Polytope of Type {680}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {680}*1360
Also Known As : 680-gon, {680}. if this polytope has another name.
Group : SmallGroup(1360,71)
Rank : 2
Schlafli Type : {680}
Number of vertices, edges, etc : 680, 680
Order of s₀s₁ : 680
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 : {340}*680
   4-fold quotients : {170}*340
   5-fold quotients : {136}*272
   8-fold quotients : {85}*170
   10-fold quotients : {68}*136
   17-fold quotients : {40}*80
   20-fold quotients : {34}*68
   34-fold quotients : {20}*40
   40-fold quotients : {17}*34
   68-fold quotients : {10}*20
   85-fold quotients : {8}*16
   136-fold quotients : {5}*10
   170-fold quotients : {4}*8
   340-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 17)(  3, 16)(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)(  9, 10)
( 18, 69)( 19, 85)( 20, 84)( 21, 83)( 22, 82)( 23, 81)( 24, 80)( 25, 79)
( 26, 78)( 27, 77)( 28, 76)( 29, 75)( 30, 74)( 31, 73)( 32, 72)( 33, 71)
( 34, 70)( 35, 52)( 36, 68)( 37, 67)( 38, 66)( 39, 65)( 40, 64)( 41, 63)
( 42, 62)( 43, 61)( 44, 60)( 45, 59)( 46, 58)( 47, 57)( 48, 56)( 49, 55)
( 50, 54)( 51, 53)( 87,102)( 88,101)( 89,100)( 90, 99)( 91, 98)( 92, 97)
( 93, 96)( 94, 95)(103,154)(104,170)(105,169)(106,168)(107,167)(108,166)
(109,165)(110,164)(111,163)(112,162)(113,161)(114,160)(115,159)(116,158)
(117,157)(118,156)(119,155)(120,137)(121,153)(122,152)(123,151)(124,150)
(125,149)(126,148)(127,147)(128,146)(129,145)(130,144)(131,143)(132,142)
(133,141)(134,140)(135,139)(136,138)(171,256)(172,272)(173,271)(174,270)
(175,269)(176,268)(177,267)(178,266)(179,265)(180,264)(181,263)(182,262)
(183,261)(184,260)(185,259)(186,258)(187,257)(188,324)(189,340)(190,339)
(191,338)(192,337)(193,336)(194,335)(195,334)(196,333)(197,332)(198,331)
(199,330)(200,329)(201,328)(202,327)(203,326)(204,325)(205,307)(206,323)
(207,322)(208,321)(209,320)(210,319)(211,318)(212,317)(213,316)(214,315)
(215,314)(216,313)(217,312)(218,311)(219,310)(220,309)(221,308)(222,290)
(223,306)(224,305)(225,304)(226,303)(227,302)(228,301)(229,300)(230,299)
(231,298)(232,297)(233,296)(234,295)(235,294)(236,293)(237,292)(238,291)
(239,273)(240,289)(241,288)(242,287)(243,286)(244,285)(245,284)(246,283)
(247,282)(248,281)(249,280)(250,279)(251,278)(252,277)(253,276)(254,275)
(255,274)(341,511)(342,527)(343,526)(344,525)(345,524)(346,523)(347,522)
(348,521)(349,520)(350,519)(351,518)(352,517)(353,516)(354,515)(355,514)
(356,513)(357,512)(358,579)(359,595)(360,594)(361,593)(362,592)(363,591)
(364,590)(365,589)(366,588)(367,587)(368,586)(369,585)(370,584)(371,583)
(372,582)(373,581)(374,580)(375,562)(376,578)(377,577)(378,576)(379,575)
(380,574)(381,573)(382,572)(383,571)(384,570)(385,569)(386,568)(387,567)
(388,566)(389,565)(390,564)(391,563)(392,545)(393,561)(394,560)(395,559)
(396,558)(397,557)(398,556)(399,555)(400,554)(401,553)(402,552)(403,551)
(404,550)(405,549)(406,548)(407,547)(408,546)(409,528)(410,544)(411,543)
(412,542)(413,541)(414,540)(415,539)(416,538)(417,537)(418,536)(419,535)
(420,534)(421,533)(422,532)(423,531)(424,530)(425,529)(426,596)(427,612)
(428,611)(429,610)(430,609)(431,608)(432,607)(433,606)(434,605)(435,604)
(436,603)(437,602)(438,601)(439,600)(440,599)(441,598)(442,597)(443,664)
(444,680)(445,679)(446,678)(447,677)(448,676)(449,675)(450,674)(451,673)
(452,672)(453,671)(454,670)(455,669)(456,668)(457,667)(458,666)(459,665)
(460,647)(461,663)(462,662)(463,661)(464,660)(465,659)(466,658)(467,657)
(468,656)(469,655)(470,654)(471,653)(472,652)(473,651)(474,650)(475,649)
(476,648)(477,630)(478,646)(479,645)(480,644)(481,643)(482,642)(483,641)
(484,640)(485,639)(486,638)(487,637)(488,636)(489,635)(490,634)(491,633)
(492,632)(493,631)(494,613)(495,629)(496,628)(497,627)(498,626)(499,625)
(500,624)(501,623)(502,622)(503,621)(504,620)(505,619)(506,618)(507,617)
(508,616)(509,615)(510,614);;
s1 := (  1,359)(  2,358)(  3,374)(  4,373)(  5,372)(  6,371)(  7,370)(  8,369)
(  9,368)( 10,367)( 11,366)( 12,365)( 13,364)( 14,363)( 15,362)( 16,361)
( 17,360)( 18,342)( 19,341)( 20,357)( 21,356)( 22,355)( 23,354)( 24,353)
( 25,352)( 26,351)( 27,350)( 28,349)( 29,348)( 30,347)( 31,346)( 32,345)
( 33,344)( 34,343)( 35,410)( 36,409)( 37,425)( 38,424)( 39,423)( 40,422)
( 41,421)( 42,420)( 43,419)( 44,418)( 45,417)( 46,416)( 47,415)( 48,414)
( 49,413)( 50,412)( 51,411)( 52,393)( 53,392)( 54,408)( 55,407)( 56,406)
( 57,405)( 58,404)( 59,403)( 60,402)( 61,401)( 62,400)( 63,399)( 64,398)
( 65,397)( 66,396)( 67,395)( 68,394)( 69,376)( 70,375)( 71,391)( 72,390)
( 73,389)( 74,388)( 75,387)( 76,386)( 77,385)( 78,384)( 79,383)( 80,382)
( 81,381)( 82,380)( 83,379)( 84,378)( 85,377)( 86,444)( 87,443)( 88,459)
( 89,458)( 90,457)( 91,456)( 92,455)( 93,454)( 94,453)( 95,452)( 96,451)
( 97,450)( 98,449)( 99,448)(100,447)(101,446)(102,445)(103,427)(104,426)
(105,442)(106,441)(107,440)(108,439)(109,438)(110,437)(111,436)(112,435)
(113,434)(114,433)(115,432)(116,431)(117,430)(118,429)(119,428)(120,495)
(121,494)(122,510)(123,509)(124,508)(125,507)(126,506)(127,505)(128,504)
(129,503)(130,502)(131,501)(132,500)(133,499)(134,498)(135,497)(136,496)
(137,478)(138,477)(139,493)(140,492)(141,491)(142,490)(143,489)(144,488)
(145,487)(146,486)(147,485)(148,484)(149,483)(150,482)(151,481)(152,480)
(153,479)(154,461)(155,460)(156,476)(157,475)(158,474)(159,473)(160,472)
(161,471)(162,470)(163,469)(164,468)(165,467)(166,466)(167,465)(168,464)
(169,463)(170,462)(171,614)(172,613)(173,629)(174,628)(175,627)(176,626)
(177,625)(178,624)(179,623)(180,622)(181,621)(182,620)(183,619)(184,618)
(185,617)(186,616)(187,615)(188,597)(189,596)(190,612)(191,611)(192,610)
(193,609)(194,608)(195,607)(196,606)(197,605)(198,604)(199,603)(200,602)
(201,601)(202,600)(203,599)(204,598)(205,665)(206,664)(207,680)(208,679)
(209,678)(210,677)(211,676)(212,675)(213,674)(214,673)(215,672)(216,671)
(217,670)(218,669)(219,668)(220,667)(221,666)(222,648)(223,647)(224,663)
(225,662)(226,661)(227,660)(228,659)(229,658)(230,657)(231,656)(232,655)
(233,654)(234,653)(235,652)(236,651)(237,650)(238,649)(239,631)(240,630)
(241,646)(242,645)(243,644)(244,643)(245,642)(246,641)(247,640)(248,639)
(249,638)(250,637)(251,636)(252,635)(253,634)(254,633)(255,632)(256,529)
(257,528)(258,544)(259,543)(260,542)(261,541)(262,540)(263,539)(264,538)
(265,537)(266,536)(267,535)(268,534)(269,533)(270,532)(271,531)(272,530)
(273,512)(274,511)(275,527)(276,526)(277,525)(278,524)(279,523)(280,522)
(281,521)(282,520)(283,519)(284,518)(285,517)(286,516)(287,515)(288,514)
(289,513)(290,580)(291,579)(292,595)(293,594)(294,593)(295,592)(296,591)
(297,590)(298,589)(299,588)(300,587)(301,586)(302,585)(303,584)(304,583)
(305,582)(306,581)(307,563)(308,562)(309,578)(310,577)(311,576)(312,575)
(313,574)(314,573)(315,572)(316,571)(317,570)(318,569)(319,568)(320,567)
(321,566)(322,565)(323,564)(324,546)(325,545)(326,561)(327,560)(328,559)
(329,558)(330,557)(331,556)(332,555)(333,554)(334,553)(335,552)(336,551)
(337,550)(338,549)(339,548)(340,547);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(680)!(  2, 17)(  3, 16)(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)
(  9, 10)( 18, 69)( 19, 85)( 20, 84)( 21, 83)( 22, 82)( 23, 81)( 24, 80)
( 25, 79)( 26, 78)( 27, 77)( 28, 76)( 29, 75)( 30, 74)( 31, 73)( 32, 72)
( 33, 71)( 34, 70)( 35, 52)( 36, 68)( 37, 67)( 38, 66)( 39, 65)( 40, 64)
( 41, 63)( 42, 62)( 43, 61)( 44, 60)( 45, 59)( 46, 58)( 47, 57)( 48, 56)
( 49, 55)( 50, 54)( 51, 53)( 87,102)( 88,101)( 89,100)( 90, 99)( 91, 98)
( 92, 97)( 93, 96)( 94, 95)(103,154)(104,170)(105,169)(106,168)(107,167)
(108,166)(109,165)(110,164)(111,163)(112,162)(113,161)(114,160)(115,159)
(116,158)(117,157)(118,156)(119,155)(120,137)(121,153)(122,152)(123,151)
(124,150)(125,149)(126,148)(127,147)(128,146)(129,145)(130,144)(131,143)
(132,142)(133,141)(134,140)(135,139)(136,138)(171,256)(172,272)(173,271)
(174,270)(175,269)(176,268)(177,267)(178,266)(179,265)(180,264)(181,263)
(182,262)(183,261)(184,260)(185,259)(186,258)(187,257)(188,324)(189,340)
(190,339)(191,338)(192,337)(193,336)(194,335)(195,334)(196,333)(197,332)
(198,331)(199,330)(200,329)(201,328)(202,327)(203,326)(204,325)(205,307)
(206,323)(207,322)(208,321)(209,320)(210,319)(211,318)(212,317)(213,316)
(214,315)(215,314)(216,313)(217,312)(218,311)(219,310)(220,309)(221,308)
(222,290)(223,306)(224,305)(225,304)(226,303)(227,302)(228,301)(229,300)
(230,299)(231,298)(232,297)(233,296)(234,295)(235,294)(236,293)(237,292)
(238,291)(239,273)(240,289)(241,288)(242,287)(243,286)(244,285)(245,284)
(246,283)(247,282)(248,281)(249,280)(250,279)(251,278)(252,277)(253,276)
(254,275)(255,274)(341,511)(342,527)(343,526)(344,525)(345,524)(346,523)
(347,522)(348,521)(349,520)(350,519)(351,518)(352,517)(353,516)(354,515)
(355,514)(356,513)(357,512)(358,579)(359,595)(360,594)(361,593)(362,592)
(363,591)(364,590)(365,589)(366,588)(367,587)(368,586)(369,585)(370,584)
(371,583)(372,582)(373,581)(374,580)(375,562)(376,578)(377,577)(378,576)
(379,575)(380,574)(381,573)(382,572)(383,571)(384,570)(385,569)(386,568)
(387,567)(388,566)(389,565)(390,564)(391,563)(392,545)(393,561)(394,560)
(395,559)(396,558)(397,557)(398,556)(399,555)(400,554)(401,553)(402,552)
(403,551)(404,550)(405,549)(406,548)(407,547)(408,546)(409,528)(410,544)
(411,543)(412,542)(413,541)(414,540)(415,539)(416,538)(417,537)(418,536)
(419,535)(420,534)(421,533)(422,532)(423,531)(424,530)(425,529)(426,596)
(427,612)(428,611)(429,610)(430,609)(431,608)(432,607)(433,606)(434,605)
(435,604)(436,603)(437,602)(438,601)(439,600)(440,599)(441,598)(442,597)
(443,664)(444,680)(445,679)(446,678)(447,677)(448,676)(449,675)(450,674)
(451,673)(452,672)(453,671)(454,670)(455,669)(456,668)(457,667)(458,666)
(459,665)(460,647)(461,663)(462,662)(463,661)(464,660)(465,659)(466,658)
(467,657)(468,656)(469,655)(470,654)(471,653)(472,652)(473,651)(474,650)
(475,649)(476,648)(477,630)(478,646)(479,645)(480,644)(481,643)(482,642)
(483,641)(484,640)(485,639)(486,638)(487,637)(488,636)(489,635)(490,634)
(491,633)(492,632)(493,631)(494,613)(495,629)(496,628)(497,627)(498,626)
(499,625)(500,624)(501,623)(502,622)(503,621)(504,620)(505,619)(506,618)
(507,617)(508,616)(509,615)(510,614);
s1 := Sym(680)!(  1,359)(  2,358)(  3,374)(  4,373)(  5,372)(  6,371)(  7,370)
(  8,369)(  9,368)( 10,367)( 11,366)( 12,365)( 13,364)( 14,363)( 15,362)
( 16,361)( 17,360)( 18,342)( 19,341)( 20,357)( 21,356)( 22,355)( 23,354)
( 24,353)( 25,352)( 26,351)( 27,350)( 28,349)( 29,348)( 30,347)( 31,346)
( 32,345)( 33,344)( 34,343)( 35,410)( 36,409)( 37,425)( 38,424)( 39,423)
( 40,422)( 41,421)( 42,420)( 43,419)( 44,418)( 45,417)( 46,416)( 47,415)
( 48,414)( 49,413)( 50,412)( 51,411)( 52,393)( 53,392)( 54,408)( 55,407)
( 56,406)( 57,405)( 58,404)( 59,403)( 60,402)( 61,401)( 62,400)( 63,399)
( 64,398)( 65,397)( 66,396)( 67,395)( 68,394)( 69,376)( 70,375)( 71,391)
( 72,390)( 73,389)( 74,388)( 75,387)( 76,386)( 77,385)( 78,384)( 79,383)
( 80,382)( 81,381)( 82,380)( 83,379)( 84,378)( 85,377)( 86,444)( 87,443)
( 88,459)( 89,458)( 90,457)( 91,456)( 92,455)( 93,454)( 94,453)( 95,452)
( 96,451)( 97,450)( 98,449)( 99,448)(100,447)(101,446)(102,445)(103,427)
(104,426)(105,442)(106,441)(107,440)(108,439)(109,438)(110,437)(111,436)
(112,435)(113,434)(114,433)(115,432)(116,431)(117,430)(118,429)(119,428)
(120,495)(121,494)(122,510)(123,509)(124,508)(125,507)(126,506)(127,505)
(128,504)(129,503)(130,502)(131,501)(132,500)(133,499)(134,498)(135,497)
(136,496)(137,478)(138,477)(139,493)(140,492)(141,491)(142,490)(143,489)
(144,488)(145,487)(146,486)(147,485)(148,484)(149,483)(150,482)(151,481)
(152,480)(153,479)(154,461)(155,460)(156,476)(157,475)(158,474)(159,473)
(160,472)(161,471)(162,470)(163,469)(164,468)(165,467)(166,466)(167,465)
(168,464)(169,463)(170,462)(171,614)(172,613)(173,629)(174,628)(175,627)
(176,626)(177,625)(178,624)(179,623)(180,622)(181,621)(182,620)(183,619)
(184,618)(185,617)(186,616)(187,615)(188,597)(189,596)(190,612)(191,611)
(192,610)(193,609)(194,608)(195,607)(196,606)(197,605)(198,604)(199,603)
(200,602)(201,601)(202,600)(203,599)(204,598)(205,665)(206,664)(207,680)
(208,679)(209,678)(210,677)(211,676)(212,675)(213,674)(214,673)(215,672)
(216,671)(217,670)(218,669)(219,668)(220,667)(221,666)(222,648)(223,647)
(224,663)(225,662)(226,661)(227,660)(228,659)(229,658)(230,657)(231,656)
(232,655)(233,654)(234,653)(235,652)(236,651)(237,650)(238,649)(239,631)
(240,630)(241,646)(242,645)(243,644)(244,643)(245,642)(246,641)(247,640)
(248,639)(249,638)(250,637)(251,636)(252,635)(253,634)(254,633)(255,632)
(256,529)(257,528)(258,544)(259,543)(260,542)(261,541)(262,540)(263,539)
(264,538)(265,537)(266,536)(267,535)(268,534)(269,533)(270,532)(271,531)
(272,530)(273,512)(274,511)(275,527)(276,526)(277,525)(278,524)(279,523)
(280,522)(281,521)(282,520)(283,519)(284,518)(285,517)(286,516)(287,515)
(288,514)(289,513)(290,580)(291,579)(292,595)(293,594)(294,593)(295,592)
(296,591)(297,590)(298,589)(299,588)(300,587)(301,586)(302,585)(303,584)
(304,583)(305,582)(306,581)(307,563)(308,562)(309,578)(310,577)(311,576)
(312,575)(313,574)(314,573)(315,572)(316,571)(317,570)(318,569)(319,568)
(320,567)(321,566)(322,565)(323,564)(324,546)(325,545)(326,561)(327,560)
(328,559)(329,558)(330,557)(331,556)(332,555)(333,554)(334,553)(335,552)
(336,551)(337,550)(338,549)(339,548)(340,547);
poly := sub<Sym(680)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope