Polytope of Type {638}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {638}*1276
Also Known As : 638-gon, {638}. if this polytope has another name.
Group : SmallGroup(1276,10)
Rank : 2
Schlafli Type : {638}
Number of vertices, edges, etc : 638, 638
Order of s₀s₁ : 638
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 : {319}*638
   11-fold quotients : {58}*116
   22-fold quotients : {29}*58
   29-fold quotients : {22}*44
   58-fold quotients : {11}*22
   319-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 29)(  3, 28)(  4, 27)(  5, 26)(  6, 25)(  7, 24)(  8, 23)(  9, 22)
( 10, 21)( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 30,291)( 31,319)
( 32,318)( 33,317)( 34,316)( 35,315)( 36,314)( 37,313)( 38,312)( 39,311)
( 40,310)( 41,309)( 42,308)( 43,307)( 44,306)( 45,305)( 46,304)( 47,303)
( 48,302)( 49,301)( 50,300)( 51,299)( 52,298)( 53,297)( 54,296)( 55,295)
( 56,294)( 57,293)( 58,292)( 59,262)( 60,290)( 61,289)( 62,288)( 63,287)
( 64,286)( 65,285)( 66,284)( 67,283)( 68,282)( 69,281)( 70,280)( 71,279)
( 72,278)( 73,277)( 74,276)( 75,275)( 76,274)( 77,273)( 78,272)( 79,271)
( 80,270)( 81,269)( 82,268)( 83,267)( 84,266)( 85,265)( 86,264)( 87,263)
( 88,233)( 89,261)( 90,260)( 91,259)( 92,258)( 93,257)( 94,256)( 95,255)
( 96,254)( 97,253)( 98,252)( 99,251)(100,250)(101,249)(102,248)(103,247)
(104,246)(105,245)(106,244)(107,243)(108,242)(109,241)(110,240)(111,239)
(112,238)(113,237)(114,236)(115,235)(116,234)(117,204)(118,232)(119,231)
(120,230)(121,229)(122,228)(123,227)(124,226)(125,225)(126,224)(127,223)
(128,222)(129,221)(130,220)(131,219)(132,218)(133,217)(134,216)(135,215)
(136,214)(137,213)(138,212)(139,211)(140,210)(141,209)(142,208)(143,207)
(144,206)(145,205)(146,175)(147,203)(148,202)(149,201)(150,200)(151,199)
(152,198)(153,197)(154,196)(155,195)(156,194)(157,193)(158,192)(159,191)
(160,190)(161,189)(162,188)(163,187)(164,186)(165,185)(166,184)(167,183)
(168,182)(169,181)(170,180)(171,179)(172,178)(173,177)(174,176)(321,348)
(322,347)(323,346)(324,345)(325,344)(326,343)(327,342)(328,341)(329,340)
(330,339)(331,338)(332,337)(333,336)(334,335)(349,610)(350,638)(351,637)
(352,636)(353,635)(354,634)(355,633)(356,632)(357,631)(358,630)(359,629)
(360,628)(361,627)(362,626)(363,625)(364,624)(365,623)(366,622)(367,621)
(368,620)(369,619)(370,618)(371,617)(372,616)(373,615)(374,614)(375,613)
(376,612)(377,611)(378,581)(379,609)(380,608)(381,607)(382,606)(383,605)
(384,604)(385,603)(386,602)(387,601)(388,600)(389,599)(390,598)(391,597)
(392,596)(393,595)(394,594)(395,593)(396,592)(397,591)(398,590)(399,589)
(400,588)(401,587)(402,586)(403,585)(404,584)(405,583)(406,582)(407,552)
(408,580)(409,579)(410,578)(411,577)(412,576)(413,575)(414,574)(415,573)
(416,572)(417,571)(418,570)(419,569)(420,568)(421,567)(422,566)(423,565)
(424,564)(425,563)(426,562)(427,561)(428,560)(429,559)(430,558)(431,557)
(432,556)(433,555)(434,554)(435,553)(436,523)(437,551)(438,550)(439,549)
(440,548)(441,547)(442,546)(443,545)(444,544)(445,543)(446,542)(447,541)
(448,540)(449,539)(450,538)(451,537)(452,536)(453,535)(454,534)(455,533)
(456,532)(457,531)(458,530)(459,529)(460,528)(461,527)(462,526)(463,525)
(464,524)(465,494)(466,522)(467,521)(468,520)(469,519)(470,518)(471,517)
(472,516)(473,515)(474,514)(475,513)(476,512)(477,511)(478,510)(479,509)
(480,508)(481,507)(482,506)(483,505)(484,504)(485,503)(486,502)(487,501)
(488,500)(489,499)(490,498)(491,497)(492,496)(493,495);;
s1 := (  1,350)(  2,349)(  3,377)(  4,376)(  5,375)(  6,374)(  7,373)(  8,372)
(  9,371)( 10,370)( 11,369)( 12,368)( 13,367)( 14,366)( 15,365)( 16,364)
( 17,363)( 18,362)( 19,361)( 20,360)( 21,359)( 22,358)( 23,357)( 24,356)
( 25,355)( 26,354)( 27,353)( 28,352)( 29,351)( 30,321)( 31,320)( 32,348)
( 33,347)( 34,346)( 35,345)( 36,344)( 37,343)( 38,342)( 39,341)( 40,340)
( 41,339)( 42,338)( 43,337)( 44,336)( 45,335)( 46,334)( 47,333)( 48,332)
( 49,331)( 50,330)( 51,329)( 52,328)( 53,327)( 54,326)( 55,325)( 56,324)
( 57,323)( 58,322)( 59,611)( 60,610)( 61,638)( 62,637)( 63,636)( 64,635)
( 65,634)( 66,633)( 67,632)( 68,631)( 69,630)( 70,629)( 71,628)( 72,627)
( 73,626)( 74,625)( 75,624)( 76,623)( 77,622)( 78,621)( 79,620)( 80,619)
( 81,618)( 82,617)( 83,616)( 84,615)( 85,614)( 86,613)( 87,612)( 88,582)
( 89,581)( 90,609)( 91,608)( 92,607)( 93,606)( 94,605)( 95,604)( 96,603)
( 97,602)( 98,601)( 99,600)(100,599)(101,598)(102,597)(103,596)(104,595)
(105,594)(106,593)(107,592)(108,591)(109,590)(110,589)(111,588)(112,587)
(113,586)(114,585)(115,584)(116,583)(117,553)(118,552)(119,580)(120,579)
(121,578)(122,577)(123,576)(124,575)(125,574)(126,573)(127,572)(128,571)
(129,570)(130,569)(131,568)(132,567)(133,566)(134,565)(135,564)(136,563)
(137,562)(138,561)(139,560)(140,559)(141,558)(142,557)(143,556)(144,555)
(145,554)(146,524)(147,523)(148,551)(149,550)(150,549)(151,548)(152,547)
(153,546)(154,545)(155,544)(156,543)(157,542)(158,541)(159,540)(160,539)
(161,538)(162,537)(163,536)(164,535)(165,534)(166,533)(167,532)(168,531)
(169,530)(170,529)(171,528)(172,527)(173,526)(174,525)(175,495)(176,494)
(177,522)(178,521)(179,520)(180,519)(181,518)(182,517)(183,516)(184,515)
(185,514)(186,513)(187,512)(188,511)(189,510)(190,509)(191,508)(192,507)
(193,506)(194,505)(195,504)(196,503)(197,502)(198,501)(199,500)(200,499)
(201,498)(202,497)(203,496)(204,466)(205,465)(206,493)(207,492)(208,491)
(209,490)(210,489)(211,488)(212,487)(213,486)(214,485)(215,484)(216,483)
(217,482)(218,481)(219,480)(220,479)(221,478)(222,477)(223,476)(224,475)
(225,474)(226,473)(227,472)(228,471)(229,470)(230,469)(231,468)(232,467)
(233,437)(234,436)(235,464)(236,463)(237,462)(238,461)(239,460)(240,459)
(241,458)(242,457)(243,456)(244,455)(245,454)(246,453)(247,452)(248,451)
(249,450)(250,449)(251,448)(252,447)(253,446)(254,445)(255,444)(256,443)
(257,442)(258,441)(259,440)(260,439)(261,438)(262,408)(263,407)(264,435)
(265,434)(266,433)(267,432)(268,431)(269,430)(270,429)(271,428)(272,427)
(273,426)(274,425)(275,424)(276,423)(277,422)(278,421)(279,420)(280,419)
(281,418)(282,417)(283,416)(284,415)(285,414)(286,413)(287,412)(288,411)
(289,410)(290,409)(291,379)(292,378)(293,406)(294,405)(295,404)(296,403)
(297,402)(298,401)(299,400)(300,399)(301,398)(302,397)(303,396)(304,395)
(305,394)(306,393)(307,392)(308,391)(309,390)(310,389)(311,388)(312,387)
(313,386)(314,385)(315,384)(316,383)(317,382)(318,381)(319,380);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope