672)( 59,671)( 60,670)( 61,677)( 62,680)( 63,679)( 64,678)
( 65,673)( 66,676)( 67,675)( 68,674)( 69,681)( 70,684)( 71,683)( 72,682)
( 73,725)( 74,728)( 75,727)( 76,726)( 77,721)( 78,724)( 79,723)( 80,722)
( 81,729)( 82,732)( 83,731)( 84,730)( 85,737)( 86,740)( 87,739)( 88,738)
( 89,733)( 90,736)( 91,735)( 92,734)( 93,741)( 94,744)( 95,743)( 96,742)
( 97,749)( 98,752)( 99,751)(100,750)(101,745)(102,748)(103,747)(104,746)
(105,753)(106,756)(107,755)(108,754)(109,797)(110,800)(111,799)(112,798)
(113,793)(114,796)(115,795)(116,794)(117,801)(118,804)(119,803)(120,802)
(121,809)(122,812)(123,811)(124,810)(125,805)(126,808)(127,807)(128,806)
(129,813)(130,816)(131,815)(132,814)(133,821)(134,824)(135,823)(136,822)
(137,817)(138,820)(139,819)(140,818)(141,825)(142,828)(143,827)(144,826)
(145,761)(146,764)(147,763)(148,762)(149,757)(150,760)(151,759)(152,758)
(153,765)(154,768)(155,767)(156,766)(157,773)(158,776)(159,775)(160,774)
(161,769)(162,772)(163,771)(164,770)(165,777)(166,780)(167,779)(168,778)
(169,785)(170,788)(171,787)(172,786)(173,781)(174,784)(175,783)(176,782)
(177,789)(178,792)(179,791)(180,790)(181,833)(182,836)(183,835)(184,834)
(185,829)(186,832)(187,831)(188,830)(189,837)(190,840)(191,839)(192,838)
(193,845)(194,848)(195,847)(196,846)(197,841)(198,844)(199,843)(200,842)
(201,849)(202,852)(203,851)(204,850)(205,857)(206,860)(207,859)(208,858)
(209,853)(210,856)(211,855)(212,854)(213,861)(214,864)(215,863)(216,862)
(217,581)(218,584)(219,583)(220,582)(221,577)(222,580)(223,579)(224,578)
(225,585)(226,588)(227,587)(228,586)(229,593)(230,596)(231,595)(232,594)
(233,589)(234,592)(235,591)(236,590)(237,597)(238,600)(239,599)(240,598)
(241,605)(242,608)(243,607)(244,606)(245,601)(246,604)(247,603)(248,602)
(249,609)(250,612)(251,611)(252,610)(253,545)(254,548)(255,547)(256,546)
(257,541)(258,544)(259,543)(260,542)(261,549)(262,552)(263,551)(264,550)
(265,557)(266,560)(267,559)(268,558)(269,553)(270,556)(271,555)(272,554)
(273,561)(274,564)(275,563)(276,562)(277,569)(278,572)(279,571)(280,570)
(281,565)(282,568)(283,567)(284,566)(285,573)(286,576)(287,575)(288,574)
(289,617)(290,620)(291,619)(292,618)(293,613)(294,616)(295,615)(296,614)
(297,621)(298,624)(299,623)(300,622)(301,629)(302,632)(303,631)(304,630)
(305,625)(306,628)(307,627)(308,626)(309,633)(310,636)(311,635)(312,634)
(313,641)(314,644)(315,643)(316,642)(317,637)(318,640)(319,639)(320,638)
(321,645)(322,648)(323,647)(324,646)(325,473)(326,476)(327,475)(328,474)
(329,469)(330,472)(331,471)(332,470)(333,477)(334,480)(335,479)(336,478)
(337,485)(338,488)(339,487)(340,486)(341,481)(342,484)(343,483)(344,482)
(345,489)(346,492)(347,491)(348,490)(349,497)(350,500)(351,499)(352,498)
(353,493)(354,496)(355,495)(356,494)(357,501)(358,504)(359,503)(360,502)
(361,437)(362,440)(363,439)(364,438)(365,433)(366,436)(367,435)(368,434)
(369,441)(370,444)(371,443)(372,442)(373,449)(374,452)(375,451)(376,450)
(377,445)(378,448)(379,447)(380,446)(381,453)(382,456)(383,455)(384,454)
(385,461)(386,464)(387,463)(388,462)(389,457)(390,460)(391,459)(392,458)
(393,465)(394,468)(395,467)(396,466)(397,509)(398,512)(399,511)(400,510)
(401,505)(402,508)(403,507)(404,506)(405,513)(406,516)(407,515)(408,514)
(409,521)(410,524)(411,523)(412,522)(413,517)(414,520)(415,519)(416,518)
(417,525)(418,528)(419,527)(420,526)(421,533)(422,536)(423,535)(424,534)
(425,529)(426,532)(427,531)(428,530)(429,537)(430,540)(431,539)(432,538);;
s3 := ( 1,433)( 2,434)( 3,435)( 4,436)( 5,441)( 6,442)( 7,443)( 8,444)
( 9,437)( 10,438)( 11,439)( 12,440)( 13,457)( 14,458)( 15,459)( 16,460)
( 17,465)( 18,466)( 19,467)( 20,468)( 21,461)( 22,462)( 23,463)( 24,464)
( 25,445)( 26,446)( 27,447)( 28,448)( 29,453)( 30,454)( 31,455)( 32,456)
( 33,449)( 34,450)( 35,451)( 36,452)( 37,469)( 38,470)( 39,471)( 40,472)
( 41,477)( 42,478)( 43,479)( 44,480)( 45,473)( 46,474)( 47,475)( 48,476)
( 49,493)( 50,494)( 51,495)( 52,496)( 53,501)( 54,502)( 55,503)( 56,504)
( 57,497)( 58,498)( 59,499)( 60,500)( 61,481)( 62,482)( 63,483)( 64,484)
( 65,489)( 66,490)( 67,491)( 68,492)( 69,485)( 70,486)( 71,487)( 72,488)
( 73,505)( 74,506)( 75,507)( 76,508)( 77,513)( 78,514)( 79,515)( 80,516)
( 81,509)( 82,510)( 83,511)( 84,512)( 85,529)( 86,530)( 87,531)( 88,532)
( 89,537)( 90,538)( 91,539)( 92,540)( 93,533)( 94,534)( 95,535)( 96,536)
( 97,517)( 98,518)( 99,519)(100,520)(101,525)(102,526)(103,527)(104,528)
(105,521)(106,522)(107,523)(108,524)(109,541)(110,542)(111,543)(112,544)
(113,549)(114,550)(115,551)(116,552)(117,545)(118,546)(119,547)(120,548)
(121,565)(122,566)(123,567)(124,568)(125,573)(126,574)(127,575)(128,576)
(129,569)(130,570)(131,571)(132,572)(133,553)(134,554)(135,555)(136,556)
(137,561)(138,562)(139,563)(140,564)(141,557)(142,558)(143,559)(144,560)
(145,577)(146,578)(147,579)(148,580)(149,585)(150,586)(151,587)(152,588)
(153,581)(154,582)(155,583)(156,584)(157,601)(158,602)(159,603)(160,604)
(161,609)(162,610)(163,611)(164,612)(165,605)(166,606)(167,607)(168,608)
(169,589)(170,590)(171,591)(172,592)(173,597)(174,598)(175,599)(176,600)
(177,593)(178,594)(179,595)(180,596)(181,613)(182,614)(183,615)(184,616)
(185,621)(186,622)(187,623)(188,624)(189,617)(190,618)(191,619)(192,620)
(193,637)(194,638)(195,639)(196,640)(197,645)(198,646)(199,647)(200,648)
(201,641)(202,642)(203,643)(204,644)(205,625)(206,626)(207,627)(208,628)
(209,633)(210,634)(211,635)(212,636)(213,629)(214,630)(215,631)(216,632)
(217,757)(218,758)(219,759)(220,760)(221,765)(222,766)(223,767)(224,768)
(225,761)(226,762)(227,763)(228,764)(229,781)(230,782)(231,783)(232,784)
(233,789)(234,790)(235,791)(236,792)(237,785)(238,786)(239,787)(240,788)
(241,769)(242,770)(243,771)(244,772)(245,777)(246,778)(247,779)(248,780)
(249,773)(250,774)(251,775)(252,776)(253,793)(254,794)(255,795)(256,796)
(257,801)(258,802)(259,803)(260,804)(261,797)(262,798)(263,799)(264,800)
(265,817)(266,818)(267,819)(268,820)(269,825)(270,826)(271,827)(272,828)
(273,821)(274,822)(275,823)(276,824)(277,805)(278,806)(279,807)(280,808)
(281,813)(282,814)(283,815)(284,816)(285,809)(286,810)(287,811)(288,812)
(289,829)(290,830)(291,831)(292,832)(293,837)(294,838)(295,839)(296,840)
(297,833)(298,834)(299,835)(300,836)(301,853)(302,854)(303,855)(304,856)
(305,861)(306,862)(307,863)(308,864)(309,857)(310,858)(311,859)(312,860)
(313,841)(314,842)(315,843)(316,844)(317,849)(318,850)(319,851)(320,852)
(321,845)(322,846)(323,847)(324,848)(325,649)(326,650)(327,651)(328,652)
(329,657)(330,658)(331,659)(332,660)(333,653)(334,654)(335,655)(336,656)
(337,673)(338,674)(339,675)(340,676)(341,681)(342,682)(343,683)(344,684)
(345,677)(346,678)(347,679)(348,680)(349,661)(350,662)(351,663)(352,664)
(353,669)(354,670)(355,671)(356,672)(357,665)(358,666)(359,667)(360,668)
(361,685)(362,686)(363,687)(364,688)(365,693)(366,694)(367,695)(368,696)
(369,689)(370,690)(371,691)(372,692)(373,709)(374,710)(375,711)(376,712)
(377,717)(378,718)(379,719)(380,720)(381,713)(382,714)(383,715)(384,716)
(385,697)(386,698)(387,699)(388,700)(389,705)(390,706)(391,707)(392,708)
(393,701)(394,702)(395,703)(396,704)(397,721)(398,722)(399,723)(400,724)
(401,729)(402,730)(403,731)(404,732)(405,725)(406,726)(407,727)(408,728)
(409,745)(410,746)(411,747)(412,748)(413,753)(414,754)(415,755)(416,756)
(417,749)(418,750)(419,751)(420,752)(421,733)(422,734)(423,735)(424,736)
(425,741)(426,742)(427,743)(428,744)(429,737)(430,738)(431,739)(432,740);;
s4 := ( 1, 13)( 2, 14)( 3, 15)( 4, 16)( 5, 17)( 6, 18)( 7, 19)( 8, 20)
( 9, 21)( 10, 22)( 11, 23)( 12, 24)( 37, 49)( 38, 50)( 39, 51)( 40, 52)
( 41, 53)( 42, 54)( 43, 55)( 44, 56)( 45, 57)( 46, 58)( 47, 59)( 48, 60)
( 73, 85)( 74, 86)( 75, 87)( 76, 88)( 77, 89)( 78, 90)( 79, 91)( 80, 92)
( 81, 93)( 82, 94)( 83, 95)( 84, 96)(109,121)(110,122)(111,123)(112,124)
(113,125)(114,126)(115,127)(116,128)(117,129)(118,130)(119,131)(120,132)
(145,157)(146,158)(147,159)(148,160)(149,161)(150,162)(151,163)(152,164)
(153,165)(154,166)(155,167)(156,168)(181,193)(182,194)(183,195)(184,196)
(185,197)(186,198)(187,199)(188,200)(189,201)(190,202)(191,203)(192,204)
(217,337)(218,338)(219,339)(220,340)(221,341)(222,342)(223,343)(224,344)
(225,345)(226,346)(227,347)(228,348)(229,325)(230,326)(231,327)(232,328)
(233,329)(234,330)(235,331)(236,332)(237,333)(238,334)(239,335)(240,336)
(241,349)(242,350)(243,351)(244,352)(245,353)(246,354)(247,355)(248,356)
(249,357)(250,358)(251,359)(252,360)(253,373)(254,374)(255,375)(256,376)
(257,377)(258,378)(259,379)(260,380)(261,381)(262,382)(263,383)(264,384)
(265,361)(266,362)(267,363)(268,364)(269,365)(270,366)(271,367)(272,368)
(273,369)(274,370)(275,371)(276,372)(277,385)(278,386)(279,387)(280,388)
(281,389)(282,390)(283,391)(284,392)(285,393)(286,394)(287,395)(288,396)
(289,409)(290,410)(291,411)(292,412)(293,413)(294,414)(295,415)(296,416)
(297,417)(298,418)(299,419)(300,420)(301,397)(302,398)(303,399)(304,400)
(305,401)(306,402)(307,403)(308,404)(309,405)(310,406)(311,407)(312,408)
(313,421)(314,422)(315,423)(316,424)(317,425)(318,426)(319,427)(320,428)
(321,429)(322,430)(323,431)(324,432)(433,553)(434,554)(435,555)(436,556)
(437,557)(438,558)(439,559)(440,560)(441,561)(442,562)(443,563)(444,564)
(445,541)(446,542)(447,543)(448,544)(449,545)(450,546)(451,547)(452,548)
(453,549)(454,550)(455,551)(456,552)(457,565)(458,566)(459,567)(460,568)
(461,569)(462,570)(463,571)(464,572)(465,573)(466,574)(467,575)(468,576)
(469,589)(470,590)(471,591)(472,592)(473,593)(474,594)(475,595)(476,596)
(477,597)(478,598)(479,599)(480,600)(481,577)(482,578)(483,579)(484,580)
(485,581)(486,582)(487,583)(488,584)(489,585)(490,586)(491,587)(492,588)
(493,601)(494,602)(495,603)(496,604)(497,605)(498,606)(499,607)(500,608)
(501,609)(502,610)(503,611)(504,612)(505,625)(506,626)(507,627)(508,628)
(509,629)(510,630)(511,631)(512,632)(513,633)(514,634)(515,635)(516,636)
(517,613)(518,614)(519,615)(520,616)(521,617)(522,618)(523,619)(524,620)
(525,621)(526,622)(527,623)(528,624)(529,637)(530,638)(531,639)(532,640)
(533,641)(534,642)(535,643)(536,644)(537,645)(538,646)(539,647)(540,648)
(649,661)(650,662)(651,663)(652,664)(653,665)(654,666)(655,667)(656,668)
(657,669)(658,670)(659,671)(660,672)(685,697)(686,698)(687,699)(688,700)
(689,701)(690,702)(691,703)(692,704)(693,705)(694,706)(695,707)(696,708)
(721,733)(722,734)(723,735)(724,736)(725,737)(726,738)(727,739)(728,740)
(729,741)(730,742)(731,743)(732,744)(757,769)(758,770)(759,771)(760,772)
(761,773)(762,774)(763,775)(764,776)(765,777)(766,778)(767,779)(768,780)
(793,805)(794,806)(795,807)(796,808)(797,809)(798,810)(799,811)(800,812)
(801,813)(802,814)(803,815)(804,816)(829,841)(830,842)(831,843)(832,844)
(833,845)(834,846)(835,847)(836,848)(837,849)(838,850)(839,851)(840,852);;
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, s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3,
s2*s0*s1*s2*s0*s1*s2*s0*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)
( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)
( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)
(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)
(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)
(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)
(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)
(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)
(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)
(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)
(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)
(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)
(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)
(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)
(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)
(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)
(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)
(334,336)(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)
(350,352)(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)
(366,368)(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)
(382,384)(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)
(398,400)(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)
(414,416)(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)
(430,432)(433,435)(434,436)(437,439)(438,440)(441,443)(442,444)(445,447)
(446,448)(449,451)(450,452)(453,455)(454,456)(457,459)(458,460)(461,463)
(462,464)(465,467)(466,468)(469,471)(470,472)(473,475)(474,476)(477,479)
(478,480)(481,483)(482,484)(485,487)(486,488)(489,491)(490,492)(493,495)
(494,496)(497,499)(498,500)(501,503)(502,504)(505,507)(506,508)(509,511)
(510,512)(513,515)(514,516)(517,519)(518,520)(521,523)(522,524)(525,527)
(526,528)(529,531)(530,532)(533,535)(534,536)(537,539)(538,540)(541,543)
(542,544)(545,547)(546,548)(549,551)(550,552)(553,555)(554,556)(557,559)
(558,560)(561,563)(562,564)(565,567)(566,568)(569,571)(570,572)(573,575)
(574,576)(577,579)(578,580)(581,583)(582,584)(585,587)(586,588)(589,591)
(590,592)(593,595)(594,596)(597,599)(598,600)(601,603)(602,604)(605,607)
(606,608)(609,611)(610,612)(613,615)(614,616)(617,619)(618,620)(621,623)
(622,624)(625,627)(626,628)(629,631)(630,632)(633,635)(634,636)(637,639)
(638,640)(641,643)(642,644)(645,647)(646,648)(649,651)(650,652)(653,655)
(654,656)(657,659)(658,660)(661,663)(662,664)(665,667)(666,668)(669,671)
(670,672)(673,675)(674,676)(677,679)(678,680)(681,683)(682,684)(685,687)
(686,688)(689,691)(690,692)(693,695)(694,696)(697,699)(698,700)(701,703)
(702,704)(705,707)(706,708)(709,711)(710,712)(713,715)(714,716)(717,719)
(718,720)(721,723)(722,724)(725,727)(726,728)(729,731)(730,732)(733,735)
(734,736)(737,739)(738,740)(741,743)(742,744)(745,747)(746,748)(749,751)
(750,752)(753,755)(754,756)(757,759)(758,760)(761,763)(762,764)(765,767)
(766,768)(769,771)(770,772)(773,775)(774,776)(777,779)(778,780)(781,783)
(782,784)(785,787)(786,788)(789,791)(790,792)(793,795)(794,796)(797,799)
(798,800)(801,803)(802,804)(805,807)(806,808)(809,811)(810,812)(813,815)
(814,816)(817,819)(818,820)(821,823)(822,824)(825,827)(826,828)(829,831)
(830,832)(833,835)(834,836)(837,839)(838,840)(841,843)(842,844)(845,847)
(846,848)(849,851)(850,852)(853,855)(854,856)(857,859)(858,860)(861,863)
(862,864);
s1 := Sym(864)!( 1,649)( 2,650)( 3,652)( 4,651)( 5,657)( 6,658)( 7,660)
( 8,659)( 9,653)( 10,654)( 11,656)( 12,655)( 13,661)( 14,662)( 15,664)
( 16,663)( 17,669)( 18,670)( 19,672)( 20,671)( 21,665)( 22,666)( 23,668)
( 24,667)( 25,673)( 26,674)( 27,676)( 28,675)( 29,681)( 30,682)( 31,684)
( 32,683)( 33,677)( 34,678)( 35,680)( 36,679)( 37,721)( 38,722)( 39,724)
( 40,723)( 41,729)( 42,730)( 43,732)( 44,731)( 45,725)( 46,726)( 47,728)
( 48,727)( 49,733)( 50,734)( 51,736)( 52,735)( 53,741)( 54,742)( 55,744)
( 56,743)( 57,737)( 58,738)( 59,740)( 60,739)( 61,745)( 62,746)( 63,748)
( 64,747)( 65,753)( 66,754)( 67,756)( 68,755)( 69,749)( 70,750)( 71,752)
( 72,751)( 73,685)( 74,686)( 75,688)( 76,687)( 77,693)( 78,694)( 79,696)
( 80,695)( 81,689)( 82,690)( 83,692)( 84,691)( 85,697)( 86,698)( 87,700)
( 88,699)( 89,705)( 90,706)( 91,708)( 92,707)( 93,701)( 94,702)( 95,704)
( 96,703)( 97,709)( 98,710)( 99,712)(100,711)(101,717)(102,718)(103,720)
(104,719)(105,713)(106,714)(107,716)(108,715)(109,757)(110,758)(111,760)
(112,759)(113,765)(114,766)(115,768)(116,767)(117,761)(118,762)(119,764)
(120,763)(121,769)(122,770)(123,772)(124,771)(125,777)(126,778)(127,780)
(128,779)(129,773)(130,774)(131,776)(132,775)(133,781)(134,782)(135,784)
(136,783)(137,789)(138,790)(139,792)(140,791)(141,785)(142,786)(143,788)
(144,787)(145,829)(146,830)(147,832)(148,831)(149,837)(150,838)(151,840)
(152,839)(153,833)(154,834)(155,836)(156,835)(157,841)(158,842)(159,844)
(160,843)(161,849)(162,850)(163,852)(164,851)(165,845)(166,846)(167,848)
(168,847)(169,853)(170,854)(171,856)(172,855)(173,861)(174,862)(175,864)
(176,863)(177,857)(178,858)(179,860)(180,859)(181,793)(182,794)(183,796)
(184,795)(185,801)(186,802)(187,804)(188,803)(189,797)(190,798)(191,800)
(192,799)(193,805)(194,806)(195,808)(196,807)(197,813)(198,814)(199,816)
(200,815)(201,809)(202,810)(203,812)(204,811)(205,817)(206,818)(207,820)
(208,819)(209,825)(210,826)(211,828)(212,827)(213,821)(214,822)(215,824)
(216,823)(217,541)(218,542)(219,544)(220,543)(221,549)(222,550)(223,552)
(224,551)(225,545)(226,546)(227,548)(228,547)(229,553)(230,554)(231,556)
(232,555)(233,561)(234,562)(235,564)(236,563)(237,557)(238,558)(239,560)
(240,559)(241,565)(242,566)(243,568)(244,567)(245,573)(246,574)(247,576)
(248,575)(249,569)(250,570)(251,572)(252,571)(253,613)(254,614)(255,616)
(256,615)(257,621)(258,622)(259,624)(260,623)(261,617)(262,618)(263,620)
(264,619)(265,625)(266,626)(267,628)(268,627)(269,633)(270,634)(271,636)
(272,635)(273,629)(274,630)(275,632)(276,631)(277,637)(278,638)(279,640)
(280,639)(281,645)(282,646)(283,648)(284,647)(285,641)(286,642)(287,644)
(288,643)(289,577)(290,578)(291,580)(292,579)(293,585)(294,586)(295,588)
(296,587)(297,581)(298,582)(299,584)(300,583)(301,589)(302,590)(303,592)
(304,591)(305,597)(306,598)(307,600)(308,599)(309,593)(310,594)(311,596)
(312,595)(313,601)(314,602)(315,604)(316,603)(317,609)(318,610)(319,612)
(320,611)(321,605)(322,606)(323,608)(324,607)(325,433)(326,434)(327,436)
(328,435)(329,441)(330,442)(331,444)(332,443)(333,437)(334,438)(335,440)
(336,439)(337,445)(338,446)(339,448)(340,447)(341,453)(342,454)(343,456)
(344,455)(345,449)(346,450)(347,452)(348,451)(349,457)(350,458)(351,460)
(352,459)(353,465)(354,466)(355,468)(356,467)(357,461)(358,462)(359,464)
(360,463)(361,505)(362,506)(363,508)(364,507)(365,513)(366,514)(367,516)
(368,515)(369,509)(370,510)(371,512)(372,511)(373,517)(374,518)(375,520)
(376,519)(377,525)(378,526)(379,528)(380,527)(381,521)(382,522)(383,524)
(384,523)(385,529)(386,530)(387,532)(388,531)(389,537)(390,538)(391,540)
(392,539)(393,533)(394,534)(395,536)(396,535)(397,469)(398,470)(399,472)
(400,471)(401,477)(402,478)(403,480)(404,479)(405,473)(406,474)(407,476)
(408,475)(409,481)(410,482)(411,484)(412,483)(413,489)(414,490)(415,492)
(416,491)(417,485)(418,486)(419,488)(420,487)(421,493)(422,494)(423,496)
(424,495)(425,501)(426,502)(427,504)(428,503)(429,497)(430,498)(431,500)
(432,499);
s2 := Sym(864)!( 1,689)( 2,692)( 3,691)( 4,690)( 5,685)( 6,688)( 7,687)
( 8,686)( 9,693)( 10,696)( 11,695)( 12,694)( 13,701)( 14,704)( 15,703)
( 16,702)( 17,697)( 18,700)( 19,699)( 20,698)( 21,705)( 22,708)( 23,707)
( 24,706)( 25,713)( 26,716)( 27,715)( 28,714)( 29,709)( 30,712)( 31,711)
( 32,710)( 33,717)( 34,720)( 35,719)( 36,718)( 37,653)( 38,656)( 39,655)
( 40,654)( 41,649)( 42,652)( 43,651)( 44,650)( 45,657)( 46,660)( 47,659)
( 48,658)( 49,665)( 50,668)( 51,667)( 52,666)( 53,661)( 54,664)( 55,663)
( 56,662)( 57,669)( 58,672)( 59,671)( 60,670)( 61,677)( 62,680)( 63,679)
( 64,678)( 65,673)( 66,676)( 67,675)( 68,674)( 69,681)( 70,684)( 71,683)
( 72,682)( 73,725)( 74,728)( 75,727)( 76,726)( 77,721)( 78,724)( 79,723)
( 80,722)( 81,729)( 82,732)( 83,731)( 84,730)( 85,737)( 86,740)( 87,739)
( 88,738)( 89,733)( 90,736)( 91,735)( 92,734)( 93,741)( 94,744)( 95,743)
( 96,742)( 97,749)( 98,752)( 99,751)(100,750)(101,745)(102,748)(103,747)
(104,746)(105,753)(106,756)(107,755)(108,754)(109,797)(110,800)(111,799)
(112,798)(113,793)(114,796)(115,795)(116,794)(117,801)(118,804)(119,803)
(120,802)(121,809)(122,812)(123,811)(124,810)(125,805)(126,808)(127,807)
(128,806)(129,813)(130,816)(131,815)(132,814)(133,821)(134,824)(135,823)
(136,822)(137,817)(138,820)(139,819)(140,818)(141,825)(142,828)(143,827)
(144,826)(145,761)(146,764)(147,763)(148,762)(149,757)(150,760)(151,759)
(152,758)(153,765)(154,768)(155,767)(156,766)(157,773)(158,776)(159,775)
(160,774)(161,769)(162,772)(163,771)(164,770)(165,777)(166,780)(167,779)
(168,778)(169,785)(170,788)(171,787)(172,786)(173,781)(174,784)(175,783)
(176,782)(177,789)(178,792)(179,791)(180,790)(181,833)(182,836)(183,835)
(184,834)(185,829)(186,832)(187,831)(188,830)(189,837)(190,840)(191,839)
(192,838)(193,845)(194,848)(195,847)(196,846)(197,841)(198,844)(199,843)
(200,842)(201,849)(202,852)(203,851)(204,850)(205,857)(206,860)(207,859)
(208,858)(209,853)(210,856)(211,855)(212,854)(213,861)(214,864)(215,863)
(216,862)(217,581)(218,584)(219,583)(220,582)(221,577)(222,580)(223,579)
(224,578)(225,585)(226,588)(227,587)(228,586)(229,593)(230,596)(231,595)
(232,594)(233,589)(234,592)(235,591)(236,590)(237,597)(238,600)(239,599)
(240,598)(241,605)(242,608)(243,607)(244,606)(245,601)(246,604)(247,603)
(248,602)(249,609)(250,612)(251,611)(252,610)(253,545)(254,548)(255,547)
(256,546)(257,541)(258,544)(259,543)(260,542)(261,549)(262,552)(263,551)
(264,550)(265,557)(266,560)(267,559)(268,558)(269,553)(270,556)(271,555)
(272,554)(273,561)(274,564)(275,563)(276,562)(277,569)(278,572)(279,571)
(280,570)(281,565)(282,568)(283,567)(284,566)(285,573)(286,576)(287,575)
(288,574)(289,617)(290,620)(291,619)(292,618)(293,613)(294,616)(295,615)
(296,614)(297,621)(298,624)(299,623)(300,622)(301,629)(302,632)(303,631)
(304,630)(305,625)(306,628)(307,627)(308,626)(309,633)(310,636)(311,635)
(312,634)(313,641)(314,644)(315,643)(316,642)(317,637)(318,640)(319,639)
(320,638)(321,645)(322,648)(323,647)(324,646)(325,473)(326,476)(327,475)
(328,474)(329,469)(330,472)(331,471)(332,470)(333,477)(334,480)(335,479)
(336,478)(337,485)(338,488)(339,487)(340,486)(341,481)(342,484)(343,483)
(344,482)(345,489)(346,492)(347,491)(348,490)(349,497)(350,500)(351,499)
(352,498)(353,493)(354,496)(355,495)(356,494)(357,501)(358,504)(359,503)
(360,502)(361,437)(362,440)(363,439)(364,438)(365,433)(366,436)(367,435)
(368,434)(369,441)(370,444)(371,443)(372,442)(373,449)(374,452)(375,451)
(376,450)(377,445)(378,448)(379,447)(380,446)(381,453)(382,456)(383,455)
(384,454)(385,461)(386,464)(387,463)(388,462)(389,457)(390,460)(391,459)
(392,458)(393,465)(394,468)(395,467)(396,466)(397,509)(398,512)(399,511)
(400,510)(401,505)(402,508)(403,507)(404,506)(405,513)(406,516)(407,515)
(408,514)(409,521)(410,524)(411,523)(412,522)(413,517)(414,520)(415,519)
(416,518)(417,525)(418,528)(419,527)(420,526)(421,533)(422,536)(423,535)
(424,534)(425,529)(426,532)(427,531)(428,530)(429,537)(430,540)(431,539)
(432,538);
s3 := Sym(864)!( 1,433)( 2,434)( 3,435)( 4,436)( 5,441)( 6,442)( 7,443)
( 8,444)( 9,437)( 10,438)( 11,439)( 12,440)( 13,457)( 14,458)( 15,459)
( 16,460)( 17,465)( 18,466)( 19,467)( 20,468)( 21,461)( 22,462)( 23,463)
( 24,464)( 25,445)( 26,446)( 27,447)( 28,448)( 29,453)( 30,454)( 31,455)
( 32,456)( 33,449)( 34,450)( 35,451)( 36,452)( 37,469)( 38,470)( 39,471)
( 40,472)( 41,477)( 42,478)( 43,479)( 44,480)( 45,473)( 46,474)( 47,475)
( 48,476)( 49,493)( 50,494)( 51,495)( 52,496)( 53,501)( 54,502)( 55,503)
( 56,504)( 57,497)( 58,498)( 59,499)( 60,500)( 61,481)( 62,482)( 63,483)
( 64,484)( 65,489)( 66,490)( 67,491)( 68,492)( 69,485)( 70,486)( 71,487)
( 72,488)( 73,505)( 74,506)( 75,507)( 76,508)( 77,513)( 78,514)( 79,515)
( 80,516)( 81,509)( 82,510)( 83,511)( 84,512)( 85,529)( 86,530)( 87,531)
( 88,532)( 89,537)( 90,538)( 91,539)( 92,540)( 93,533)( 94,534)( 95,535)
( 96,536)( 97,517)( 98,518)( 99,519)(100,520)(101,525)(102,526)(103,527)
(104,528)(105,521)(106,522)(107,523)(108,524)(109,541)(110,542)(111,543)
(112,544)(113,549)(114,550)(115,551)(116,552)(117,545)(118,546)(119,547)
(120,548)(121,565)(122,566)(123,567)(124,568)(125,573)(126,574)(127,575)
(128,576)(129,569)(130,570)(131,571)(132,572)(133,553)(134,554)(135,555)
(136,556)(137,561)(138,562)(139,563)(140,564)(141,557)(142,558)(143,559)
(144,560)(145,577)(146,578)(147,579)(148,580)(149,585)(150,586)(151,587)
(152,588)(153,581)(154,582)(155,583)(156,584)(157,601)(158,602)(159,603)
(160,604)(161,609)(162,610)(163,611)(164,612)(165,605)(166,606)(167,607)
(168,608)(169,589)(170,590)(171,591)(172,592)(173,597)(174,598)(175,599)
(176,600)(177,593)(178,594)(179,595)(180,596)(181,613)(182,614)(183,615)
(184,616)(185,621)(186,622)(187,623)(188,624)(189,617)(190,618)(191,619)
(192,620)(193,637)(194,638)(195,639)(196,640)(197,645)(198,646)(199,647)
(200,648)(201,641)(202,642)(203,643)(204,644)(205,625)(206,626)(207,627)
(208,628)(209,633)(210,634)(211,635)(212,636)(213,629)(214,630)(215,631)
(216,632)(217,757)(218,758)(219,759)(220,760)(221,765)(222,766)(223,767)
(224,768)(225,761)(226,762)(227,763)(228,764)(229,781)(230,782)(231,783)
(232,784)(233,789)(234,790)(235,791)(236,792)(237,785)(238,786)(239,787)
(240,788)(241,769)(242,770)(243,771)(244,772)(245,777)(246,778)(247,779)
(248,780)(249,773)(250,774)(251,775)(252,776)(253,793)(254,794)(255,795)
(256,796)(257,801)(258,802)(259,803)(260,804)(261,797)(262,798)(263,799)
(264,800)(265,817)(266,818)(267,819)(268,820)(269,825)(270,826)(271,827)
(272,828)(273,821)(274,822)(275,823)(276,824)(277,805)(278,806)(279,807)
(280,808)(281,813)(282,814)(283,815)(284,816)(285,809)(286,810)(287,811)
(288,812)(289,829)(290,830)(291,831)(292,832)(293,837)(294,838)(295,839)
(296,840)(297,833)(298,834)(299,835)(300,836)(301,853)(302,854)(303,855)
(304,856)(305,861)(306,862)(307,863)(308,864)(309,857)(310,858)(311,859)
(312,860)(313,841)(314,842)(315,843)(316,844)(317,849)(318,850)(319,851)
(320,852)(321,845)(322,846)(323,847)(324,848)(325,649)(326,650)(327,651)
(328,652)(329,657)(330,658)(331,659)(332,660)(333,653)(334,654)(335,655)
(336,656)(337,673)(338,674)(339,675)(340,676)(341,681)(342,682)(343,683)
(344,684)(345,677)(346,678)(347,679)(348,680)(349,661)(350,662)(351,663)
(352,664)(353,669)(354,670)(355,671)(356,672)(357,665)(358,666)(359,667)
(360,668)(361,685)(362,686)(363,687)(364,688)(365,693)(366,694)(367,695)
(368,696)(369,689)(370,690)(371,691)(372,692)(373,709)(374,710)(375,711)
(376,712)(377,717)(378,718)(379,719)(380,720)(381,713)(382,714)(383,715)
(384,716)(385,697)(386,698)(387,699)(388,700)(389,705)(390,706)(391,707)
(392,708)(393,701)(394,702)(395,703)(396,704)(397,721)(398,722)(399,723)
(400,724)(401,729)(402,730)(403,731)(404,732)(405,725)(406,726)(407,727)
(408,728)(409,745)(410,746)(411,747)(412,748)(413,753)(414,754)(415,755)
(416,756)(417,749)(418,750)(419,751)(420,752)(421,733)(422,734)(423,735)
(424,736)(425,741)(426,742)(427,743)(428,744)(429,737)(430,738)(431,739)
(432,740);
s4 := Sym(864)!( 1, 13)( 2, 14)( 3, 15)( 4, 16)( 5, 17)( 6, 18)( 7, 19)
( 8, 20)( 9, 21)( 10, 22)( 11, 23)( 12, 24)( 37, 49)( 38, 50)( 39, 51)
( 40, 52)( 41, 53)( 42, 54)( 43, 55)( 44, 56)( 45, 57)( 46, 58)( 47, 59)
( 48, 60)( 73, 85)( 74, 86)( 75, 87)( 76, 88)( 77, 89)( 78, 90)( 79, 91)
( 80, 92)( 81, 93)( 82, 94)( 83, 95)( 84, 96)(109,121)(110,122)(111,123)
(112,124)(113,125)(114,126)(115,127)(116,128)(117,129)(118,130)(119,131)
(120,132)(145,157)(146,158)(147,159)(148,160)(149,161)(150,162)(151,163)
(152,164)(153,165)(154,166)(155,167)(156,168)(181,193)(182,194)(183,195)
(184,196)(185,197)(186,198)(187,199)(188,200)(189,201)(190,202)(191,203)
(192,204)(217,337)(218,338)(219,339)(220,340)(221,341)(222,342)(223,343)
(224,344)(225,345)(226,346)(227,347)(228,348)(229,325)(230,326)(231,327)
(232,328)(233,329)(234,330)(235,331)(236,332)(237,333)(238,334)(239,335)
(240,336)(241,349)(242,350)(243,351)(244,352)(245,353)(246,354)(247,355)
(248,356)(249,357)(250,358)(251,359)(252,360)(253,373)(254,374)(255,375)
(256,376)(257,377)(258,378)(259,379)(260,380)(261,381)(262,382)(263,383)
(264,384)(265,361)(266,362)(267,363)(268,364)(269,365)(270,366)(271,367)
(272,368)(273,369)(274,370)(275,371)(276,372)(277,385)(278,386)(279,387)
(280,388)(281,389)(282,390)(283,391)(284,392)(285,393)(286,394)(287,395)
(288,396)(289,409)(290,410)(291,411)(292,412)(293,413)(294,414)(295,415)
(296,416)(297,417)(298,418)(299,419)(300,420)(301,397)(302,398)(303,399)
(304,400)(305,401)(306,402)(307,403)(308,404)(309,405)(310,406)(311,407)
(312,408)(313,421)(314,422)(315,423)(316,424)(317,425)(318,426)(319,427)
(320,428)(321,429)(322,430)(323,431)(324,432)(433,553)(434,554)(435,555)
(436,556)(437,557)(438,558)(439,559)(440,560)(441,561)(442,562)(443,563)
(444,564)(445,541)(446,542)(447,543)(448,544)(449,545)(450,546)(451,547)
(452,548)(453,549)(454,550)(455,551)(456,552)(457,565)(458,566)(459,567)
(460,568)(461,569)(462,570)(463,571)(464,572)(465,573)(466,574)(467,575)
(468,576)(469,589)(470,590)(471,591)(472,592)(473,593)(474,594)(475,595)
(476,596)(477,597)(478,598)(479,599)(480,600)(481,577)(482,578)(483,579)
(484,580)(485,581)(486,582)(487,583)(488,584)(489,585)(490,586)(491,587)
(492,588)(493,601)(494,602)(495,603)(496,604)(497,605)(498,606)(499,607)
(500,608)(501,609)(502,610)(503,611)(504,612)(505,625)(506,626)(507,627)
(508,628)(509,629)(510,630)(511,631)(512,632)(513,633)(514,634)(515,635)
(516,636)(517,613)(518,614)(519,615)(520,616)(521,617)(522,618)(523,619)
(524,620)(525,621)(526,622)(527,623)(528,624)(529,637)(530,638)(531,639)
(532,640)(533,641)(534,642)(535,643)(536,644)(537,645)(538,646)(539,647)
(540,648)(649,661)(650,662)(651,663)(652,664)(653,665)(654,666)(655,667)
(656,668)(657,669)(658,670)(659,671)(660,672)(685,697)(686,698)(687,699)
(688,700)(689,701)(690,702)(691,703)(692,704)(693,705)(694,706)(695,707)
(696,708)(721,733)(722,734)(723,735)(724,736)(725,737)(726,738)(727,739)
(728,740)(729,741)(730,742)(731,743)(732,744)(757,769)(758,770)(759,771)
(760,772)(761,773)(762,774)(763,775)(764,776)(765,777)(766,778)(767,779)
(768,780)(793,805)(794,806)(795,807)(796,808)(797,809)(798,810)(799,811)
(800,812)(801,813)(802,814)(803,815)(804,816)(829,841)(830,842)(831,843)
(832,844)(833,845)(834,846)(835,847)(836,848)(837,849)(838,850)(839,851)
(840,852);
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, s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s4*s3*s2*s3*s4*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
References : None.
to this polytope