Polytope of Type {626}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {626}*1252
Also Known As : 626-gon, {626}. if this polytope has another name.
Group : SmallGroup(1252,4)
Rank : 2
Schlafli Type : {626}
Number of vertices, edges, etc : 626, 626
Order of s₀s₁ : 626
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 : {313}*626
   313-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,313)(  3,312)(  4,311)(  5,310)(  6,309)(  7,308)(  8,307)(  9,306)
( 10,305)( 11,304)( 12,303)( 13,302)( 14,301)( 15,300)( 16,299)( 17,298)
( 18,297)( 19,296)( 20,295)( 21,294)( 22,293)( 23,292)( 24,291)( 25,290)
( 26,289)( 27,288)( 28,287)( 29,286)( 30,285)( 31,284)( 32,283)( 33,282)
( 34,281)( 35,280)( 36,279)( 37,278)( 38,277)( 39,276)( 40,275)( 41,274)
( 42,273)( 43,272)( 44,271)( 45,270)( 46,269)( 47,268)( 48,267)( 49,266)
( 50,265)( 51,264)( 52,263)( 53,262)( 54,261)( 55,260)( 56,259)( 57,258)
( 58,257)( 59,256)( 60,255)( 61,254)( 62,253)( 63,252)( 64,251)( 65,250)
( 66,249)( 67,248)( 68,247)( 69,246)( 70,245)( 71,244)( 72,243)( 73,242)
( 74,241)( 75,240)( 76,239)( 77,238)( 78,237)( 79,236)( 80,235)( 81,234)
( 82,233)( 83,232)( 84,231)( 85,230)( 86,229)( 87,228)( 88,227)( 89,226)
( 90,225)( 91,224)( 92,223)( 93,222)( 94,221)( 95,220)( 96,219)( 97,218)
( 98,217)( 99,216)(100,215)(101,214)(102,213)(103,212)(104,211)(105,210)
(106,209)(107,208)(108,207)(109,206)(110,205)(111,204)(112,203)(113,202)
(114,201)(115,200)(116,199)(117,198)(118,197)(119,196)(120,195)(121,194)
(122,193)(123,192)(124,191)(125,190)(126,189)(127,188)(128,187)(129,186)
(130,185)(131,184)(132,183)(133,182)(134,181)(135,180)(136,179)(137,178)
(138,177)(139,176)(140,175)(141,174)(142,173)(143,172)(144,171)(145,170)
(146,169)(147,168)(148,167)(149,166)(150,165)(151,164)(152,163)(153,162)
(154,161)(155,160)(156,159)(157,158)(315,626)(316,625)(317,624)(318,623)
(319,622)(320,621)(321,620)(322,619)(323,618)(324,617)(325,616)(326,615)
(327,614)(328,613)(329,612)(330,611)(331,610)(332,609)(333,608)(334,607)
(335,606)(336,605)(337,604)(338,603)(339,602)(340,601)(341,600)(342,599)
(343,598)(344,597)(345,596)(346,595)(347,594)(348,593)(349,592)(350,591)
(351,590)(352,589)(353,588)(354,587)(355,586)(356,585)(357,584)(358,583)
(359,582)(360,581)(361,580)(362,579)(363,578)(364,577)(365,576)(366,575)
(367,574)(368,573)(369,572)(370,571)(371,570)(372,569)(373,568)(374,567)
(375,566)(376,565)(377,564)(378,563)(379,562)(380,561)(381,560)(382,559)
(383,558)(384,557)(385,556)(386,555)(387,554)(388,553)(389,552)(390,551)
(391,550)(392,549)(393,548)(394,547)(395,546)(396,545)(397,544)(398,543)
(399,542)(400,541)(401,540)(402,539)(403,538)(404,537)(405,536)(406,535)
(407,534)(408,533)(409,532)(410,531)(411,530)(412,529)(413,528)(414,527)
(415,526)(416,525)(417,524)(418,523)(419,522)(420,521)(421,520)(422,519)
(423,518)(424,517)(425,516)(426,515)(427,514)(428,513)(429,512)(430,511)
(431,510)(432,509)(433,508)(434,507)(435,506)(436,505)(437,504)(438,503)
(439,502)(440,501)(441,500)(442,499)(443,498)(444,497)(445,496)(446,495)
(447,494)(448,493)(449,492)(450,491)(451,490)(452,489)(453,488)(454,487)
(455,486)(456,485)(457,484)(458,483)(459,482)(460,481)(461,480)(462,479)
(463,478)(464,477)(465,476)(466,475)(467,474)(468,473)(469,472)(470,471);;
s1 := (  1,315)(  2,314)(  3,626)(  4,625)(  5,624)(  6,623)(  7,622)(  8,621)
(  9,620)( 10,619)( 11,618)( 12,617)( 13,616)( 14,615)( 15,614)( 16,613)
( 17,612)( 18,611)( 19,610)( 20,609)( 21,608)( 22,607)( 23,606)( 24,605)
( 25,604)( 26,603)( 27,602)( 28,601)( 29,600)( 30,599)( 31,598)( 32,597)
( 33,596)( 34,595)( 35,594)( 36,593)( 37,592)( 38,591)( 39,590)( 40,589)
( 41,588)( 42,587)( 43,586)( 44,585)( 45,584)( 46,583)( 47,582)( 48,581)
( 49,580)( 50,579)( 51,578)( 52,577)( 53,576)( 54,575)( 55,574)( 56,573)
( 57,572)( 58,571)( 59,570)( 60,569)( 61,568)( 62,567)( 63,566)( 64,565)
( 65,564)( 66,563)( 67,562)( 68,561)( 69,560)( 70,559)( 71,558)( 72,557)
( 73,556)( 74,555)( 75,554)( 76,553)( 77,552)( 78,551)( 79,550)( 80,549)
( 81,548)( 82,547)( 83,546)( 84,545)( 85,544)( 86,543)( 87,542)( 88,541)
( 89,540)( 90,539)( 91,538)( 92,537)( 93,536)( 94,535)( 95,534)( 96,533)
( 97,532)( 98,531)( 99,530)(100,529)(101,528)(102,527)(103,526)(104,525)
(105,524)(106,523)(107,522)(108,521)(109,520)(110,519)(111,518)(112,517)
(113,516)(114,515)(115,514)(116,513)(117,512)(118,511)(119,510)(120,509)
(121,508)(122,507)(123,506)(124,505)(125,504)(126,503)(127,502)(128,501)
(129,500)(130,499)(131,498)(132,497)(133,496)(134,495)(135,494)(136,493)
(137,492)(138,491)(139,490)(140,489)(141,488)(142,487)(143,486)(144,485)
(145,484)(146,483)(147,482)(148,481)(149,480)(150,479)(151,478)(152,477)
(153,476)(154,475)(155,474)(156,473)(157,472)(158,471)(159,470)(160,469)
(161,468)(162,467)(163,466)(164,465)(165,464)(166,463)(167,462)(168,461)
(169,460)(170,459)(171,458)(172,457)(173,456)(174,455)(175,454)(176,453)
(177,452)(178,451)(179,450)(180,449)(181,448)(182,447)(183,446)(184,445)
(185,444)(186,443)(187,442)(188,441)(189,440)(190,439)(191,438)(192,437)
(193,436)(194,435)(195,434)(196,433)(197,432)(198,431)(199,430)(200,429)
(201,428)(202,427)(203,426)(204,425)(205,424)(206,423)(207,422)(208,421)
(209,420)(210,419)(211,418)(212,417)(213,416)(214,415)(215,414)(216,413)
(217,412)(218,411)(219,410)(220,409)(221,408)(222,407)(223,406)(224,405)
(225,404)(226,403)(227,402)(228,401)(229,400)(230,399)(231,398)(232,397)
(233,396)(234,395)(235,394)(236,393)(237,392)(238,391)(239,390)(240,389)
(241,388)(242,387)(243,386)(244,385)(245,384)(246,383)(247,382)(248,381)
(249,380)(250,379)(251,378)(252,377)(253,376)(254,375)(255,374)(256,373)
(257,372)(258,371)(259,370)(260,369)(261,368)(262,367)(263,366)(264,365)
(265,364)(266,363)(267,362)(268,361)(269,360)(270,359)(271,358)(272,357)
(273,356)(274,355)(275,354)(276,353)(277,352)(278,351)(279,350)(280,349)
(281,348)(282,347)(283,346)(284,345)(285,344)(286,343)(287,342)(288,341)
(289,340)(290,339)(291,338)(292,337)(293,336)(294,335)(295,334)(296,333)
(297,332)(298,331)(299,330)(300,329)(301,328)(302,327)(303,326)(304,325)
(305,324)(306,323)(307,322)(308,321)(309,320)(310,319)(311,318)(312,317)
(313,316);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(626)!(  2,313)(  3,312)(  4,311)(  5,310)(  6,309)(  7,308)(  8,307)
(  9,306)( 10,305)( 11,304)( 12,303)( 13,302)( 14,301)( 15,300)( 16,299)
( 17,298)( 18,297)( 19,296)( 20,295)( 21,294)( 22,293)( 23,292)( 24,291)
( 25,290)( 26,289)( 27,288)( 28,287)( 29,286)( 30,285)( 31,284)( 32,283)
( 33,282)( 34,281)( 35,280)( 36,279)( 37,278)( 38,277)( 39,276)( 40,275)
( 41,274)( 42,273)( 43,272)( 44,271)( 45,270)( 46,269)( 47,268)( 48,267)
( 49,266)( 50,265)( 51,264)( 52,263)( 53,262)( 54,261)( 55,260)( 56,259)
( 57,258)( 58,257)( 59,256)( 60,255)( 61,254)( 62,253)( 63,252)( 64,251)
( 65,250)( 66,249)( 67,248)( 68,247)( 69,246)( 70,245)( 71,244)( 72,243)
( 73,242)( 74,241)( 75,240)( 76,239)( 77,238)( 78,237)( 79,236)( 80,235)
( 81,234)( 82,233)( 83,232)( 84,231)( 85,230)( 86,229)( 87,228)( 88,227)
( 89,226)( 90,225)( 91,224)( 92,223)( 93,222)( 94,221)( 95,220)( 96,219)
( 97,218)( 98,217)( 99,216)(100,215)(101,214)(102,213)(103,212)(104,211)
(105,210)(106,209)(107,208)(108,207)(109,206)(110,205)(111,204)(112,203)
(113,202)(114,201)(115,200)(116,199)(117,198)(118,197)(119,196)(120,195)
(121,194)(122,193)(123,192)(124,191)(125,190)(126,189)(127,188)(128,187)
(129,186)(130,185)(131,184)(132,183)(133,182)(134,181)(135,180)(136,179)
(137,178)(138,177)(139,176)(140,175)(141,174)(142,173)(143,172)(144,171)
(145,170)(146,169)(147,168)(148,167)(149,166)(150,165)(151,164)(152,163)
(153,162)(154,161)(155,160)(156,159)(157,158)(315,626)(316,625)(317,624)
(318,623)(319,622)(320,621)(321,620)(322,619)(323,618)(324,617)(325,616)
(326,615)(327,614)(328,613)(329,612)(330,611)(331,610)(332,609)(333,608)
(334,607)(335,606)(336,605)(337,604)(338,603)(339,602)(340,601)(341,600)
(342,599)(343,598)(344,597)(345,596)(346,595)(347,594)(348,593)(349,592)
(350,591)(351,590)(352,589)(353,588)(354,587)(355,586)(356,585)(357,584)
(358,583)(359,582)(360,581)(361,580)(362,579)(363,578)(364,577)(365,576)
(366,575)(367,574)(368,573)(369,572)(370,571)(371,570)(372,569)(373,568)
(374,567)(375,566)(376,565)(377,564)(378,563)(379,562)(380,561)(381,560)
(382,559)(383,558)(384,557)(385,556)(386,555)(387,554)(388,553)(389,552)
(390,551)(391,550)(392,549)(393,548)(394,547)(395,546)(396,545)(397,544)
(398,543)(399,542)(400,541)(401,540)(402,539)(403,538)(404,537)(405,536)
(406,535)(407,534)(408,533)(409,532)(410,531)(411,530)(412,529)(413,528)
(414,527)(415,526)(416,525)(417,524)(418,523)(419,522)(420,521)(421,520)
(422,519)(423,518)(424,517)(425,516)(426,515)(427,514)(428,513)(429,512)
(430,511)(431,510)(432,509)(433,508)(434,507)(435,506)(436,505)(437,504)
(438,503)(439,502)(440,501)(441,500)(442,499)(443,498)(444,497)(445,496)
(446,495)(447,494)(448,493)(449,492)(450,491)(451,490)(452,489)(453,488)
(454,487)(455,486)(456,485)(457,484)(458,483)(459,482)(460,481)(461,480)
(462,479)(463,478)(464,477)(465,476)(466,475)(467,474)(468,473)(469,472)
(470,471);
s1 := Sym(626)!(  1,315)(  2,314)(  3,626)(  4,625)(  5,624)(  6,623)(  7,622)
(  8,621)(  9,620)( 10,619)( 11,618)( 12,617)( 13,616)( 14,615)( 15,614)
( 16,613)( 17,612)( 18,611)( 19,610)( 20,609)( 21,608)( 22,607)( 23,606)
( 24,605)( 25,604)( 26,603)( 27,602)( 28,601)( 29,600)( 30,599)( 31,598)
( 32,597)( 33,596)( 34,595)( 35,594)( 36,593)( 37,592)( 38,591)( 39,590)
( 40,589)( 41,588)( 42,587)( 43,586)( 44,585)( 45,584)( 46,583)( 47,582)
( 48,581)( 49,580)( 50,579)( 51,578)( 52,577)( 53,576)( 54,575)( 55,574)
( 56,573)( 57,572)( 58,571)( 59,570)( 60,569)( 61,568)( 62,567)( 63,566)
( 64,565)( 65,564)( 66,563)( 67,562)( 68,561)( 69,560)( 70,559)( 71,558)
( 72,557)( 73,556)( 74,555)( 75,554)( 76,553)( 77,552)( 78,551)( 79,550)
( 80,549)( 81,548)( 82,547)( 83,546)( 84,545)( 85,544)( 86,543)( 87,542)
( 88,541)( 89,540)( 90,539)( 91,538)( 92,537)( 93,536)( 94,535)( 95,534)
( 96,533)( 97,532)( 98,531)( 99,530)(100,529)(101,528)(102,527)(103,526)
(104,525)(105,524)(106,523)(107,522)(108,521)(109,520)(110,519)(111,518)
(112,517)(113,516)(114,515)(115,514)(116,513)(117,512)(118,511)(119,510)
(120,509)(121,508)(122,507)(123,506)(124,505)(125,504)(126,503)(127,502)
(128,501)(129,500)(130,499)(131,498)(132,497)(133,496)(134,495)(135,494)
(136,493)(137,492)(138,491)(139,490)(140,489)(141,488)(142,487)(143,486)
(144,485)(145,484)(146,483)(147,482)(148,481)(149,480)(150,479)(151,478)
(152,477)(153,476)(154,475)(155,474)(156,473)(157,472)(158,471)(159,470)
(160,469)(161,468)(162,467)(163,466)(164,465)(165,464)(166,463)(167,462)
(168,461)(169,460)(170,459)(171,458)(172,457)(173,456)(174,455)(175,454)
(176,453)(177,452)(178,451)(179,450)(180,449)(181,448)(182,447)(183,446)
(184,445)(185,444)(186,443)(187,442)(188,441)(189,440)(190,439)(191,438)
(192,437)(193,436)(194,435)(195,434)(196,433)(197,432)(198,431)(199,430)
(200,429)(201,428)(202,427)(203,426)(204,425)(205,424)(206,423)(207,422)
(208,421)(209,420)(210,419)(211,418)(212,417)(213,416)(214,415)(215,414)
(216,413)(217,412)(218,411)(219,410)(220,409)(221,408)(222,407)(223,406)
(224,405)(225,404)(226,403)(227,402)(228,401)(229,400)(230,399)(231,398)
(232,397)(233,396)(234,395)(235,394)(236,393)(237,392)(238,391)(239,390)
(240,389)(241,388)(242,387)(243,386)(244,385)(245,384)(246,383)(247,382)
(248,381)(249,380)(250,379)(251,378)(252,377)(253,376)(254,375)(255,374)
(256,373)(257,372)(258,371)(259,370)(260,369)(261,368)(262,367)(263,366)
(264,365)(265,364)(266,363)(267,362)(268,361)(269,360)(270,359)(271,358)
(272,357)(273,356)(274,355)(275,354)(276,353)(277,352)(278,351)(279,350)
(280,349)(281,348)(282,347)(283,346)(284,345)(285,344)(286,343)(287,342)
(288,341)(289,340)(290,339)(291,338)(292,337)(293,336)(294,335)(295,334)
(296,333)(297,332)(298,331)(299,330)(300,329)(301,328)(302,327)(303,326)
(304,325)(305,324)(306,323)(307,322)(308,321)(309,320)(310,319)(311,318)
(312,317)(313,316);
poly := sub<Sym(626)|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 >;

References : None.
to this polytope