Polytope of Type {714}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {714}*1428
Also Known As : 714-gon, {714}. if this polytope has another name.
Group : SmallGroup(1428,39)
Rank : 2
Schlafli Type : {714}
Number of vertices, edges, etc : 714, 714
Order of s₀s₁ : 714
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 : {357}*714
   3-fold quotients : {238}*476
   6-fold quotients : {119}*238
   7-fold quotients : {102}*204
   14-fold quotients : {51}*102
   17-fold quotients : {42}*84
   21-fold quotients : {34}*68
   34-fold quotients : {21}*42
   42-fold quotients : {17}*34
   51-fold quotients : {14}*28
   102-fold quotients : {7}*14
   119-fold quotients : {6}*12
   238-fold quotients : {3}*6
   357-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)
( 18,103)( 19,119)( 20,118)( 21,117)( 22,116)( 23,115)( 24,114)( 25,113)
( 26,112)( 27,111)( 28,110)( 29,109)( 30,108)( 31,107)( 32,106)( 33,105)
( 34,104)( 35, 86)( 36,102)( 37,101)( 38,100)( 39, 99)( 40, 98)( 41, 97)
( 42, 96)( 43, 95)( 44, 94)( 45, 93)( 46, 92)( 47, 91)( 48, 90)( 49, 89)
( 50, 88)( 51, 87)( 52, 69)( 53, 85)( 54, 84)( 55, 83)( 56, 82)( 57, 81)
( 58, 80)( 59, 79)( 60, 78)( 61, 77)( 62, 76)( 63, 75)( 64, 74)( 65, 73)
( 66, 72)( 67, 71)( 68, 70)(120,239)(121,255)(122,254)(123,253)(124,252)
(125,251)(126,250)(127,249)(128,248)(129,247)(130,246)(131,245)(132,244)
(133,243)(134,242)(135,241)(136,240)(137,341)(138,357)(139,356)(140,355)
(141,354)(142,353)(143,352)(144,351)(145,350)(146,349)(147,348)(148,347)
(149,346)(150,345)(151,344)(152,343)(153,342)(154,324)(155,340)(156,339)
(157,338)(158,337)(159,336)(160,335)(161,334)(162,333)(163,332)(164,331)
(165,330)(166,329)(167,328)(168,327)(169,326)(170,325)(171,307)(172,323)
(173,322)(174,321)(175,320)(176,319)(177,318)(178,317)(179,316)(180,315)
(181,314)(182,313)(183,312)(184,311)(185,310)(186,309)(187,308)(188,290)
(189,306)(190,305)(191,304)(192,303)(193,302)(194,301)(195,300)(196,299)
(197,298)(198,297)(199,296)(200,295)(201,294)(202,293)(203,292)(204,291)
(205,273)(206,289)(207,288)(208,287)(209,286)(210,285)(211,284)(212,283)
(213,282)(214,281)(215,280)(216,279)(217,278)(218,277)(219,276)(220,275)
(221,274)(222,256)(223,272)(224,271)(225,270)(226,269)(227,268)(228,267)
(229,266)(230,265)(231,264)(232,263)(233,262)(234,261)(235,260)(236,259)
(237,258)(238,257)(359,374)(360,373)(361,372)(362,371)(363,370)(364,369)
(365,368)(366,367)(375,460)(376,476)(377,475)(378,474)(379,473)(380,472)
(381,471)(382,470)(383,469)(384,468)(385,467)(386,466)(387,465)(388,464)
(389,463)(390,462)(391,461)(392,443)(393,459)(394,458)(395,457)(396,456)
(397,455)(398,454)(399,453)(400,452)(401,451)(402,450)(403,449)(404,448)
(405,447)(406,446)(407,445)(408,444)(409,426)(410,442)(411,441)(412,440)
(413,439)(414,438)(415,437)(416,436)(417,435)(418,434)(419,433)(420,432)
(421,431)(422,430)(423,429)(424,428)(425,427)(477,596)(478,612)(479,611)
(480,610)(481,609)(482,608)(483,607)(484,606)(485,605)(486,604)(487,603)
(488,602)(489,601)(490,600)(491,599)(492,598)(493,597)(494,698)(495,714)
(496,713)(497,712)(498,711)(499,710)(500,709)(501,708)(502,707)(503,706)
(504,705)(505,704)(506,703)(507,702)(508,701)(509,700)(510,699)(511,681)
(512,697)(513,696)(514,695)(515,694)(516,693)(517,692)(518,691)(519,690)
(520,689)(521,688)(522,687)(523,686)(524,685)(525,684)(526,683)(527,682)
(528,664)(529,680)(530,679)(531,678)(532,677)(533,676)(534,675)(535,674)
(536,673)(537,672)(538,671)(539,670)(540,669)(541,668)(542,667)(543,666)
(544,665)(545,647)(546,663)(547,662)(548,661)(549,660)(550,659)(551,658)
(552,657)(553,656)(554,655)(555,654)(556,653)(557,652)(558,651)(559,650)
(560,649)(561,648)(562,630)(563,646)(564,645)(565,644)(566,643)(567,642)
(568,641)(569,640)(570,639)(571,638)(572,637)(573,636)(574,635)(575,634)
(576,633)(577,632)(578,631)(579,613)(580,629)(581,628)(582,627)(583,626)
(584,625)(585,624)(586,623)(587,622)(588,621)(589,620)(590,619)(591,618)
(592,617)(593,616)(594,615)(595,614);;
s1 := (  1,495)(  2,494)(  3,510)(  4,509)(  5,508)(  6,507)(  7,506)(  8,505)
(  9,504)( 10,503)( 11,502)( 12,501)( 13,500)( 14,499)( 15,498)( 16,497)
( 17,496)( 18,478)( 19,477)( 20,493)( 21,492)( 22,491)( 23,490)( 24,489)
( 25,488)( 26,487)( 27,486)( 28,485)( 29,484)( 30,483)( 31,482)( 32,481)
( 33,480)( 34,479)( 35,580)( 36,579)( 37,595)( 38,594)( 39,593)( 40,592)
( 41,591)( 42,590)( 43,589)( 44,588)( 45,587)( 46,586)( 47,585)( 48,584)
( 49,583)( 50,582)( 51,581)( 52,563)( 53,562)( 54,578)( 55,577)( 56,576)
( 57,575)( 58,574)( 59,573)( 60,572)( 61,571)( 62,570)( 63,569)( 64,568)
( 65,567)( 66,566)( 67,565)( 68,564)( 69,546)( 70,545)( 71,561)( 72,560)
( 73,559)( 74,558)( 75,557)( 76,556)( 77,555)( 78,554)( 79,553)( 80,552)
( 81,551)( 82,550)( 83,549)( 84,548)( 85,547)( 86,529)( 87,528)( 88,544)
( 89,543)( 90,542)( 91,541)( 92,540)( 93,539)( 94,538)( 95,537)( 96,536)
( 97,535)( 98,534)( 99,533)(100,532)(101,531)(102,530)(103,512)(104,511)
(105,527)(106,526)(107,525)(108,524)(109,523)(110,522)(111,521)(112,520)
(113,519)(114,518)(115,517)(116,516)(117,515)(118,514)(119,513)(120,376)
(121,375)(122,391)(123,390)(124,389)(125,388)(126,387)(127,386)(128,385)
(129,384)(130,383)(131,382)(132,381)(133,380)(134,379)(135,378)(136,377)
(137,359)(138,358)(139,374)(140,373)(141,372)(142,371)(143,370)(144,369)
(145,368)(146,367)(147,366)(148,365)(149,364)(150,363)(151,362)(152,361)
(153,360)(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)(171,444)(172,443)(173,459)(174,458)(175,457)(176,456)
(177,455)(178,454)(179,453)(180,452)(181,451)(182,450)(183,449)(184,448)
(185,447)(186,446)(187,445)(188,427)(189,426)(190,442)(191,441)(192,440)
(193,439)(194,438)(195,437)(196,436)(197,435)(198,434)(199,433)(200,432)
(201,431)(202,430)(203,429)(204,428)(205,410)(206,409)(207,425)(208,424)
(209,423)(210,422)(211,421)(212,420)(213,419)(214,418)(215,417)(216,416)
(217,415)(218,414)(219,413)(220,412)(221,411)(222,393)(223,392)(224,408)
(225,407)(226,406)(227,405)(228,404)(229,403)(230,402)(231,401)(232,400)
(233,399)(234,398)(235,397)(236,396)(237,395)(238,394)(239,614)(240,613)
(241,629)(242,628)(243,627)(244,626)(245,625)(246,624)(247,623)(248,622)
(249,621)(250,620)(251,619)(252,618)(253,617)(254,616)(255,615)(256,597)
(257,596)(258,612)(259,611)(260,610)(261,609)(262,608)(263,607)(264,606)
(265,605)(266,604)(267,603)(268,602)(269,601)(270,600)(271,599)(272,598)
(273,699)(274,698)(275,714)(276,713)(277,712)(278,711)(279,710)(280,709)
(281,708)(282,707)(283,706)(284,705)(285,704)(286,703)(287,702)(288,701)
(289,700)(290,682)(291,681)(292,697)(293,696)(294,695)(295,694)(296,693)
(297,692)(298,691)(299,690)(300,689)(301,688)(302,687)(303,686)(304,685)
(305,684)(306,683)(307,665)(308,664)(309,680)(310,679)(311,678)(312,677)
(313,676)(314,675)(315,674)(316,673)(317,672)(318,671)(319,670)(320,669)
(321,668)(322,667)(323,666)(324,648)(325,647)(326,663)(327,662)(328,661)
(329,660)(330,659)(331,658)(332,657)(333,656)(334,655)(335,654)(336,653)
(337,652)(338,651)(339,650)(340,649)(341,631)(342,630)(343,646)(344,645)
(345,644)(346,643)(347,642)(348,641)(349,640)(350,639)(351,638)(352,637)
(353,636)(354,635)(355,634)(356,633)(357,632);;
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*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(714)!(  2, 17)(  3, 16)(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)
(  9, 10)( 18,103)( 19,119)( 20,118)( 21,117)( 22,116)( 23,115)( 24,114)
( 25,113)( 26,112)( 27,111)( 28,110)( 29,109)( 30,108)( 31,107)( 32,106)
( 33,105)( 34,104)( 35, 86)( 36,102)( 37,101)( 38,100)( 39, 99)( 40, 98)
( 41, 97)( 42, 96)( 43, 95)( 44, 94)( 45, 93)( 46, 92)( 47, 91)( 48, 90)
( 49, 89)( 50, 88)( 51, 87)( 52, 69)( 53, 85)( 54, 84)( 55, 83)( 56, 82)
( 57, 81)( 58, 80)( 59, 79)( 60, 78)( 61, 77)( 62, 76)( 63, 75)( 64, 74)
( 65, 73)( 66, 72)( 67, 71)( 68, 70)(120,239)(121,255)(122,254)(123,253)
(124,252)(125,251)(126,250)(127,249)(128,248)(129,247)(130,246)(131,245)
(132,244)(133,243)(134,242)(135,241)(136,240)(137,341)(138,357)(139,356)
(140,355)(141,354)(142,353)(143,352)(144,351)(145,350)(146,349)(147,348)
(148,347)(149,346)(150,345)(151,344)(152,343)(153,342)(154,324)(155,340)
(156,339)(157,338)(158,337)(159,336)(160,335)(161,334)(162,333)(163,332)
(164,331)(165,330)(166,329)(167,328)(168,327)(169,326)(170,325)(171,307)
(172,323)(173,322)(174,321)(175,320)(176,319)(177,318)(178,317)(179,316)
(180,315)(181,314)(182,313)(183,312)(184,311)(185,310)(186,309)(187,308)
(188,290)(189,306)(190,305)(191,304)(192,303)(193,302)(194,301)(195,300)
(196,299)(197,298)(198,297)(199,296)(200,295)(201,294)(202,293)(203,292)
(204,291)(205,273)(206,289)(207,288)(208,287)(209,286)(210,285)(211,284)
(212,283)(213,282)(214,281)(215,280)(216,279)(217,278)(218,277)(219,276)
(220,275)(221,274)(222,256)(223,272)(224,271)(225,270)(226,269)(227,268)
(228,267)(229,266)(230,265)(231,264)(232,263)(233,262)(234,261)(235,260)
(236,259)(237,258)(238,257)(359,374)(360,373)(361,372)(362,371)(363,370)
(364,369)(365,368)(366,367)(375,460)(376,476)(377,475)(378,474)(379,473)
(380,472)(381,471)(382,470)(383,469)(384,468)(385,467)(386,466)(387,465)
(388,464)(389,463)(390,462)(391,461)(392,443)(393,459)(394,458)(395,457)
(396,456)(397,455)(398,454)(399,453)(400,452)(401,451)(402,450)(403,449)
(404,448)(405,447)(406,446)(407,445)(408,444)(409,426)(410,442)(411,441)
(412,440)(413,439)(414,438)(415,437)(416,436)(417,435)(418,434)(419,433)
(420,432)(421,431)(422,430)(423,429)(424,428)(425,427)(477,596)(478,612)
(479,611)(480,610)(481,609)(482,608)(483,607)(484,606)(485,605)(486,604)
(487,603)(488,602)(489,601)(490,600)(491,599)(492,598)(493,597)(494,698)
(495,714)(496,713)(497,712)(498,711)(499,710)(500,709)(501,708)(502,707)
(503,706)(504,705)(505,704)(506,703)(507,702)(508,701)(509,700)(510,699)
(511,681)(512,697)(513,696)(514,695)(515,694)(516,693)(517,692)(518,691)
(519,690)(520,689)(521,688)(522,687)(523,686)(524,685)(525,684)(526,683)
(527,682)(528,664)(529,680)(530,679)(531,678)(532,677)(533,676)(534,675)
(535,674)(536,673)(537,672)(538,671)(539,670)(540,669)(541,668)(542,667)
(543,666)(544,665)(545,647)(546,663)(547,662)(548,661)(549,660)(550,659)
(551,658)(552,657)(553,656)(554,655)(555,654)(556,653)(557,652)(558,651)
(559,650)(560,649)(561,648)(562,630)(563,646)(564,645)(565,644)(566,643)
(567,642)(568,641)(569,640)(570,639)(571,638)(572,637)(573,636)(574,635)
(575,634)(576,633)(577,632)(578,631)(579,613)(580,629)(581,628)(582,627)
(583,626)(584,625)(585,624)(586,623)(587,622)(588,621)(589,620)(590,619)
(591,618)(592,617)(593,616)(594,615)(595,614);
s1 := Sym(714)!(  1,495)(  2,494)(  3,510)(  4,509)(  5,508)(  6,507)(  7,506)
(  8,505)(  9,504)( 10,503)( 11,502)( 12,501)( 13,500)( 14,499)( 15,498)
( 16,497)( 17,496)( 18,478)( 19,477)( 20,493)( 21,492)( 22,491)( 23,490)
( 24,489)( 25,488)( 26,487)( 27,486)( 28,485)( 29,484)( 30,483)( 31,482)
( 32,481)( 33,480)( 34,479)( 35,580)( 36,579)( 37,595)( 38,594)( 39,593)
( 40,592)( 41,591)( 42,590)( 43,589)( 44,588)( 45,587)( 46,586)( 47,585)
( 48,584)( 49,583)( 50,582)( 51,581)( 52,563)( 53,562)( 54,578)( 55,577)
( 56,576)( 57,575)( 58,574)( 59,573)( 60,572)( 61,571)( 62,570)( 63,569)
( 64,568)( 65,567)( 66,566)( 67,565)( 68,564)( 69,546)( 70,545)( 71,561)
( 72,560)( 73,559)( 74,558)( 75,557)( 76,556)( 77,555)( 78,554)( 79,553)
( 80,552)( 81,551)( 82,550)( 83,549)( 84,548)( 85,547)( 86,529)( 87,528)
( 88,544)( 89,543)( 90,542)( 91,541)( 92,540)( 93,539)( 94,538)( 95,537)
( 96,536)( 97,535)( 98,534)( 99,533)(100,532)(101,531)(102,530)(103,512)
(104,511)(105,527)(106,526)(107,525)(108,524)(109,523)(110,522)(111,521)
(112,520)(113,519)(114,518)(115,517)(116,516)(117,515)(118,514)(119,513)
(120,376)(121,375)(122,391)(123,390)(124,389)(125,388)(126,387)(127,386)
(128,385)(129,384)(130,383)(131,382)(132,381)(133,380)(134,379)(135,378)
(136,377)(137,359)(138,358)(139,374)(140,373)(141,372)(142,371)(143,370)
(144,369)(145,368)(146,367)(147,366)(148,365)(149,364)(150,363)(151,362)
(152,361)(153,360)(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)(171,444)(172,443)(173,459)(174,458)(175,457)
(176,456)(177,455)(178,454)(179,453)(180,452)(181,451)(182,450)(183,449)
(184,448)(185,447)(186,446)(187,445)(188,427)(189,426)(190,442)(191,441)
(192,440)(193,439)(194,438)(195,437)(196,436)(197,435)(198,434)(199,433)
(200,432)(201,431)(202,430)(203,429)(204,428)(205,410)(206,409)(207,425)
(208,424)(209,423)(210,422)(211,421)(212,420)(213,419)(214,418)(215,417)
(216,416)(217,415)(218,414)(219,413)(220,412)(221,411)(222,393)(223,392)
(224,408)(225,407)(226,406)(227,405)(228,404)(229,403)(230,402)(231,401)
(232,400)(233,399)(234,398)(235,397)(236,396)(237,395)(238,394)(239,614)
(240,613)(241,629)(242,628)(243,627)(244,626)(245,625)(246,624)(247,623)
(248,622)(249,621)(250,620)(251,619)(252,618)(253,617)(254,616)(255,615)
(256,597)(257,596)(258,612)(259,611)(260,610)(261,609)(262,608)(263,607)
(264,606)(265,605)(266,604)(267,603)(268,602)(269,601)(270,600)(271,599)
(272,598)(273,699)(274,698)(275,714)(276,713)(277,712)(278,711)(279,710)
(280,709)(281,708)(282,707)(283,706)(284,705)(285,704)(286,703)(287,702)
(288,701)(289,700)(290,682)(291,681)(292,697)(293,696)(294,695)(295,694)
(296,693)(297,692)(298,691)(299,690)(300,689)(301,688)(302,687)(303,686)
(304,685)(305,684)(306,683)(307,665)(308,664)(309,680)(310,679)(311,678)
(312,677)(313,676)(314,675)(315,674)(316,673)(317,672)(318,671)(319,670)
(320,669)(321,668)(322,667)(323,666)(324,648)(325,647)(326,663)(327,662)
(328,661)(329,660)(330,659)(331,658)(332,657)(333,656)(334,655)(335,654)
(336,653)(337,652)(338,651)(339,650)(340,649)(341,631)(342,630)(343,646)
(344,645)(345,644)(346,643)(347,642)(348,641)(349,640)(350,639)(351,638)
(352,637)(353,636)(354,635)(355,634)(356,633)(357,632);
poly := sub<Sym(714)|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*s0*s1*s0*s1 >;

References : None.
to this polytope