Polytope of Type {702}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {702}*1404
Also Known As : 702-gon, {702}. if this polytope has another name.
Group : SmallGroup(1404,17)
Rank : 2
Schlafli Type : {702}
Number of vertices, edges, etc : 702, 702
Order of s₀s₁ : 702
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 : {351}*702
   3-fold quotients : {234}*468
   6-fold quotients : {117}*234
   9-fold quotients : {78}*156
   13-fold quotients : {54}*108
   18-fold quotients : {39}*78
   26-fold quotients : {27}*54
   27-fold quotients : {26}*52
   39-fold quotients : {18}*36
   54-fold quotients : {13}*26
   78-fold quotients : {9}*18
   117-fold quotients : {6}*12
   234-fold quotients : {3}*6
   351-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope