Polytope of Type {670}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {670}*1340
Also Known As : 670-gon, {670}. if this polytope has another name.
Group : SmallGroup(1340,10)
Rank : 2
Schlafli Type : {670}
Number of vertices, edges, etc : 670, 670
Order of s₀s₁ : 670
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 : {335}*670
   5-fold quotients : {134}*268
   10-fold quotients : {67}*134
   67-fold quotients : {10}*20
   134-fold quotients : {5}*10
   335-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope