Polytope of Type {708}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {708}*1416
Also Known As : 708-gon, {708}. if this polytope has another name.
Group : SmallGroup(1416,25)
Rank : 2
Schlafli Type : {708}
Number of vertices, edges, etc : 708, 708
Order of s₀s₁ : 708
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 : {354}*708
   3-fold quotients : {236}*472
   4-fold quotients : {177}*354
   6-fold quotients : {118}*236
   12-fold quotients : {59}*118
   59-fold quotients : {12}*24
   118-fold quotients : {6}*12
   177-fold quotients : {4}*8
   236-fold quotients : {3}*6
   354-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope