Polytope of Type {704}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {704}*1408
Also Known As : 704-gon, {704}. if this polytope has another name.
Group : SmallGroup(1408,2723)
Rank : 2
Schlafli Type : {704}
Number of vertices, edges, etc : 704, 704
Order of s₀s₁ : 704
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 : {352}*704
   4-fold quotients : {176}*352
   8-fold quotients : {88}*176
   11-fold quotients : {64}*128
   16-fold quotients : {44}*88
   22-fold quotients : {32}*64
   32-fold quotients : {22}*44
   44-fold quotients : {16}*32
   64-fold quotients : {11}*22
   88-fold quotients : {8}*16
   176-fold quotients : {4}*8
   352-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope