Polytope of Type {712}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {712}*1424
Also Known As : 712-gon, {712}. if this polytope has another name.
Group : SmallGroup(1424,26)
Rank : 2
Schlafli Type : {712}
Number of vertices, edges, etc : 712, 712
Order of s₀s₁ : 712
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 : {356}*712
   4-fold quotients : {178}*356
   8-fold quotients : {89}*178
   89-fold quotients : {8}*16
   178-fold quotients : {4}*8
   356-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 89)(  3, 88)(  4, 87)(  5, 86)(  6, 85)(  7, 84)(  8, 83)(  9, 82)
( 10, 81)( 11, 80)( 12, 79)( 13, 78)( 14, 77)( 15, 76)( 16, 75)( 17, 74)
( 18, 73)( 19, 72)( 20, 71)( 21, 70)( 22, 69)( 23, 68)( 24, 67)( 25, 66)
( 26, 65)( 27, 64)( 28, 63)( 29, 62)( 30, 61)( 31, 60)( 32, 59)( 33, 58)
( 34, 57)( 35, 56)( 36, 55)( 37, 54)( 38, 53)( 39, 52)( 40, 51)( 41, 50)
( 42, 49)( 43, 48)( 44, 47)( 45, 46)( 91,178)( 92,177)( 93,176)( 94,175)
( 95,174)( 96,173)( 97,172)( 98,171)( 99,170)(100,169)(101,168)(102,167)
(103,166)(104,165)(105,164)(106,163)(107,162)(108,161)(109,160)(110,159)
(111,158)(112,157)(113,156)(114,155)(115,154)(116,153)(117,152)(118,151)
(119,150)(120,149)(121,148)(122,147)(123,146)(124,145)(125,144)(126,143)
(127,142)(128,141)(129,140)(130,139)(131,138)(132,137)(133,136)(134,135)
(179,268)(180,356)(181,355)(182,354)(183,353)(184,352)(185,351)(186,350)
(187,349)(188,348)(189,347)(190,346)(191,345)(192,344)(193,343)(194,342)
(195,341)(196,340)(197,339)(198,338)(199,337)(200,336)(201,335)(202,334)
(203,333)(204,332)(205,331)(206,330)(207,329)(208,328)(209,327)(210,326)
(211,325)(212,324)(213,323)(214,322)(215,321)(216,320)(217,319)(218,318)
(219,317)(220,316)(221,315)(222,314)(223,313)(224,312)(225,311)(226,310)
(227,309)(228,308)(229,307)(230,306)(231,305)(232,304)(233,303)(234,302)
(235,301)(236,300)(237,299)(238,298)(239,297)(240,296)(241,295)(242,294)
(243,293)(244,292)(245,291)(246,290)(247,289)(248,288)(249,287)(250,286)
(251,285)(252,284)(253,283)(254,282)(255,281)(256,280)(257,279)(258,278)
(259,277)(260,276)(261,275)(262,274)(263,273)(264,272)(265,271)(266,270)
(267,269)(357,535)(358,623)(359,622)(360,621)(361,620)(362,619)(363,618)
(364,617)(365,616)(366,615)(367,614)(368,613)(369,612)(370,611)(371,610)
(372,609)(373,608)(374,607)(375,606)(376,605)(377,604)(378,603)(379,602)
(380,601)(381,600)(382,599)(383,598)(384,597)(385,596)(386,595)(387,594)
(388,593)(389,592)(390,591)(391,590)(392,589)(393,588)(394,587)(395,586)
(396,585)(397,584)(398,583)(399,582)(400,581)(401,580)(402,579)(403,578)
(404,577)(405,576)(406,575)(407,574)(408,573)(409,572)(410,571)(411,570)
(412,569)(413,568)(414,567)(415,566)(416,565)(417,564)(418,563)(419,562)
(420,561)(421,560)(422,559)(423,558)(424,557)(425,556)(426,555)(427,554)
(428,553)(429,552)(430,551)(431,550)(432,549)(433,548)(434,547)(435,546)
(436,545)(437,544)(438,543)(439,542)(440,541)(441,540)(442,539)(443,538)
(444,537)(445,536)(446,624)(447,712)(448,711)(449,710)(450,709)(451,708)
(452,707)(453,706)(454,705)(455,704)(456,703)(457,702)(458,701)(459,700)
(460,699)(461,698)(462,697)(463,696)(464,695)(465,694)(466,693)(467,692)
(468,691)(469,690)(470,689)(471,688)(472,687)(473,686)(474,685)(475,684)
(476,683)(477,682)(478,681)(479,680)(480,679)(481,678)(482,677)(483,676)
(484,675)(485,674)(486,673)(487,672)(488,671)(489,670)(490,669)(491,668)
(492,667)(493,666)(494,665)(495,664)(496,663)(497,662)(498,661)(499,660)
(500,659)(501,658)(502,657)(503,656)(504,655)(505,654)(506,653)(507,652)
(508,651)(509,650)(510,649)(511,648)(512,647)(513,646)(514,645)(515,644)
(516,643)(517,642)(518,641)(519,640)(520,639)(521,638)(522,637)(523,636)
(524,635)(525,634)(526,633)(527,632)(528,631)(529,630)(530,629)(531,628)
(532,627)(533,626)(534,625);;
s1 := (  1,358)(  2,357)(  3,445)(  4,444)(  5,443)(  6,442)(  7,441)(  8,440)
(  9,439)( 10,438)( 11,437)( 12,436)( 13,435)( 14,434)( 15,433)( 16,432)
( 17,431)( 18,430)( 19,429)( 20,428)( 21,427)( 22,426)( 23,425)( 24,424)
( 25,423)( 26,422)( 27,421)( 28,420)( 29,419)( 30,418)( 31,417)( 32,416)
( 33,415)( 34,414)( 35,413)( 36,412)( 37,411)( 38,410)( 39,409)( 40,408)
( 41,407)( 42,406)( 43,405)( 44,404)( 45,403)( 46,402)( 47,401)( 48,400)
( 49,399)( 50,398)( 51,397)( 52,396)( 53,395)( 54,394)( 55,393)( 56,392)
( 57,391)( 58,390)( 59,389)( 60,388)( 61,387)( 62,386)( 63,385)( 64,384)
( 65,383)( 66,382)( 67,381)( 68,380)( 69,379)( 70,378)( 71,377)( 72,376)
( 73,375)( 74,374)( 75,373)( 76,372)( 77,371)( 78,370)( 79,369)( 80,368)
( 81,367)( 82,366)( 83,365)( 84,364)( 85,363)( 86,362)( 87,361)( 88,360)
( 89,359)( 90,447)( 91,446)( 92,534)( 93,533)( 94,532)( 95,531)( 96,530)
( 97,529)( 98,528)( 99,527)(100,526)(101,525)(102,524)(103,523)(104,522)
(105,521)(106,520)(107,519)(108,518)(109,517)(110,516)(111,515)(112,514)
(113,513)(114,512)(115,511)(116,510)(117,509)(118,508)(119,507)(120,506)
(121,505)(122,504)(123,503)(124,502)(125,501)(126,500)(127,499)(128,498)
(129,497)(130,496)(131,495)(132,494)(133,493)(134,492)(135,491)(136,490)
(137,489)(138,488)(139,487)(140,486)(141,485)(142,484)(143,483)(144,482)
(145,481)(146,480)(147,479)(148,478)(149,477)(150,476)(151,475)(152,474)
(153,473)(154,472)(155,471)(156,470)(157,469)(158,468)(159,467)(160,466)
(161,465)(162,464)(163,463)(164,462)(165,461)(166,460)(167,459)(168,458)
(169,457)(170,456)(171,455)(172,454)(173,453)(174,452)(175,451)(176,450)
(177,449)(178,448)(179,625)(180,624)(181,712)(182,711)(183,710)(184,709)
(185,708)(186,707)(187,706)(188,705)(189,704)(190,703)(191,702)(192,701)
(193,700)(194,699)(195,698)(196,697)(197,696)(198,695)(199,694)(200,693)
(201,692)(202,691)(203,690)(204,689)(205,688)(206,687)(207,686)(208,685)
(209,684)(210,683)(211,682)(212,681)(213,680)(214,679)(215,678)(216,677)
(217,676)(218,675)(219,674)(220,673)(221,672)(222,671)(223,670)(224,669)
(225,668)(226,667)(227,666)(228,665)(229,664)(230,663)(231,662)(232,661)
(233,660)(234,659)(235,658)(236,657)(237,656)(238,655)(239,654)(240,653)
(241,652)(242,651)(243,650)(244,649)(245,648)(246,647)(247,646)(248,645)
(249,644)(250,643)(251,642)(252,641)(253,640)(254,639)(255,638)(256,637)
(257,636)(258,635)(259,634)(260,633)(261,632)(262,631)(263,630)(264,629)
(265,628)(266,627)(267,626)(268,536)(269,535)(270,623)(271,622)(272,621)
(273,620)(274,619)(275,618)(276,617)(277,616)(278,615)(279,614)(280,613)
(281,612)(282,611)(283,610)(284,609)(285,608)(286,607)(287,606)(288,605)
(289,604)(290,603)(291,602)(292,601)(293,600)(294,599)(295,598)(296,597)
(297,596)(298,595)(299,594)(300,593)(301,592)(302,591)(303,590)(304,589)
(305,588)(306,587)(307,586)(308,585)(309,584)(310,583)(311,582)(312,581)
(313,580)(314,579)(315,578)(316,577)(317,576)(318,575)(319,574)(320,573)
(321,572)(322,571)(323,570)(324,569)(325,568)(326,567)(327,566)(328,565)
(329,564)(330,563)(331,562)(332,561)(333,560)(334,559)(335,558)(336,557)
(337,556)(338,555)(339,554)(340,553)(341,552)(342,551)(343,550)(344,549)
(345,548)(346,547)(347,546)(348,545)(349,544)(350,543)(351,542)(352,541)
(353,540)(354,539)(355,538)(356,537);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(712)!(  2, 89)(  3, 88)(  4, 87)(  5, 86)(  6, 85)(  7, 84)(  8, 83)
(  9, 82)( 10, 81)( 11, 80)( 12, 79)( 13, 78)( 14, 77)( 15, 76)( 16, 75)
( 17, 74)( 18, 73)( 19, 72)( 20, 71)( 21, 70)( 22, 69)( 23, 68)( 24, 67)
( 25, 66)( 26, 65)( 27, 64)( 28, 63)( 29, 62)( 30, 61)( 31, 60)( 32, 59)
( 33, 58)( 34, 57)( 35, 56)( 36, 55)( 37, 54)( 38, 53)( 39, 52)( 40, 51)
( 41, 50)( 42, 49)( 43, 48)( 44, 47)( 45, 46)( 91,178)( 92,177)( 93,176)
( 94,175)( 95,174)( 96,173)( 97,172)( 98,171)( 99,170)(100,169)(101,168)
(102,167)(103,166)(104,165)(105,164)(106,163)(107,162)(108,161)(109,160)
(110,159)(111,158)(112,157)(113,156)(114,155)(115,154)(116,153)(117,152)
(118,151)(119,150)(120,149)(121,148)(122,147)(123,146)(124,145)(125,144)
(126,143)(127,142)(128,141)(129,140)(130,139)(131,138)(132,137)(133,136)
(134,135)(179,268)(180,356)(181,355)(182,354)(183,353)(184,352)(185,351)
(186,350)(187,349)(188,348)(189,347)(190,346)(191,345)(192,344)(193,343)
(194,342)(195,341)(196,340)(197,339)(198,338)(199,337)(200,336)(201,335)
(202,334)(203,333)(204,332)(205,331)(206,330)(207,329)(208,328)(209,327)
(210,326)(211,325)(212,324)(213,323)(214,322)(215,321)(216,320)(217,319)
(218,318)(219,317)(220,316)(221,315)(222,314)(223,313)(224,312)(225,311)
(226,310)(227,309)(228,308)(229,307)(230,306)(231,305)(232,304)(233,303)
(234,302)(235,301)(236,300)(237,299)(238,298)(239,297)(240,296)(241,295)
(242,294)(243,293)(244,292)(245,291)(246,290)(247,289)(248,288)(249,287)
(250,286)(251,285)(252,284)(253,283)(254,282)(255,281)(256,280)(257,279)
(258,278)(259,277)(260,276)(261,275)(262,274)(263,273)(264,272)(265,271)
(266,270)(267,269)(357,535)(358,623)(359,622)(360,621)(361,620)(362,619)
(363,618)(364,617)(365,616)(366,615)(367,614)(368,613)(369,612)(370,611)
(371,610)(372,609)(373,608)(374,607)(375,606)(376,605)(377,604)(378,603)
(379,602)(380,601)(381,600)(382,599)(383,598)(384,597)(385,596)(386,595)
(387,594)(388,593)(389,592)(390,591)(391,590)(392,589)(393,588)(394,587)
(395,586)(396,585)(397,584)(398,583)(399,582)(400,581)(401,580)(402,579)
(403,578)(404,577)(405,576)(406,575)(407,574)(408,573)(409,572)(410,571)
(411,570)(412,569)(413,568)(414,567)(415,566)(416,565)(417,564)(418,563)
(419,562)(420,561)(421,560)(422,559)(423,558)(424,557)(425,556)(426,555)
(427,554)(428,553)(429,552)(430,551)(431,550)(432,549)(433,548)(434,547)
(435,546)(436,545)(437,544)(438,543)(439,542)(440,541)(441,540)(442,539)
(443,538)(444,537)(445,536)(446,624)(447,712)(448,711)(449,710)(450,709)
(451,708)(452,707)(453,706)(454,705)(455,704)(456,703)(457,702)(458,701)
(459,700)(460,699)(461,698)(462,697)(463,696)(464,695)(465,694)(466,693)
(467,692)(468,691)(469,690)(470,689)(471,688)(472,687)(473,686)(474,685)
(475,684)(476,683)(477,682)(478,681)(479,680)(480,679)(481,678)(482,677)
(483,676)(484,675)(485,674)(486,673)(487,672)(488,671)(489,670)(490,669)
(491,668)(492,667)(493,666)(494,665)(495,664)(496,663)(497,662)(498,661)
(499,660)(500,659)(501,658)(502,657)(503,656)(504,655)(505,654)(506,653)
(507,652)(508,651)(509,650)(510,649)(511,648)(512,647)(513,646)(514,645)
(515,644)(516,643)(517,642)(518,641)(519,640)(520,639)(521,638)(522,637)
(523,636)(524,635)(525,634)(526,633)(527,632)(528,631)(529,630)(530,629)
(531,628)(532,627)(533,626)(534,625);
s1 := Sym(712)!(  1,358)(  2,357)(  3,445)(  4,444)(  5,443)(  6,442)(  7,441)
(  8,440)(  9,439)( 10,438)( 11,437)( 12,436)( 13,435)( 14,434)( 15,433)
( 16,432)( 17,431)( 18,430)( 19,429)( 20,428)( 21,427)( 22,426)( 23,425)
( 24,424)( 25,423)( 26,422)( 27,421)( 28,420)( 29,419)( 30,418)( 31,417)
( 32,416)( 33,415)( 34,414)( 35,413)( 36,412)( 37,411)( 38,410)( 39,409)
( 40,408)( 41,407)( 42,406)( 43,405)( 44,404)( 45,403)( 46,402)( 47,401)
( 48,400)( 49,399)( 50,398)( 51,397)( 52,396)( 53,395)( 54,394)( 55,393)
( 56,392)( 57,391)( 58,390)( 59,389)( 60,388)( 61,387)( 62,386)( 63,385)
( 64,384)( 65,383)( 66,382)( 67,381)( 68,380)( 69,379)( 70,378)( 71,377)
( 72,376)( 73,375)( 74,374)( 75,373)( 76,372)( 77,371)( 78,370)( 79,369)
( 80,368)( 81,367)( 82,366)( 83,365)( 84,364)( 85,363)( 86,362)( 87,361)
( 88,360)( 89,359)( 90,447)( 91,446)( 92,534)( 93,533)( 94,532)( 95,531)
( 96,530)( 97,529)( 98,528)( 99,527)(100,526)(101,525)(102,524)(103,523)
(104,522)(105,521)(106,520)(107,519)(108,518)(109,517)(110,516)(111,515)
(112,514)(113,513)(114,512)(115,511)(116,510)(117,509)(118,508)(119,507)
(120,506)(121,505)(122,504)(123,503)(124,502)(125,501)(126,500)(127,499)
(128,498)(129,497)(130,496)(131,495)(132,494)(133,493)(134,492)(135,491)
(136,490)(137,489)(138,488)(139,487)(140,486)(141,485)(142,484)(143,483)
(144,482)(145,481)(146,480)(147,479)(148,478)(149,477)(150,476)(151,475)
(152,474)(153,473)(154,472)(155,471)(156,470)(157,469)(158,468)(159,467)
(160,466)(161,465)(162,464)(163,463)(164,462)(165,461)(166,460)(167,459)
(168,458)(169,457)(170,456)(171,455)(172,454)(173,453)(174,452)(175,451)
(176,450)(177,449)(178,448)(179,625)(180,624)(181,712)(182,711)(183,710)
(184,709)(185,708)(186,707)(187,706)(188,705)(189,704)(190,703)(191,702)
(192,701)(193,700)(194,699)(195,698)(196,697)(197,696)(198,695)(199,694)
(200,693)(201,692)(202,691)(203,690)(204,689)(205,688)(206,687)(207,686)
(208,685)(209,684)(210,683)(211,682)(212,681)(213,680)(214,679)(215,678)
(216,677)(217,676)(218,675)(219,674)(220,673)(221,672)(222,671)(223,670)
(224,669)(225,668)(226,667)(227,666)(228,665)(229,664)(230,663)(231,662)
(232,661)(233,660)(234,659)(235,658)(236,657)(237,656)(238,655)(239,654)
(240,653)(241,652)(242,651)(243,650)(244,649)(245,648)(246,647)(247,646)
(248,645)(249,644)(250,643)(251,642)(252,641)(253,640)(254,639)(255,638)
(256,637)(257,636)(258,635)(259,634)(260,633)(261,632)(262,631)(263,630)
(264,629)(265,628)(266,627)(267,626)(268,536)(269,535)(270,623)(271,622)
(272,621)(273,620)(274,619)(275,618)(276,617)(277,616)(278,615)(279,614)
(280,613)(281,612)(282,611)(283,610)(284,609)(285,608)(286,607)(287,606)
(288,605)(289,604)(290,603)(291,602)(292,601)(293,600)(294,599)(295,598)
(296,597)(297,596)(298,595)(299,594)(300,593)(301,592)(302,591)(303,590)
(304,589)(305,588)(306,587)(307,586)(308,585)(309,584)(310,583)(311,582)
(312,581)(313,580)(314,579)(315,578)(316,577)(317,576)(318,575)(319,574)
(320,573)(321,572)(322,571)(323,570)(324,569)(325,568)(326,567)(327,566)
(328,565)(329,564)(330,563)(331,562)(332,561)(333,560)(334,559)(335,558)
(336,557)(337,556)(338,555)(339,554)(340,553)(341,552)(342,551)(343,550)
(344,549)(345,548)(346,547)(347,546)(348,545)(349,544)(350,543)(351,542)
(352,541)(353,540)(354,539)(355,538)(356,537);
poly := sub<Sym(712)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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