Polytope of Type {696}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {696}*1392
Also Known As : 696-gon, {696}. if this polytope has another name.
Group : SmallGroup(1392,68)
Rank : 2
Schlafli Type : {696}
Number of vertices, edges, etc : 696, 696
Order of s₀s₁ : 696
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 : {348}*696
   3-fold quotients : {232}*464
   4-fold quotients : {174}*348
   6-fold quotients : {116}*232
   8-fold quotients : {87}*174
   12-fold quotients : {58}*116
   24-fold quotients : {29}*58
   29-fold quotients : {24}*48
   58-fold quotients : {12}*24
   87-fold quotients : {8}*16
   116-fold quotients : {6}*12
   174-fold quotients : {4}*8
   232-fold quotients : {3}*6
   348-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope