Polytope of Type {784}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {784}*1568
Also Known As : 784-gon, {784}. if this polytope has another name.
Group : SmallGroup(1568,6)
Rank : 2
Schlafli Type : {784}
Number of vertices, edges, etc : 784, 784
Order of s0s1 : 784
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 : {392}*784
4-fold quotients : {196}*392
7-fold quotients : {112}*224
8-fold quotients : {98}*196
14-fold quotients : {56}*112
16-fold quotients : {49}*98
28-fold quotients : {28}*56
49-fold quotients : {16}*32
56-fold quotients : {14}*28
98-fold quotients : {8}*16
112-fold quotients : {7}*14
196-fold quotients : {4}*8
392-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 7)( 3, 6)( 4, 5)( 8, 49)( 9, 48)( 10, 47)( 11, 46)( 12, 45)
( 13, 44)( 14, 43)( 15, 42)( 16, 41)( 17, 40)( 18, 39)( 19, 38)( 20, 37)
( 21, 36)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)
( 51, 56)( 52, 55)( 53, 54)( 57, 98)( 58, 97)( 59, 96)( 60, 95)( 61, 94)
( 62, 93)( 63, 92)( 64, 91)( 65, 90)( 66, 89)( 67, 88)( 68, 87)( 69, 86)
( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 80)( 76, 79)( 77, 78)
( 99,148)(100,154)(101,153)(102,152)(103,151)(104,150)(105,149)(106,196)
(107,195)(108,194)(109,193)(110,192)(111,191)(112,190)(113,189)(114,188)
(115,187)(116,186)(117,185)(118,184)(119,183)(120,182)(121,181)(122,180)
(123,179)(124,178)(125,177)(126,176)(127,175)(128,174)(129,173)(130,172)
(131,171)(132,170)(133,169)(134,168)(135,167)(136,166)(137,165)(138,164)
(139,163)(140,162)(141,161)(142,160)(143,159)(144,158)(145,157)(146,156)
(147,155)(197,295)(198,301)(199,300)(200,299)(201,298)(202,297)(203,296)
(204,343)(205,342)(206,341)(207,340)(208,339)(209,338)(210,337)(211,336)
(212,335)(213,334)(214,333)(215,332)(216,331)(217,330)(218,329)(219,328)
(220,327)(221,326)(222,325)(223,324)(224,323)(225,322)(226,321)(227,320)
(228,319)(229,318)(230,317)(231,316)(232,315)(233,314)(234,313)(235,312)
(236,311)(237,310)(238,309)(239,308)(240,307)(241,306)(242,305)(243,304)
(244,303)(245,302)(246,344)(247,350)(248,349)(249,348)(250,347)(251,346)
(252,345)(253,392)(254,391)(255,390)(256,389)(257,388)(258,387)(259,386)
(260,385)(261,384)(262,383)(263,382)(264,381)(265,380)(266,379)(267,378)
(268,377)(269,376)(270,375)(271,374)(272,373)(273,372)(274,371)(275,370)
(276,369)(277,368)(278,367)(279,366)(280,365)(281,364)(282,363)(283,362)
(284,361)(285,360)(286,359)(287,358)(288,357)(289,356)(290,355)(291,354)
(292,353)(293,352)(294,351)(393,589)(394,595)(395,594)(396,593)(397,592)
(398,591)(399,590)(400,637)(401,636)(402,635)(403,634)(404,633)(405,632)
(406,631)(407,630)(408,629)(409,628)(410,627)(411,626)(412,625)(413,624)
(414,623)(415,622)(416,621)(417,620)(418,619)(419,618)(420,617)(421,616)
(422,615)(423,614)(424,613)(425,612)(426,611)(427,610)(428,609)(429,608)
(430,607)(431,606)(432,605)(433,604)(434,603)(435,602)(436,601)(437,600)
(438,599)(439,598)(440,597)(441,596)(442,638)(443,644)(444,643)(445,642)
(446,641)(447,640)(448,639)(449,686)(450,685)(451,684)(452,683)(453,682)
(454,681)(455,680)(456,679)(457,678)(458,677)(459,676)(460,675)(461,674)
(462,673)(463,672)(464,671)(465,670)(466,669)(467,668)(468,667)(469,666)
(470,665)(471,664)(472,663)(473,662)(474,661)(475,660)(476,659)(477,658)
(478,657)(479,656)(480,655)(481,654)(482,653)(483,652)(484,651)(485,650)
(486,649)(487,648)(488,647)(489,646)(490,645)(491,736)(492,742)(493,741)
(494,740)(495,739)(496,738)(497,737)(498,784)(499,783)(500,782)(501,781)
(502,780)(503,779)(504,778)(505,777)(506,776)(507,775)(508,774)(509,773)
(510,772)(511,771)(512,770)(513,769)(514,768)(515,767)(516,766)(517,765)
(518,764)(519,763)(520,762)(521,761)(522,760)(523,759)(524,758)(525,757)
(526,756)(527,755)(528,754)(529,753)(530,752)(531,751)(532,750)(533,749)
(534,748)(535,747)(536,746)(537,745)(538,744)(539,743)(540,687)(541,693)
(542,692)(543,691)(544,690)(545,689)(546,688)(547,735)(548,734)(549,733)
(550,732)(551,731)(552,730)(553,729)(554,728)(555,727)(556,726)(557,725)
(558,724)(559,723)(560,722)(561,721)(562,720)(563,719)(564,718)(565,717)
(566,716)(567,715)(568,714)(569,713)(570,712)(571,711)(572,710)(573,709)
(574,708)(575,707)(576,706)(577,705)(578,704)(579,703)(580,702)(581,701)
(582,700)(583,699)(584,698)(585,697)(586,696)(587,695)(588,694);;
s1 := ( 1,400)( 2,406)( 3,405)( 4,404)( 5,403)( 6,402)( 7,401)( 8,393)
( 9,399)( 10,398)( 11,397)( 12,396)( 13,395)( 14,394)( 15,441)( 16,440)
( 17,439)( 18,438)( 19,437)( 20,436)( 21,435)( 22,434)( 23,433)( 24,432)
( 25,431)( 26,430)( 27,429)( 28,428)( 29,427)( 30,426)( 31,425)( 32,424)
( 33,423)( 34,422)( 35,421)( 36,420)( 37,419)( 38,418)( 39,417)( 40,416)
( 41,415)( 42,414)( 43,413)( 44,412)( 45,411)( 46,410)( 47,409)( 48,408)
( 49,407)( 50,449)( 51,455)( 52,454)( 53,453)( 54,452)( 55,451)( 56,450)
( 57,442)( 58,448)( 59,447)( 60,446)( 61,445)( 62,444)( 63,443)( 64,490)
( 65,489)( 66,488)( 67,487)( 68,486)( 69,485)( 70,484)( 71,483)( 72,482)
( 73,481)( 74,480)( 75,479)( 76,478)( 77,477)( 78,476)( 79,475)( 80,474)
( 81,473)( 82,472)( 83,471)( 84,470)( 85,469)( 86,468)( 87,467)( 88,466)
( 89,465)( 90,464)( 91,463)( 92,462)( 93,461)( 94,460)( 95,459)( 96,458)
( 97,457)( 98,456)( 99,547)(100,553)(101,552)(102,551)(103,550)(104,549)
(105,548)(106,540)(107,546)(108,545)(109,544)(110,543)(111,542)(112,541)
(113,588)(114,587)(115,586)(116,585)(117,584)(118,583)(119,582)(120,581)
(121,580)(122,579)(123,578)(124,577)(125,576)(126,575)(127,574)(128,573)
(129,572)(130,571)(131,570)(132,569)(133,568)(134,567)(135,566)(136,565)
(137,564)(138,563)(139,562)(140,561)(141,560)(142,559)(143,558)(144,557)
(145,556)(146,555)(147,554)(148,498)(149,504)(150,503)(151,502)(152,501)
(153,500)(154,499)(155,491)(156,497)(157,496)(158,495)(159,494)(160,493)
(161,492)(162,539)(163,538)(164,537)(165,536)(166,535)(167,534)(168,533)
(169,532)(170,531)(171,530)(172,529)(173,528)(174,527)(175,526)(176,525)
(177,524)(178,523)(179,522)(180,521)(181,520)(182,519)(183,518)(184,517)
(185,516)(186,515)(187,514)(188,513)(189,512)(190,511)(191,510)(192,509)
(193,508)(194,507)(195,506)(196,505)(197,694)(198,700)(199,699)(200,698)
(201,697)(202,696)(203,695)(204,687)(205,693)(206,692)(207,691)(208,690)
(209,689)(210,688)(211,735)(212,734)(213,733)(214,732)(215,731)(216,730)
(217,729)(218,728)(219,727)(220,726)(221,725)(222,724)(223,723)(224,722)
(225,721)(226,720)(227,719)(228,718)(229,717)(230,716)(231,715)(232,714)
(233,713)(234,712)(235,711)(236,710)(237,709)(238,708)(239,707)(240,706)
(241,705)(242,704)(243,703)(244,702)(245,701)(246,743)(247,749)(248,748)
(249,747)(250,746)(251,745)(252,744)(253,736)(254,742)(255,741)(256,740)
(257,739)(258,738)(259,737)(260,784)(261,783)(262,782)(263,781)(264,780)
(265,779)(266,778)(267,777)(268,776)(269,775)(270,774)(271,773)(272,772)
(273,771)(274,770)(275,769)(276,768)(277,767)(278,766)(279,765)(280,764)
(281,763)(282,762)(283,761)(284,760)(285,759)(286,758)(287,757)(288,756)
(289,755)(290,754)(291,753)(292,752)(293,751)(294,750)(295,596)(296,602)
(297,601)(298,600)(299,599)(300,598)(301,597)(302,589)(303,595)(304,594)
(305,593)(306,592)(307,591)(308,590)(309,637)(310,636)(311,635)(312,634)
(313,633)(314,632)(315,631)(316,630)(317,629)(318,628)(319,627)(320,626)
(321,625)(322,624)(323,623)(324,622)(325,621)(326,620)(327,619)(328,618)
(329,617)(330,616)(331,615)(332,614)(333,613)(334,612)(335,611)(336,610)
(337,609)(338,608)(339,607)(340,606)(341,605)(342,604)(343,603)(344,645)
(345,651)(346,650)(347,649)(348,648)(349,647)(350,646)(351,638)(352,644)
(353,643)(354,642)(355,641)(356,640)(357,639)(358,686)(359,685)(360,684)
(361,683)(362,682)(363,681)(364,680)(365,679)(366,678)(367,677)(368,676)
(369,675)(370,674)(371,673)(372,672)(373,671)(374,670)(375,669)(376,668)
(377,667)(378,666)(379,665)(380,664)(381,663)(382,662)(383,661)(384,660)
(385,659)(386,658)(387,657)(388,656)(389,655)(390,654)(391,653)(392,652);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(784)!( 2, 7)( 3, 6)( 4, 5)( 8, 49)( 9, 48)( 10, 47)( 11, 46)
( 12, 45)( 13, 44)( 14, 43)( 15, 42)( 16, 41)( 17, 40)( 18, 39)( 19, 38)
( 20, 37)( 21, 36)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 31)( 27, 30)
( 28, 29)( 51, 56)( 52, 55)( 53, 54)( 57, 98)( 58, 97)( 59, 96)( 60, 95)
( 61, 94)( 62, 93)( 63, 92)( 64, 91)( 65, 90)( 66, 89)( 67, 88)( 68, 87)
( 69, 86)( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 80)( 76, 79)
( 77, 78)( 99,148)(100,154)(101,153)(102,152)(103,151)(104,150)(105,149)
(106,196)(107,195)(108,194)(109,193)(110,192)(111,191)(112,190)(113,189)
(114,188)(115,187)(116,186)(117,185)(118,184)(119,183)(120,182)(121,181)
(122,180)(123,179)(124,178)(125,177)(126,176)(127,175)(128,174)(129,173)
(130,172)(131,171)(132,170)(133,169)(134,168)(135,167)(136,166)(137,165)
(138,164)(139,163)(140,162)(141,161)(142,160)(143,159)(144,158)(145,157)
(146,156)(147,155)(197,295)(198,301)(199,300)(200,299)(201,298)(202,297)
(203,296)(204,343)(205,342)(206,341)(207,340)(208,339)(209,338)(210,337)
(211,336)(212,335)(213,334)(214,333)(215,332)(216,331)(217,330)(218,329)
(219,328)(220,327)(221,326)(222,325)(223,324)(224,323)(225,322)(226,321)
(227,320)(228,319)(229,318)(230,317)(231,316)(232,315)(233,314)(234,313)
(235,312)(236,311)(237,310)(238,309)(239,308)(240,307)(241,306)(242,305)
(243,304)(244,303)(245,302)(246,344)(247,350)(248,349)(249,348)(250,347)
(251,346)(252,345)(253,392)(254,391)(255,390)(256,389)(257,388)(258,387)
(259,386)(260,385)(261,384)(262,383)(263,382)(264,381)(265,380)(266,379)
(267,378)(268,377)(269,376)(270,375)(271,374)(272,373)(273,372)(274,371)
(275,370)(276,369)(277,368)(278,367)(279,366)(280,365)(281,364)(282,363)
(283,362)(284,361)(285,360)(286,359)(287,358)(288,357)(289,356)(290,355)
(291,354)(292,353)(293,352)(294,351)(393,589)(394,595)(395,594)(396,593)
(397,592)(398,591)(399,590)(400,637)(401,636)(402,635)(403,634)(404,633)
(405,632)(406,631)(407,630)(408,629)(409,628)(410,627)(411,626)(412,625)
(413,624)(414,623)(415,622)(416,621)(417,620)(418,619)(419,618)(420,617)
(421,616)(422,615)(423,614)(424,613)(425,612)(426,611)(427,610)(428,609)
(429,608)(430,607)(431,606)(432,605)(433,604)(434,603)(435,602)(436,601)
(437,600)(438,599)(439,598)(440,597)(441,596)(442,638)(443,644)(444,643)
(445,642)(446,641)(447,640)(448,639)(449,686)(450,685)(451,684)(452,683)
(453,682)(454,681)(455,680)(456,679)(457,678)(458,677)(459,676)(460,675)
(461,674)(462,673)(463,672)(464,671)(465,670)(466,669)(467,668)(468,667)
(469,666)(470,665)(471,664)(472,663)(473,662)(474,661)(475,660)(476,659)
(477,658)(478,657)(479,656)(480,655)(481,654)(482,653)(483,652)(484,651)
(485,650)(486,649)(487,648)(488,647)(489,646)(490,645)(491,736)(492,742)
(493,741)(494,740)(495,739)(496,738)(497,737)(498,784)(499,783)(500,782)
(501,781)(502,780)(503,779)(504,778)(505,777)(506,776)(507,775)(508,774)
(509,773)(510,772)(511,771)(512,770)(513,769)(514,768)(515,767)(516,766)
(517,765)(518,764)(519,763)(520,762)(521,761)(522,760)(523,759)(524,758)
(525,757)(526,756)(527,755)(528,754)(529,753)(530,752)(531,751)(532,750)
(533,749)(534,748)(535,747)(536,746)(537,745)(538,744)(539,743)(540,687)
(541,693)(542,692)(543,691)(544,690)(545,689)(546,688)(547,735)(548,734)
(549,733)(550,732)(551,731)(552,730)(553,729)(554,728)(555,727)(556,726)
(557,725)(558,724)(559,723)(560,722)(561,721)(562,720)(563,719)(564,718)
(565,717)(566,716)(567,715)(568,714)(569,713)(570,712)(571,711)(572,710)
(573,709)(574,708)(575,707)(576,706)(577,705)(578,704)(579,703)(580,702)
(581,701)(582,700)(583,699)(584,698)(585,697)(586,696)(587,695)(588,694);
s1 := Sym(784)!( 1,400)( 2,406)( 3,405)( 4,404)( 5,403)( 6,402)( 7,401)
( 8,393)( 9,399)( 10,398)( 11,397)( 12,396)( 13,395)( 14,394)( 15,441)
( 16,440)( 17,439)( 18,438)( 19,437)( 20,436)( 21,435)( 22,434)( 23,433)
( 24,432)( 25,431)( 26,430)( 27,429)( 28,428)( 29,427)( 30,426)( 31,425)
( 32,424)( 33,423)( 34,422)( 35,421)( 36,420)( 37,419)( 38,418)( 39,417)
( 40,416)( 41,415)( 42,414)( 43,413)( 44,412)( 45,411)( 46,410)( 47,409)
( 48,408)( 49,407)( 50,449)( 51,455)( 52,454)( 53,453)( 54,452)( 55,451)
( 56,450)( 57,442)( 58,448)( 59,447)( 60,446)( 61,445)( 62,444)( 63,443)
( 64,490)( 65,489)( 66,488)( 67,487)( 68,486)( 69,485)( 70,484)( 71,483)
( 72,482)( 73,481)( 74,480)( 75,479)( 76,478)( 77,477)( 78,476)( 79,475)
( 80,474)( 81,473)( 82,472)( 83,471)( 84,470)( 85,469)( 86,468)( 87,467)
( 88,466)( 89,465)( 90,464)( 91,463)( 92,462)( 93,461)( 94,460)( 95,459)
( 96,458)( 97,457)( 98,456)( 99,547)(100,553)(101,552)(102,551)(103,550)
(104,549)(105,548)(106,540)(107,546)(108,545)(109,544)(110,543)(111,542)
(112,541)(113,588)(114,587)(115,586)(116,585)(117,584)(118,583)(119,582)
(120,581)(121,580)(122,579)(123,578)(124,577)(125,576)(126,575)(127,574)
(128,573)(129,572)(130,571)(131,570)(132,569)(133,568)(134,567)(135,566)
(136,565)(137,564)(138,563)(139,562)(140,561)(141,560)(142,559)(143,558)
(144,557)(145,556)(146,555)(147,554)(148,498)(149,504)(150,503)(151,502)
(152,501)(153,500)(154,499)(155,491)(156,497)(157,496)(158,495)(159,494)
(160,493)(161,492)(162,539)(163,538)(164,537)(165,536)(166,535)(167,534)
(168,533)(169,532)(170,531)(171,530)(172,529)(173,528)(174,527)(175,526)
(176,525)(177,524)(178,523)(179,522)(180,521)(181,520)(182,519)(183,518)
(184,517)(185,516)(186,515)(187,514)(188,513)(189,512)(190,511)(191,510)
(192,509)(193,508)(194,507)(195,506)(196,505)(197,694)(198,700)(199,699)
(200,698)(201,697)(202,696)(203,695)(204,687)(205,693)(206,692)(207,691)
(208,690)(209,689)(210,688)(211,735)(212,734)(213,733)(214,732)(215,731)
(216,730)(217,729)(218,728)(219,727)(220,726)(221,725)(222,724)(223,723)
(224,722)(225,721)(226,720)(227,719)(228,718)(229,717)(230,716)(231,715)
(232,714)(233,713)(234,712)(235,711)(236,710)(237,709)(238,708)(239,707)
(240,706)(241,705)(242,704)(243,703)(244,702)(245,701)(246,743)(247,749)
(248,748)(249,747)(250,746)(251,745)(252,744)(253,736)(254,742)(255,741)
(256,740)(257,739)(258,738)(259,737)(260,784)(261,783)(262,782)(263,781)
(264,780)(265,779)(266,778)(267,777)(268,776)(269,775)(270,774)(271,773)
(272,772)(273,771)(274,770)(275,769)(276,768)(277,767)(278,766)(279,765)
(280,764)(281,763)(282,762)(283,761)(284,760)(285,759)(286,758)(287,757)
(288,756)(289,755)(290,754)(291,753)(292,752)(293,751)(294,750)(295,596)
(296,602)(297,601)(298,600)(299,599)(300,598)(301,597)(302,589)(303,595)
(304,594)(305,593)(306,592)(307,591)(308,590)(309,637)(310,636)(311,635)
(312,634)(313,633)(314,632)(315,631)(316,630)(317,629)(318,628)(319,627)
(320,626)(321,625)(322,624)(323,623)(324,622)(325,621)(326,620)(327,619)
(328,618)(329,617)(330,616)(331,615)(332,614)(333,613)(334,612)(335,611)
(336,610)(337,609)(338,608)(339,607)(340,606)(341,605)(342,604)(343,603)
(344,645)(345,651)(346,650)(347,649)(348,648)(349,647)(350,646)(351,638)
(352,644)(353,643)(354,642)(355,641)(356,640)(357,639)(358,686)(359,685)
(360,684)(361,683)(362,682)(363,681)(364,680)(365,679)(366,678)(367,677)
(368,676)(369,675)(370,674)(371,673)(372,672)(373,671)(374,670)(375,669)
(376,668)(377,667)(378,666)(379,665)(380,664)(381,663)(382,662)(383,661)
(384,660)(385,659)(386,658)(387,657)(388,656)(389,655)(390,654)(391,653)
(392,652);
poly := sub<Sym(784)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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