Polytope of Type {634}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {634}*1268
Also Known As : 634-gon, {634}. if this polytope has another name.
Group : SmallGroup(1268,4)
Rank : 2
Schlafli Type : {634}
Number of vertices, edges, etc : 634, 634
Order of s₀s₁ : 634
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 : {317}*634
   317-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,317)(  3,316)(  4,315)(  5,314)(  6,313)(  7,312)(  8,311)(  9,310)
( 10,309)( 11,308)( 12,307)( 13,306)( 14,305)( 15,304)( 16,303)( 17,302)
( 18,301)( 19,300)( 20,299)( 21,298)( 22,297)( 23,296)( 24,295)( 25,294)
( 26,293)( 27,292)( 28,291)( 29,290)( 30,289)( 31,288)( 32,287)( 33,286)
( 34,285)( 35,284)( 36,283)( 37,282)( 38,281)( 39,280)( 40,279)( 41,278)
( 42,277)( 43,276)( 44,275)( 45,274)( 46,273)( 47,272)( 48,271)( 49,270)
( 50,269)( 51,268)( 52,267)( 53,266)( 54,265)( 55,264)( 56,263)( 57,262)
( 58,261)( 59,260)( 60,259)( 61,258)( 62,257)( 63,256)( 64,255)( 65,254)
( 66,253)( 67,252)( 68,251)( 69,250)( 70,249)( 71,248)( 72,247)( 73,246)
( 74,245)( 75,244)( 76,243)( 77,242)( 78,241)( 79,240)( 80,239)( 81,238)
( 82,237)( 83,236)( 84,235)( 85,234)( 86,233)( 87,232)( 88,231)( 89,230)
( 90,229)( 91,228)( 92,227)( 93,226)( 94,225)( 95,224)( 96,223)( 97,222)
( 98,221)( 99,220)(100,219)(101,218)(102,217)(103,216)(104,215)(105,214)
(106,213)(107,212)(108,211)(109,210)(110,209)(111,208)(112,207)(113,206)
(114,205)(115,204)(116,203)(117,202)(118,201)(119,200)(120,199)(121,198)
(122,197)(123,196)(124,195)(125,194)(126,193)(127,192)(128,191)(129,190)
(130,189)(131,188)(132,187)(133,186)(134,185)(135,184)(136,183)(137,182)
(138,181)(139,180)(140,179)(141,178)(142,177)(143,176)(144,175)(145,174)
(146,173)(147,172)(148,171)(149,170)(150,169)(151,168)(152,167)(153,166)
(154,165)(155,164)(156,163)(157,162)(158,161)(159,160)(319,634)(320,633)
(321,632)(322,631)(323,630)(324,629)(325,628)(326,627)(327,626)(328,625)
(329,624)(330,623)(331,622)(332,621)(333,620)(334,619)(335,618)(336,617)
(337,616)(338,615)(339,614)(340,613)(341,612)(342,611)(343,610)(344,609)
(345,608)(346,607)(347,606)(348,605)(349,604)(350,603)(351,602)(352,601)
(353,600)(354,599)(355,598)(356,597)(357,596)(358,595)(359,594)(360,593)
(361,592)(362,591)(363,590)(364,589)(365,588)(366,587)(367,586)(368,585)
(369,584)(370,583)(371,582)(372,581)(373,580)(374,579)(375,578)(376,577)
(377,576)(378,575)(379,574)(380,573)(381,572)(382,571)(383,570)(384,569)
(385,568)(386,567)(387,566)(388,565)(389,564)(390,563)(391,562)(392,561)
(393,560)(394,559)(395,558)(396,557)(397,556)(398,555)(399,554)(400,553)
(401,552)(402,551)(403,550)(404,549)(405,548)(406,547)(407,546)(408,545)
(409,544)(410,543)(411,542)(412,541)(413,540)(414,539)(415,538)(416,537)
(417,536)(418,535)(419,534)(420,533)(421,532)(422,531)(423,530)(424,529)
(425,528)(426,527)(427,526)(428,525)(429,524)(430,523)(431,522)(432,521)
(433,520)(434,519)(435,518)(436,517)(437,516)(438,515)(439,514)(440,513)
(441,512)(442,511)(443,510)(444,509)(445,508)(446,507)(447,506)(448,505)
(449,504)(450,503)(451,502)(452,501)(453,500)(454,499)(455,498)(456,497)
(457,496)(458,495)(459,494)(460,493)(461,492)(462,491)(463,490)(464,489)
(465,488)(466,487)(467,486)(468,485)(469,484)(470,483)(471,482)(472,481)
(473,480)(474,479)(475,478)(476,477);;
s1 := (  1,319)(  2,318)(  3,634)(  4,633)(  5,632)(  6,631)(  7,630)(  8,629)
(  9,628)( 10,627)( 11,626)( 12,625)( 13,624)( 14,623)( 15,622)( 16,621)
( 17,620)( 18,619)( 19,618)( 20,617)( 21,616)( 22,615)( 23,614)( 24,613)
( 25,612)( 26,611)( 27,610)( 28,609)( 29,608)( 30,607)( 31,606)( 32,605)
( 33,604)( 34,603)( 35,602)( 36,601)( 37,600)( 38,599)( 39,598)( 40,597)
( 41,596)( 42,595)( 43,594)( 44,593)( 45,592)( 46,591)( 47,590)( 48,589)
( 49,588)( 50,587)( 51,586)( 52,585)( 53,584)( 54,583)( 55,582)( 56,581)
( 57,580)( 58,579)( 59,578)( 60,577)( 61,576)( 62,575)( 63,574)( 64,573)
( 65,572)( 66,571)( 67,570)( 68,569)( 69,568)( 70,567)( 71,566)( 72,565)
( 73,564)( 74,563)( 75,562)( 76,561)( 77,560)( 78,559)( 79,558)( 80,557)
( 81,556)( 82,555)( 83,554)( 84,553)( 85,552)( 86,551)( 87,550)( 88,549)
( 89,548)( 90,547)( 91,546)( 92,545)( 93,544)( 94,543)( 95,542)( 96,541)
( 97,540)( 98,539)( 99,538)(100,537)(101,536)(102,535)(103,534)(104,533)
(105,532)(106,531)(107,530)(108,529)(109,528)(110,527)(111,526)(112,525)
(113,524)(114,523)(115,522)(116,521)(117,520)(118,519)(119,518)(120,517)
(121,516)(122,515)(123,514)(124,513)(125,512)(126,511)(127,510)(128,509)
(129,508)(130,507)(131,506)(132,505)(133,504)(134,503)(135,502)(136,501)
(137,500)(138,499)(139,498)(140,497)(141,496)(142,495)(143,494)(144,493)
(145,492)(146,491)(147,490)(148,489)(149,488)(150,487)(151,486)(152,485)
(153,484)(154,483)(155,482)(156,481)(157,480)(158,479)(159,478)(160,477)
(161,476)(162,475)(163,474)(164,473)(165,472)(166,471)(167,470)(168,469)
(169,468)(170,467)(171,466)(172,465)(173,464)(174,463)(175,462)(176,461)
(177,460)(178,459)(179,458)(180,457)(181,456)(182,455)(183,454)(184,453)
(185,452)(186,451)(187,450)(188,449)(189,448)(190,447)(191,446)(192,445)
(193,444)(194,443)(195,442)(196,441)(197,440)(198,439)(199,438)(200,437)
(201,436)(202,435)(203,434)(204,433)(205,432)(206,431)(207,430)(208,429)
(209,428)(210,427)(211,426)(212,425)(213,424)(214,423)(215,422)(216,421)
(217,420)(218,419)(219,418)(220,417)(221,416)(222,415)(223,414)(224,413)
(225,412)(226,411)(227,410)(228,409)(229,408)(230,407)(231,406)(232,405)
(233,404)(234,403)(235,402)(236,401)(237,400)(238,399)(239,398)(240,397)
(241,396)(242,395)(243,394)(244,393)(245,392)(246,391)(247,390)(248,389)
(249,388)(250,387)(251,386)(252,385)(253,384)(254,383)(255,382)(256,381)
(257,380)(258,379)(259,378)(260,377)(261,376)(262,375)(263,374)(264,373)
(265,372)(266,371)(267,370)(268,369)(269,368)(270,367)(271,366)(272,365)
(273,364)(274,363)(275,362)(276,361)(277,360)(278,359)(279,358)(280,357)
(281,356)(282,355)(283,354)(284,353)(285,352)(286,351)(287,350)(288,349)
(289,348)(290,347)(291,346)(292,345)(293,344)(294,343)(295,342)(296,341)
(297,340)(298,339)(299,338)(300,337)(301,336)(302,335)(303,334)(304,333)
(305,332)(306,331)(307,330)(308,329)(309,328)(310,327)(311,326)(312,325)
(313,324)(314,323)(315,322)(316,321)(317,320);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(634)!(  2,317)(  3,316)(  4,315)(  5,314)(  6,313)(  7,312)(  8,311)
(  9,310)( 10,309)( 11,308)( 12,307)( 13,306)( 14,305)( 15,304)( 16,303)
( 17,302)( 18,301)( 19,300)( 20,299)( 21,298)( 22,297)( 23,296)( 24,295)
( 25,294)( 26,293)( 27,292)( 28,291)( 29,290)( 30,289)( 31,288)( 32,287)
( 33,286)( 34,285)( 35,284)( 36,283)( 37,282)( 38,281)( 39,280)( 40,279)
( 41,278)( 42,277)( 43,276)( 44,275)( 45,274)( 46,273)( 47,272)( 48,271)
( 49,270)( 50,269)( 51,268)( 52,267)( 53,266)( 54,265)( 55,264)( 56,263)
( 57,262)( 58,261)( 59,260)( 60,259)( 61,258)( 62,257)( 63,256)( 64,255)
( 65,254)( 66,253)( 67,252)( 68,251)( 69,250)( 70,249)( 71,248)( 72,247)
( 73,246)( 74,245)( 75,244)( 76,243)( 77,242)( 78,241)( 79,240)( 80,239)
( 81,238)( 82,237)( 83,236)( 84,235)( 85,234)( 86,233)( 87,232)( 88,231)
( 89,230)( 90,229)( 91,228)( 92,227)( 93,226)( 94,225)( 95,224)( 96,223)
( 97,222)( 98,221)( 99,220)(100,219)(101,218)(102,217)(103,216)(104,215)
(105,214)(106,213)(107,212)(108,211)(109,210)(110,209)(111,208)(112,207)
(113,206)(114,205)(115,204)(116,203)(117,202)(118,201)(119,200)(120,199)
(121,198)(122,197)(123,196)(124,195)(125,194)(126,193)(127,192)(128,191)
(129,190)(130,189)(131,188)(132,187)(133,186)(134,185)(135,184)(136,183)
(137,182)(138,181)(139,180)(140,179)(141,178)(142,177)(143,176)(144,175)
(145,174)(146,173)(147,172)(148,171)(149,170)(150,169)(151,168)(152,167)
(153,166)(154,165)(155,164)(156,163)(157,162)(158,161)(159,160)(319,634)
(320,633)(321,632)(322,631)(323,630)(324,629)(325,628)(326,627)(327,626)
(328,625)(329,624)(330,623)(331,622)(332,621)(333,620)(334,619)(335,618)
(336,617)(337,616)(338,615)(339,614)(340,613)(341,612)(342,611)(343,610)
(344,609)(345,608)(346,607)(347,606)(348,605)(349,604)(350,603)(351,602)
(352,601)(353,600)(354,599)(355,598)(356,597)(357,596)(358,595)(359,594)
(360,593)(361,592)(362,591)(363,590)(364,589)(365,588)(366,587)(367,586)
(368,585)(369,584)(370,583)(371,582)(372,581)(373,580)(374,579)(375,578)
(376,577)(377,576)(378,575)(379,574)(380,573)(381,572)(382,571)(383,570)
(384,569)(385,568)(386,567)(387,566)(388,565)(389,564)(390,563)(391,562)
(392,561)(393,560)(394,559)(395,558)(396,557)(397,556)(398,555)(399,554)
(400,553)(401,552)(402,551)(403,550)(404,549)(405,548)(406,547)(407,546)
(408,545)(409,544)(410,543)(411,542)(412,541)(413,540)(414,539)(415,538)
(416,537)(417,536)(418,535)(419,534)(420,533)(421,532)(422,531)(423,530)
(424,529)(425,528)(426,527)(427,526)(428,525)(429,524)(430,523)(431,522)
(432,521)(433,520)(434,519)(435,518)(436,517)(437,516)(438,515)(439,514)
(440,513)(441,512)(442,511)(443,510)(444,509)(445,508)(446,507)(447,506)
(448,505)(449,504)(450,503)(451,502)(452,501)(453,500)(454,499)(455,498)
(456,497)(457,496)(458,495)(459,494)(460,493)(461,492)(462,491)(463,490)
(464,489)(465,488)(466,487)(467,486)(468,485)(469,484)(470,483)(471,482)
(472,481)(473,480)(474,479)(475,478)(476,477);
s1 := Sym(634)!(  1,319)(  2,318)(  3,634)(  4,633)(  5,632)(  6,631)(  7,630)
(  8,629)(  9,628)( 10,627)( 11,626)( 12,625)( 13,624)( 14,623)( 15,622)
( 16,621)( 17,620)( 18,619)( 19,618)( 20,617)( 21,616)( 22,615)( 23,614)
( 24,613)( 25,612)( 26,611)( 27,610)( 28,609)( 29,608)( 30,607)( 31,606)
( 32,605)( 33,604)( 34,603)( 35,602)( 36,601)( 37,600)( 38,599)( 39,598)
( 40,597)( 41,596)( 42,595)( 43,594)( 44,593)( 45,592)( 46,591)( 47,590)
( 48,589)( 49,588)( 50,587)( 51,586)( 52,585)( 53,584)( 54,583)( 55,582)
( 56,581)( 57,580)( 58,579)( 59,578)( 60,577)( 61,576)( 62,575)( 63,574)
( 64,573)( 65,572)( 66,571)( 67,570)( 68,569)( 69,568)( 70,567)( 71,566)
( 72,565)( 73,564)( 74,563)( 75,562)( 76,561)( 77,560)( 78,559)( 79,558)
( 80,557)( 81,556)( 82,555)( 83,554)( 84,553)( 85,552)( 86,551)( 87,550)
( 88,549)( 89,548)( 90,547)( 91,546)( 92,545)( 93,544)( 94,543)( 95,542)
( 96,541)( 97,540)( 98,539)( 99,538)(100,537)(101,536)(102,535)(103,534)
(104,533)(105,532)(106,531)(107,530)(108,529)(109,528)(110,527)(111,526)
(112,525)(113,524)(114,523)(115,522)(116,521)(117,520)(118,519)(119,518)
(120,517)(121,516)(122,515)(123,514)(124,513)(125,512)(126,511)(127,510)
(128,509)(129,508)(130,507)(131,506)(132,505)(133,504)(134,503)(135,502)
(136,501)(137,500)(138,499)(139,498)(140,497)(141,496)(142,495)(143,494)
(144,493)(145,492)(146,491)(147,490)(148,489)(149,488)(150,487)(151,486)
(152,485)(153,484)(154,483)(155,482)(156,481)(157,480)(158,479)(159,478)
(160,477)(161,476)(162,475)(163,474)(164,473)(165,472)(166,471)(167,470)
(168,469)(169,468)(170,467)(171,466)(172,465)(173,464)(174,463)(175,462)
(176,461)(177,460)(178,459)(179,458)(180,457)(181,456)(182,455)(183,454)
(184,453)(185,452)(186,451)(187,450)(188,449)(189,448)(190,447)(191,446)
(192,445)(193,444)(194,443)(195,442)(196,441)(197,440)(198,439)(199,438)
(200,437)(201,436)(202,435)(203,434)(204,433)(205,432)(206,431)(207,430)
(208,429)(209,428)(210,427)(211,426)(212,425)(213,424)(214,423)(215,422)
(216,421)(217,420)(218,419)(219,418)(220,417)(221,416)(222,415)(223,414)
(224,413)(225,412)(226,411)(227,410)(228,409)(229,408)(230,407)(231,406)
(232,405)(233,404)(234,403)(235,402)(236,401)(237,400)(238,399)(239,398)
(240,397)(241,396)(242,395)(243,394)(244,393)(245,392)(246,391)(247,390)
(248,389)(249,388)(250,387)(251,386)(252,385)(253,384)(254,383)(255,382)
(256,381)(257,380)(258,379)(259,378)(260,377)(261,376)(262,375)(263,374)
(264,373)(265,372)(266,371)(267,370)(268,369)(269,368)(270,367)(271,366)
(272,365)(273,364)(274,363)(275,362)(276,361)(277,360)(278,359)(279,358)
(280,357)(281,356)(282,355)(283,354)(284,353)(285,352)(286,351)(287,350)
(288,349)(289,348)(290,347)(291,346)(292,345)(293,344)(294,343)(295,342)
(296,341)(297,340)(298,339)(299,338)(300,337)(301,336)(302,335)(303,334)
(304,333)(305,332)(306,331)(307,330)(308,329)(309,328)(310,327)(311,326)
(312,325)(313,324)(314,323)(315,322)(316,321)(317,320);
poly := sub<Sym(634)|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 >;

References : None.
to this polytope