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