Polytope of Type {598}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {598}*1196
Also Known As : 598-gon, {598}. if this polytope has another name.
Group : SmallGroup(1196,10)
Rank : 2
Schlafli Type : {598}
Number of vertices, edges, etc : 598, 598
Order of s₀s₁ : 598
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 : {299}*598
   13-fold quotients : {46}*92
   23-fold quotients : {26}*52
   26-fold quotients : {23}*46
   46-fold quotients : {13}*26
   299-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 23)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)(  9, 16)
( 10, 15)( 11, 14)( 12, 13)( 24,277)( 25,299)( 26,298)( 27,297)( 28,296)
( 29,295)( 30,294)( 31,293)( 32,292)( 33,291)( 34,290)( 35,289)( 36,288)
( 37,287)( 38,286)( 39,285)( 40,284)( 41,283)( 42,282)( 43,281)( 44,280)
( 45,279)( 46,278)( 47,254)( 48,276)( 49,275)( 50,274)( 51,273)( 52,272)
( 53,271)( 54,270)( 55,269)( 56,268)( 57,267)( 58,266)( 59,265)( 60,264)
( 61,263)( 62,262)( 63,261)( 64,260)( 65,259)( 66,258)( 67,257)( 68,256)
( 69,255)( 70,231)( 71,253)( 72,252)( 73,251)( 74,250)( 75,249)( 76,248)
( 77,247)( 78,246)( 79,245)( 80,244)( 81,243)( 82,242)( 83,241)( 84,240)
( 85,239)( 86,238)( 87,237)( 88,236)( 89,235)( 90,234)( 91,233)( 92,232)
( 93,208)( 94,230)( 95,229)( 96,228)( 97,227)( 98,226)( 99,225)(100,224)
(101,223)(102,222)(103,221)(104,220)(105,219)(106,218)(107,217)(108,216)
(109,215)(110,214)(111,213)(112,212)(113,211)(114,210)(115,209)(116,185)
(117,207)(118,206)(119,205)(120,204)(121,203)(122,202)(123,201)(124,200)
(125,199)(126,198)(127,197)(128,196)(129,195)(130,194)(131,193)(132,192)
(133,191)(134,190)(135,189)(136,188)(137,187)(138,186)(139,162)(140,184)
(141,183)(142,182)(143,181)(144,180)(145,179)(146,178)(147,177)(148,176)
(149,175)(150,174)(151,173)(152,172)(153,171)(154,170)(155,169)(156,168)
(157,167)(158,166)(159,165)(160,164)(161,163)(301,322)(302,321)(303,320)
(304,319)(305,318)(306,317)(307,316)(308,315)(309,314)(310,313)(311,312)
(323,576)(324,598)(325,597)(326,596)(327,595)(328,594)(329,593)(330,592)
(331,591)(332,590)(333,589)(334,588)(335,587)(336,586)(337,585)(338,584)
(339,583)(340,582)(341,581)(342,580)(343,579)(344,578)(345,577)(346,553)
(347,575)(348,574)(349,573)(350,572)(351,571)(352,570)(353,569)(354,568)
(355,567)(356,566)(357,565)(358,564)(359,563)(360,562)(361,561)(362,560)
(363,559)(364,558)(365,557)(366,556)(367,555)(368,554)(369,530)(370,552)
(371,551)(372,550)(373,549)(374,548)(375,547)(376,546)(377,545)(378,544)
(379,543)(380,542)(381,541)(382,540)(383,539)(384,538)(385,537)(386,536)
(387,535)(388,534)(389,533)(390,532)(391,531)(392,507)(393,529)(394,528)
(395,527)(396,526)(397,525)(398,524)(399,523)(400,522)(401,521)(402,520)
(403,519)(404,518)(405,517)(406,516)(407,515)(408,514)(409,513)(410,512)
(411,511)(412,510)(413,509)(414,508)(415,484)(416,506)(417,505)(418,504)
(419,503)(420,502)(421,501)(422,500)(423,499)(424,498)(425,497)(426,496)
(427,495)(428,494)(429,493)(430,492)(431,491)(432,490)(433,489)(434,488)
(435,487)(436,486)(437,485)(438,461)(439,483)(440,482)(441,481)(442,480)
(443,479)(444,478)(445,477)(446,476)(447,475)(448,474)(449,473)(450,472)
(451,471)(452,470)(453,469)(454,468)(455,467)(456,466)(457,465)(458,464)
(459,463)(460,462);;
s1 := (  1,324)(  2,323)(  3,345)(  4,344)(  5,343)(  6,342)(  7,341)(  8,340)
(  9,339)( 10,338)( 11,337)( 12,336)( 13,335)( 14,334)( 15,333)( 16,332)
( 17,331)( 18,330)( 19,329)( 20,328)( 21,327)( 22,326)( 23,325)( 24,301)
( 25,300)( 26,322)( 27,321)( 28,320)( 29,319)( 30,318)( 31,317)( 32,316)
( 33,315)( 34,314)( 35,313)( 36,312)( 37,311)( 38,310)( 39,309)( 40,308)
( 41,307)( 42,306)( 43,305)( 44,304)( 45,303)( 46,302)( 47,577)( 48,576)
( 49,598)( 50,597)( 51,596)( 52,595)( 53,594)( 54,593)( 55,592)( 56,591)
( 57,590)( 58,589)( 59,588)( 60,587)( 61,586)( 62,585)( 63,584)( 64,583)
( 65,582)( 66,581)( 67,580)( 68,579)( 69,578)( 70,554)( 71,553)( 72,575)
( 73,574)( 74,573)( 75,572)( 76,571)( 77,570)( 78,569)( 79,568)( 80,567)
( 81,566)( 82,565)( 83,564)( 84,563)( 85,562)( 86,561)( 87,560)( 88,559)
( 89,558)( 90,557)( 91,556)( 92,555)( 93,531)( 94,530)( 95,552)( 96,551)
( 97,550)( 98,549)( 99,548)(100,547)(101,546)(102,545)(103,544)(104,543)
(105,542)(106,541)(107,540)(108,539)(109,538)(110,537)(111,536)(112,535)
(113,534)(114,533)(115,532)(116,508)(117,507)(118,529)(119,528)(120,527)
(121,526)(122,525)(123,524)(124,523)(125,522)(126,521)(127,520)(128,519)
(129,518)(130,517)(131,516)(132,515)(133,514)(134,513)(135,512)(136,511)
(137,510)(138,509)(139,485)(140,484)(141,506)(142,505)(143,504)(144,503)
(145,502)(146,501)(147,500)(148,499)(149,498)(150,497)(151,496)(152,495)
(153,494)(154,493)(155,492)(156,491)(157,490)(158,489)(159,488)(160,487)
(161,486)(162,462)(163,461)(164,483)(165,482)(166,481)(167,480)(168,479)
(169,478)(170,477)(171,476)(172,475)(173,474)(174,473)(175,472)(176,471)
(177,470)(178,469)(179,468)(180,467)(181,466)(182,465)(183,464)(184,463)
(185,439)(186,438)(187,460)(188,459)(189,458)(190,457)(191,456)(192,455)
(193,454)(194,453)(195,452)(196,451)(197,450)(198,449)(199,448)(200,447)
(201,446)(202,445)(203,444)(204,443)(205,442)(206,441)(207,440)(208,416)
(209,415)(210,437)(211,436)(212,435)(213,434)(214,433)(215,432)(216,431)
(217,430)(218,429)(219,428)(220,427)(221,426)(222,425)(223,424)(224,423)
(225,422)(226,421)(227,420)(228,419)(229,418)(230,417)(231,393)(232,392)
(233,414)(234,413)(235,412)(236,411)(237,410)(238,409)(239,408)(240,407)
(241,406)(242,405)(243,404)(244,403)(245,402)(246,401)(247,400)(248,399)
(249,398)(250,397)(251,396)(252,395)(253,394)(254,370)(255,369)(256,391)
(257,390)(258,389)(259,388)(260,387)(261,386)(262,385)(263,384)(264,383)
(265,382)(266,381)(267,380)(268,379)(269,378)(270,377)(271,376)(272,375)
(273,374)(274,373)(275,372)(276,371)(277,347)(278,346)(279,368)(280,367)
(281,366)(282,365)(283,364)(284,363)(285,362)(286,361)(287,360)(288,359)
(289,358)(290,357)(291,356)(292,355)(293,354)(294,353)(295,352)(296,351)
(297,350)(298,349)(299,348);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(598)!(  2, 23)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)
(  9, 16)( 10, 15)( 11, 14)( 12, 13)( 24,277)( 25,299)( 26,298)( 27,297)
( 28,296)( 29,295)( 30,294)( 31,293)( 32,292)( 33,291)( 34,290)( 35,289)
( 36,288)( 37,287)( 38,286)( 39,285)( 40,284)( 41,283)( 42,282)( 43,281)
( 44,280)( 45,279)( 46,278)( 47,254)( 48,276)( 49,275)( 50,274)( 51,273)
( 52,272)( 53,271)( 54,270)( 55,269)( 56,268)( 57,267)( 58,266)( 59,265)
( 60,264)( 61,263)( 62,262)( 63,261)( 64,260)( 65,259)( 66,258)( 67,257)
( 68,256)( 69,255)( 70,231)( 71,253)( 72,252)( 73,251)( 74,250)( 75,249)
( 76,248)( 77,247)( 78,246)( 79,245)( 80,244)( 81,243)( 82,242)( 83,241)
( 84,240)( 85,239)( 86,238)( 87,237)( 88,236)( 89,235)( 90,234)( 91,233)
( 92,232)( 93,208)( 94,230)( 95,229)( 96,228)( 97,227)( 98,226)( 99,225)
(100,224)(101,223)(102,222)(103,221)(104,220)(105,219)(106,218)(107,217)
(108,216)(109,215)(110,214)(111,213)(112,212)(113,211)(114,210)(115,209)
(116,185)(117,207)(118,206)(119,205)(120,204)(121,203)(122,202)(123,201)
(124,200)(125,199)(126,198)(127,197)(128,196)(129,195)(130,194)(131,193)
(132,192)(133,191)(134,190)(135,189)(136,188)(137,187)(138,186)(139,162)
(140,184)(141,183)(142,182)(143,181)(144,180)(145,179)(146,178)(147,177)
(148,176)(149,175)(150,174)(151,173)(152,172)(153,171)(154,170)(155,169)
(156,168)(157,167)(158,166)(159,165)(160,164)(161,163)(301,322)(302,321)
(303,320)(304,319)(305,318)(306,317)(307,316)(308,315)(309,314)(310,313)
(311,312)(323,576)(324,598)(325,597)(326,596)(327,595)(328,594)(329,593)
(330,592)(331,591)(332,590)(333,589)(334,588)(335,587)(336,586)(337,585)
(338,584)(339,583)(340,582)(341,581)(342,580)(343,579)(344,578)(345,577)
(346,553)(347,575)(348,574)(349,573)(350,572)(351,571)(352,570)(353,569)
(354,568)(355,567)(356,566)(357,565)(358,564)(359,563)(360,562)(361,561)
(362,560)(363,559)(364,558)(365,557)(366,556)(367,555)(368,554)(369,530)
(370,552)(371,551)(372,550)(373,549)(374,548)(375,547)(376,546)(377,545)
(378,544)(379,543)(380,542)(381,541)(382,540)(383,539)(384,538)(385,537)
(386,536)(387,535)(388,534)(389,533)(390,532)(391,531)(392,507)(393,529)
(394,528)(395,527)(396,526)(397,525)(398,524)(399,523)(400,522)(401,521)
(402,520)(403,519)(404,518)(405,517)(406,516)(407,515)(408,514)(409,513)
(410,512)(411,511)(412,510)(413,509)(414,508)(415,484)(416,506)(417,505)
(418,504)(419,503)(420,502)(421,501)(422,500)(423,499)(424,498)(425,497)
(426,496)(427,495)(428,494)(429,493)(430,492)(431,491)(432,490)(433,489)
(434,488)(435,487)(436,486)(437,485)(438,461)(439,483)(440,482)(441,481)
(442,480)(443,479)(444,478)(445,477)(446,476)(447,475)(448,474)(449,473)
(450,472)(451,471)(452,470)(453,469)(454,468)(455,467)(456,466)(457,465)
(458,464)(459,463)(460,462);
s1 := Sym(598)!(  1,324)(  2,323)(  3,345)(  4,344)(  5,343)(  6,342)(  7,341)
(  8,340)(  9,339)( 10,338)( 11,337)( 12,336)( 13,335)( 14,334)( 15,333)
( 16,332)( 17,331)( 18,330)( 19,329)( 20,328)( 21,327)( 22,326)( 23,325)
( 24,301)( 25,300)( 26,322)( 27,321)( 28,320)( 29,319)( 30,318)( 31,317)
( 32,316)( 33,315)( 34,314)( 35,313)( 36,312)( 37,311)( 38,310)( 39,309)
( 40,308)( 41,307)( 42,306)( 43,305)( 44,304)( 45,303)( 46,302)( 47,577)
( 48,576)( 49,598)( 50,597)( 51,596)( 52,595)( 53,594)( 54,593)( 55,592)
( 56,591)( 57,590)( 58,589)( 59,588)( 60,587)( 61,586)( 62,585)( 63,584)
( 64,583)( 65,582)( 66,581)( 67,580)( 68,579)( 69,578)( 70,554)( 71,553)
( 72,575)( 73,574)( 74,573)( 75,572)( 76,571)( 77,570)( 78,569)( 79,568)
( 80,567)( 81,566)( 82,565)( 83,564)( 84,563)( 85,562)( 86,561)( 87,560)
( 88,559)( 89,558)( 90,557)( 91,556)( 92,555)( 93,531)( 94,530)( 95,552)
( 96,551)( 97,550)( 98,549)( 99,548)(100,547)(101,546)(102,545)(103,544)
(104,543)(105,542)(106,541)(107,540)(108,539)(109,538)(110,537)(111,536)
(112,535)(113,534)(114,533)(115,532)(116,508)(117,507)(118,529)(119,528)
(120,527)(121,526)(122,525)(123,524)(124,523)(125,522)(126,521)(127,520)
(128,519)(129,518)(130,517)(131,516)(132,515)(133,514)(134,513)(135,512)
(136,511)(137,510)(138,509)(139,485)(140,484)(141,506)(142,505)(143,504)
(144,503)(145,502)(146,501)(147,500)(148,499)(149,498)(150,497)(151,496)
(152,495)(153,494)(154,493)(155,492)(156,491)(157,490)(158,489)(159,488)
(160,487)(161,486)(162,462)(163,461)(164,483)(165,482)(166,481)(167,480)
(168,479)(169,478)(170,477)(171,476)(172,475)(173,474)(174,473)(175,472)
(176,471)(177,470)(178,469)(179,468)(180,467)(181,466)(182,465)(183,464)
(184,463)(185,439)(186,438)(187,460)(188,459)(189,458)(190,457)(191,456)
(192,455)(193,454)(194,453)(195,452)(196,451)(197,450)(198,449)(199,448)
(200,447)(201,446)(202,445)(203,444)(204,443)(205,442)(206,441)(207,440)
(208,416)(209,415)(210,437)(211,436)(212,435)(213,434)(214,433)(215,432)
(216,431)(217,430)(218,429)(219,428)(220,427)(221,426)(222,425)(223,424)
(224,423)(225,422)(226,421)(227,420)(228,419)(229,418)(230,417)(231,393)
(232,392)(233,414)(234,413)(235,412)(236,411)(237,410)(238,409)(239,408)
(240,407)(241,406)(242,405)(243,404)(244,403)(245,402)(246,401)(247,400)
(248,399)(249,398)(250,397)(251,396)(252,395)(253,394)(254,370)(255,369)
(256,391)(257,390)(258,389)(259,388)(260,387)(261,386)(262,385)(263,384)
(264,383)(265,382)(266,381)(267,380)(268,379)(269,378)(270,377)(271,376)
(272,375)(273,374)(274,373)(275,372)(276,371)(277,347)(278,346)(279,368)
(280,367)(281,366)(282,365)(283,364)(284,363)(285,362)(286,361)(287,360)
(288,359)(289,358)(290,357)(291,356)(292,355)(293,354)(294,353)(295,352)
(296,351)(297,350)(298,349)(299,348);
poly := sub<Sym(598)|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 >;

References : None.
to this polytope