Polytope of Type {674}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {674}*1348
Also Known As : 674-gon, {674}. if this polytope has another name.
Group : SmallGroup(1348,4)
Rank : 2
Schlafli Type : {674}
Number of vertices, edges, etc : 674, 674
Order of s₀s₁ : 674
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 : {337}*674
   337-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope