Polytope of Type {798}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {798}*1596
Also Known As : 798-gon, {798}. if this polytope has another name.
Group : SmallGroup(1596,63)
Rank : 2
Schlafli Type : {798}
Number of vertices, edges, etc : 798, 798
Order of s₀s₁ : 798
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
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 : {399}*798
   3-fold quotients : {266}*532
   6-fold quotients : {133}*266
   7-fold quotients : {114}*228
   14-fold quotients : {57}*114
   19-fold quotients : {42}*84
   21-fold quotients : {38}*76
   38-fold quotients : {21}*42
   42-fold quotients : {19}*38
   57-fold quotients : {14}*28
   114-fold quotients : {7}*14
   133-fold quotients : {6}*12
   266-fold quotients : {3}*6
   399-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)(  9, 12)
( 10, 11)( 20,115)( 21,133)( 22,132)( 23,131)( 24,130)( 25,129)( 26,128)
( 27,127)( 28,126)( 29,125)( 30,124)( 31,123)( 32,122)( 33,121)( 34,120)
( 35,119)( 36,118)( 37,117)( 38,116)( 39, 96)( 40,114)( 41,113)( 42,112)
( 43,111)( 44,110)( 45,109)( 46,108)( 47,107)( 48,106)( 49,105)( 50,104)
( 51,103)( 52,102)( 53,101)( 54,100)( 55, 99)( 56, 98)( 57, 97)( 58, 77)
( 59, 95)( 60, 94)( 61, 93)( 62, 92)( 63, 91)( 64, 90)( 65, 89)( 66, 88)
( 67, 87)( 68, 86)( 69, 85)( 70, 84)( 71, 83)( 72, 82)( 73, 81)( 74, 80)
( 75, 79)( 76, 78)(134,267)(135,285)(136,284)(137,283)(138,282)(139,281)
(140,280)(141,279)(142,278)(143,277)(144,276)(145,275)(146,274)(147,273)
(148,272)(149,271)(150,270)(151,269)(152,268)(153,381)(154,399)(155,398)
(156,397)(157,396)(158,395)(159,394)(160,393)(161,392)(162,391)(163,390)
(164,389)(165,388)(166,387)(167,386)(168,385)(169,384)(170,383)(171,382)
(172,362)(173,380)(174,379)(175,378)(176,377)(177,376)(178,375)(179,374)
(180,373)(181,372)(182,371)(183,370)(184,369)(185,368)(186,367)(187,366)
(188,365)(189,364)(190,363)(191,343)(192,361)(193,360)(194,359)(195,358)
(196,357)(197,356)(198,355)(199,354)(200,353)(201,352)(202,351)(203,350)
(204,349)(205,348)(206,347)(207,346)(208,345)(209,344)(210,324)(211,342)
(212,341)(213,340)(214,339)(215,338)(216,337)(217,336)(218,335)(219,334)
(220,333)(221,332)(222,331)(223,330)(224,329)(225,328)(226,327)(227,326)
(228,325)(229,305)(230,323)(231,322)(232,321)(233,320)(234,319)(235,318)
(236,317)(237,316)(238,315)(239,314)(240,313)(241,312)(242,311)(243,310)
(244,309)(245,308)(246,307)(247,306)(248,286)(249,304)(250,303)(251,302)
(252,301)(253,300)(254,299)(255,298)(256,297)(257,296)(258,295)(259,294)
(260,293)(261,292)(262,291)(263,290)(264,289)(265,288)(266,287)(401,418)
(402,417)(403,416)(404,415)(405,414)(406,413)(407,412)(408,411)(409,410)
(419,514)(420,532)(421,531)(422,530)(423,529)(424,528)(425,527)(426,526)
(427,525)(428,524)(429,523)(430,522)(431,521)(432,520)(433,519)(434,518)
(435,517)(436,516)(437,515)(438,495)(439,513)(440,512)(441,511)(442,510)
(443,509)(444,508)(445,507)(446,506)(447,505)(448,504)(449,503)(450,502)
(451,501)(452,500)(453,499)(454,498)(455,497)(456,496)(457,476)(458,494)
(459,493)(460,492)(461,491)(462,490)(463,489)(464,488)(465,487)(466,486)
(467,485)(468,484)(469,483)(470,482)(471,481)(472,480)(473,479)(474,478)
(475,477)(533,666)(534,684)(535,683)(536,682)(537,681)(538,680)(539,679)
(540,678)(541,677)(542,676)(543,675)(544,674)(545,673)(546,672)(547,671)
(548,670)(549,669)(550,668)(551,667)(552,780)(553,798)(554,797)(555,796)
(556,795)(557,794)(558,793)(559,792)(560,791)(561,790)(562,789)(563,788)
(564,787)(565,786)(566,785)(567,784)(568,783)(569,782)(570,781)(571,761)
(572,779)(573,778)(574,777)(575,776)(576,775)(577,774)(578,773)(579,772)
(580,771)(581,770)(582,769)(583,768)(584,767)(585,766)(586,765)(587,764)
(588,763)(589,762)(590,742)(591,760)(592,759)(593,758)(594,757)(595,756)
(596,755)(597,754)(598,753)(599,752)(600,751)(601,750)(602,749)(603,748)
(604,747)(605,746)(606,745)(607,744)(608,743)(609,723)(610,741)(611,740)
(612,739)(613,738)(614,737)(615,736)(616,735)(617,734)(618,733)(619,732)
(620,731)(621,730)(622,729)(623,728)(624,727)(625,726)(626,725)(627,724)
(628,704)(629,722)(630,721)(631,720)(632,719)(633,718)(634,717)(635,716)
(636,715)(637,714)(638,713)(639,712)(640,711)(641,710)(642,709)(643,708)
(644,707)(645,706)(646,705)(647,685)(648,703)(649,702)(650,701)(651,700)
(652,699)(653,698)(654,697)(655,696)(656,695)(657,694)(658,693)(659,692)
(660,691)(661,690)(662,689)(663,688)(664,687)(665,686);;
s1 := (  1,553)(  2,552)(  3,570)(  4,569)(  5,568)(  6,567)(  7,566)(  8,565)
(  9,564)( 10,563)( 11,562)( 12,561)( 13,560)( 14,559)( 15,558)( 16,557)
( 17,556)( 18,555)( 19,554)( 20,534)( 21,533)( 22,551)( 23,550)( 24,549)
( 25,548)( 26,547)( 27,546)( 28,545)( 29,544)( 30,543)( 31,542)( 32,541)
( 33,540)( 34,539)( 35,538)( 36,537)( 37,536)( 38,535)( 39,648)( 40,647)
( 41,665)( 42,664)( 43,663)( 44,662)( 45,661)( 46,660)( 47,659)( 48,658)
( 49,657)( 50,656)( 51,655)( 52,654)( 53,653)( 54,652)( 55,651)( 56,650)
( 57,649)( 58,629)( 59,628)( 60,646)( 61,645)( 62,644)( 63,643)( 64,642)
( 65,641)( 66,640)( 67,639)( 68,638)( 69,637)( 70,636)( 71,635)( 72,634)
( 73,633)( 74,632)( 75,631)( 76,630)( 77,610)( 78,609)( 79,627)( 80,626)
( 81,625)( 82,624)( 83,623)( 84,622)( 85,621)( 86,620)( 87,619)( 88,618)
( 89,617)( 90,616)( 91,615)( 92,614)( 93,613)( 94,612)( 95,611)( 96,591)
( 97,590)( 98,608)( 99,607)(100,606)(101,605)(102,604)(103,603)(104,602)
(105,601)(106,600)(107,599)(108,598)(109,597)(110,596)(111,595)(112,594)
(113,593)(114,592)(115,572)(116,571)(117,589)(118,588)(119,587)(120,586)
(121,585)(122,584)(123,583)(124,582)(125,581)(126,580)(127,579)(128,578)
(129,577)(130,576)(131,575)(132,574)(133,573)(134,420)(135,419)(136,437)
(137,436)(138,435)(139,434)(140,433)(141,432)(142,431)(143,430)(144,429)
(145,428)(146,427)(147,426)(148,425)(149,424)(150,423)(151,422)(152,421)
(153,401)(154,400)(155,418)(156,417)(157,416)(158,415)(159,414)(160,413)
(161,412)(162,411)(163,410)(164,409)(165,408)(166,407)(167,406)(168,405)
(169,404)(170,403)(171,402)(172,515)(173,514)(174,532)(175,531)(176,530)
(177,529)(178,528)(179,527)(180,526)(181,525)(182,524)(183,523)(184,522)
(185,521)(186,520)(187,519)(188,518)(189,517)(190,516)(191,496)(192,495)
(193,513)(194,512)(195,511)(196,510)(197,509)(198,508)(199,507)(200,506)
(201,505)(202,504)(203,503)(204,502)(205,501)(206,500)(207,499)(208,498)
(209,497)(210,477)(211,476)(212,494)(213,493)(214,492)(215,491)(216,490)
(217,489)(218,488)(219,487)(220,486)(221,485)(222,484)(223,483)(224,482)
(225,481)(226,480)(227,479)(228,478)(229,458)(230,457)(231,475)(232,474)
(233,473)(234,472)(235,471)(236,470)(237,469)(238,468)(239,467)(240,466)
(241,465)(242,464)(243,463)(244,462)(245,461)(246,460)(247,459)(248,439)
(249,438)(250,456)(251,455)(252,454)(253,453)(254,452)(255,451)(256,450)
(257,449)(258,448)(259,447)(260,446)(261,445)(262,444)(263,443)(264,442)
(265,441)(266,440)(267,686)(268,685)(269,703)(270,702)(271,701)(272,700)
(273,699)(274,698)(275,697)(276,696)(277,695)(278,694)(279,693)(280,692)
(281,691)(282,690)(283,689)(284,688)(285,687)(286,667)(287,666)(288,684)
(289,683)(290,682)(291,681)(292,680)(293,679)(294,678)(295,677)(296,676)
(297,675)(298,674)(299,673)(300,672)(301,671)(302,670)(303,669)(304,668)
(305,781)(306,780)(307,798)(308,797)(309,796)(310,795)(311,794)(312,793)
(313,792)(314,791)(315,790)(316,789)(317,788)(318,787)(319,786)(320,785)
(321,784)(322,783)(323,782)(324,762)(325,761)(326,779)(327,778)(328,777)
(329,776)(330,775)(331,774)(332,773)(333,772)(334,771)(335,770)(336,769)
(337,768)(338,767)(339,766)(340,765)(341,764)(342,763)(343,743)(344,742)
(345,760)(346,759)(347,758)(348,757)(349,756)(350,755)(351,754)(352,753)
(353,752)(354,751)(355,750)(356,749)(357,748)(358,747)(359,746)(360,745)
(361,744)(362,724)(363,723)(364,741)(365,740)(366,739)(367,738)(368,737)
(369,736)(370,735)(371,734)(372,733)(373,732)(374,731)(375,730)(376,729)
(377,728)(378,727)(379,726)(380,725)(381,705)(382,704)(383,722)(384,721)
(385,720)(386,719)(387,718)(388,717)(389,716)(390,715)(391,714)(392,713)
(393,712)(394,711)(395,710)(396,709)(397,708)(398,707)(399,706);;
poly := Group([s0,s1]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(798)!(  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)
(  9, 12)( 10, 11)( 20,115)( 21,133)( 22,132)( 23,131)( 24,130)( 25,129)
( 26,128)( 27,127)( 28,126)( 29,125)( 30,124)( 31,123)( 32,122)( 33,121)
( 34,120)( 35,119)( 36,118)( 37,117)( 38,116)( 39, 96)( 40,114)( 41,113)
( 42,112)( 43,111)( 44,110)( 45,109)( 46,108)( 47,107)( 48,106)( 49,105)
( 50,104)( 51,103)( 52,102)( 53,101)( 54,100)( 55, 99)( 56, 98)( 57, 97)
( 58, 77)( 59, 95)( 60, 94)( 61, 93)( 62, 92)( 63, 91)( 64, 90)( 65, 89)
( 66, 88)( 67, 87)( 68, 86)( 69, 85)( 70, 84)( 71, 83)( 72, 82)( 73, 81)
( 74, 80)( 75, 79)( 76, 78)(134,267)(135,285)(136,284)(137,283)(138,282)
(139,281)(140,280)(141,279)(142,278)(143,277)(144,276)(145,275)(146,274)
(147,273)(148,272)(149,271)(150,270)(151,269)(152,268)(153,381)(154,399)
(155,398)(156,397)(157,396)(158,395)(159,394)(160,393)(161,392)(162,391)
(163,390)(164,389)(165,388)(166,387)(167,386)(168,385)(169,384)(170,383)
(171,382)(172,362)(173,380)(174,379)(175,378)(176,377)(177,376)(178,375)
(179,374)(180,373)(181,372)(182,371)(183,370)(184,369)(185,368)(186,367)
(187,366)(188,365)(189,364)(190,363)(191,343)(192,361)(193,360)(194,359)
(195,358)(196,357)(197,356)(198,355)(199,354)(200,353)(201,352)(202,351)
(203,350)(204,349)(205,348)(206,347)(207,346)(208,345)(209,344)(210,324)
(211,342)(212,341)(213,340)(214,339)(215,338)(216,337)(217,336)(218,335)
(219,334)(220,333)(221,332)(222,331)(223,330)(224,329)(225,328)(226,327)
(227,326)(228,325)(229,305)(230,323)(231,322)(232,321)(233,320)(234,319)
(235,318)(236,317)(237,316)(238,315)(239,314)(240,313)(241,312)(242,311)
(243,310)(244,309)(245,308)(246,307)(247,306)(248,286)(249,304)(250,303)
(251,302)(252,301)(253,300)(254,299)(255,298)(256,297)(257,296)(258,295)
(259,294)(260,293)(261,292)(262,291)(263,290)(264,289)(265,288)(266,287)
(401,418)(402,417)(403,416)(404,415)(405,414)(406,413)(407,412)(408,411)
(409,410)(419,514)(420,532)(421,531)(422,530)(423,529)(424,528)(425,527)
(426,526)(427,525)(428,524)(429,523)(430,522)(431,521)(432,520)(433,519)
(434,518)(435,517)(436,516)(437,515)(438,495)(439,513)(440,512)(441,511)
(442,510)(443,509)(444,508)(445,507)(446,506)(447,505)(448,504)(449,503)
(450,502)(451,501)(452,500)(453,499)(454,498)(455,497)(456,496)(457,476)
(458,494)(459,493)(460,492)(461,491)(462,490)(463,489)(464,488)(465,487)
(466,486)(467,485)(468,484)(469,483)(470,482)(471,481)(472,480)(473,479)
(474,478)(475,477)(533,666)(534,684)(535,683)(536,682)(537,681)(538,680)
(539,679)(540,678)(541,677)(542,676)(543,675)(544,674)(545,673)(546,672)
(547,671)(548,670)(549,669)(550,668)(551,667)(552,780)(553,798)(554,797)
(555,796)(556,795)(557,794)(558,793)(559,792)(560,791)(561,790)(562,789)
(563,788)(564,787)(565,786)(566,785)(567,784)(568,783)(569,782)(570,781)
(571,761)(572,779)(573,778)(574,777)(575,776)(576,775)(577,774)(578,773)
(579,772)(580,771)(581,770)(582,769)(583,768)(584,767)(585,766)(586,765)
(587,764)(588,763)(589,762)(590,742)(591,760)(592,759)(593,758)(594,757)
(595,756)(596,755)(597,754)(598,753)(599,752)(600,751)(601,750)(602,749)
(603,748)(604,747)(605,746)(606,745)(607,744)(608,743)(609,723)(610,741)
(611,740)(612,739)(613,738)(614,737)(615,736)(616,735)(617,734)(618,733)
(619,732)(620,731)(621,730)(622,729)(623,728)(624,727)(625,726)(626,725)
(627,724)(628,704)(629,722)(630,721)(631,720)(632,719)(633,718)(634,717)
(635,716)(636,715)(637,714)(638,713)(639,712)(640,711)(641,710)(642,709)
(643,708)(644,707)(645,706)(646,705)(647,685)(648,703)(649,702)(650,701)
(651,700)(652,699)(653,698)(654,697)(655,696)(656,695)(657,694)(658,693)
(659,692)(660,691)(661,690)(662,689)(663,688)(664,687)(665,686);
s1 := Sym(798)!(  1,553)(  2,552)(  3,570)(  4,569)(  5,568)(  6,567)(  7,566)
(  8,565)(  9,564)( 10,563)( 11,562)( 12,561)( 13,560)( 14,559)( 15,558)
( 16,557)( 17,556)( 18,555)( 19,554)( 20,534)( 21,533)( 22,551)( 23,550)
( 24,549)( 25,548)( 26,547)( 27,546)( 28,545)( 29,544)( 30,543)( 31,542)
( 32,541)( 33,540)( 34,539)( 35,538)( 36,537)( 37,536)( 38,535)( 39,648)
( 40,647)( 41,665)( 42,664)( 43,663)( 44,662)( 45,661)( 46,660)( 47,659)
( 48,658)( 49,657)( 50,656)( 51,655)( 52,654)( 53,653)( 54,652)( 55,651)
( 56,650)( 57,649)( 58,629)( 59,628)( 60,646)( 61,645)( 62,644)( 63,643)
( 64,642)( 65,641)( 66,640)( 67,639)( 68,638)( 69,637)( 70,636)( 71,635)
( 72,634)( 73,633)( 74,632)( 75,631)( 76,630)( 77,610)( 78,609)( 79,627)
( 80,626)( 81,625)( 82,624)( 83,623)( 84,622)( 85,621)( 86,620)( 87,619)
( 88,618)( 89,617)( 90,616)( 91,615)( 92,614)( 93,613)( 94,612)( 95,611)
( 96,591)( 97,590)( 98,608)( 99,607)(100,606)(101,605)(102,604)(103,603)
(104,602)(105,601)(106,600)(107,599)(108,598)(109,597)(110,596)(111,595)
(112,594)(113,593)(114,592)(115,572)(116,571)(117,589)(118,588)(119,587)
(120,586)(121,585)(122,584)(123,583)(124,582)(125,581)(126,580)(127,579)
(128,578)(129,577)(130,576)(131,575)(132,574)(133,573)(134,420)(135,419)
(136,437)(137,436)(138,435)(139,434)(140,433)(141,432)(142,431)(143,430)
(144,429)(145,428)(146,427)(147,426)(148,425)(149,424)(150,423)(151,422)
(152,421)(153,401)(154,400)(155,418)(156,417)(157,416)(158,415)(159,414)
(160,413)(161,412)(162,411)(163,410)(164,409)(165,408)(166,407)(167,406)
(168,405)(169,404)(170,403)(171,402)(172,515)(173,514)(174,532)(175,531)
(176,530)(177,529)(178,528)(179,527)(180,526)(181,525)(182,524)(183,523)
(184,522)(185,521)(186,520)(187,519)(188,518)(189,517)(190,516)(191,496)
(192,495)(193,513)(194,512)(195,511)(196,510)(197,509)(198,508)(199,507)
(200,506)(201,505)(202,504)(203,503)(204,502)(205,501)(206,500)(207,499)
(208,498)(209,497)(210,477)(211,476)(212,494)(213,493)(214,492)(215,491)
(216,490)(217,489)(218,488)(219,487)(220,486)(221,485)(222,484)(223,483)
(224,482)(225,481)(226,480)(227,479)(228,478)(229,458)(230,457)(231,475)
(232,474)(233,473)(234,472)(235,471)(236,470)(237,469)(238,468)(239,467)
(240,466)(241,465)(242,464)(243,463)(244,462)(245,461)(246,460)(247,459)
(248,439)(249,438)(250,456)(251,455)(252,454)(253,453)(254,452)(255,451)
(256,450)(257,449)(258,448)(259,447)(260,446)(261,445)(262,444)(263,443)
(264,442)(265,441)(266,440)(267,686)(268,685)(269,703)(270,702)(271,701)
(272,700)(273,699)(274,698)(275,697)(276,696)(277,695)(278,694)(279,693)
(280,692)(281,691)(282,690)(283,689)(284,688)(285,687)(286,667)(287,666)
(288,684)(289,683)(290,682)(291,681)(292,680)(293,679)(294,678)(295,677)
(296,676)(297,675)(298,674)(299,673)(300,672)(301,671)(302,670)(303,669)
(304,668)(305,781)(306,780)(307,798)(308,797)(309,796)(310,795)(311,794)
(312,793)(313,792)(314,791)(315,790)(316,789)(317,788)(318,787)(319,786)
(320,785)(321,784)(322,783)(323,782)(324,762)(325,761)(326,779)(327,778)
(328,777)(329,776)(330,775)(331,774)(332,773)(333,772)(334,771)(335,770)
(336,769)(337,768)(338,767)(339,766)(340,765)(341,764)(342,763)(343,743)
(344,742)(345,760)(346,759)(347,758)(348,757)(349,756)(350,755)(351,754)
(352,753)(353,752)(354,751)(355,750)(356,749)(357,748)(358,747)(359,746)
(360,745)(361,744)(362,724)(363,723)(364,741)(365,740)(366,739)(367,738)
(368,737)(369,736)(370,735)(371,734)(372,733)(373,732)(374,731)(375,730)
(376,729)(377,728)(378,727)(379,726)(380,725)(381,705)(382,704)(383,722)
(384,721)(385,720)(386,719)(387,718)(388,717)(389,716)(390,715)(391,714)
(392,713)(393,712)(394,711)(395,710)(396,709)(397,708)(398,707)(399,706);
poly := sub<Sym(798)|s0,s1>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope