Polytope of Type {728}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {728}*1456
Also Known As : 728-gon, {728}. if this polytope has another name.
Group : SmallGroup(1456,67)
Rank : 2
Schlafli Type : {728}
Number of vertices, edges, etc : 728, 728
Order of s₀s₁ : 728
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 : {364}*728
   4-fold quotients : {182}*364
   7-fold quotients : {104}*208
   8-fold quotients : {91}*182
   13-fold quotients : {56}*112
   14-fold quotients : {52}*104
   26-fold quotients : {28}*56
   28-fold quotients : {26}*52
   52-fold quotients : {14}*28
   56-fold quotients : {13}*26
   91-fold quotients : {8}*16
   104-fold quotients : {7}*14
   182-fold quotients : {4}*8
   364-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 13)(  3, 12)(  4, 11)(  5, 10)(  6,  9)(  7,  8)( 14, 79)( 15, 91)
( 16, 90)( 17, 89)( 18, 88)( 19, 87)( 20, 86)( 21, 85)( 22, 84)( 23, 83)
( 24, 82)( 25, 81)( 26, 80)( 27, 66)( 28, 78)( 29, 77)( 30, 76)( 31, 75)
( 32, 74)( 33, 73)( 34, 72)( 35, 71)( 36, 70)( 37, 69)( 38, 68)( 39, 67)
( 40, 53)( 41, 65)( 42, 64)( 43, 63)( 44, 62)( 45, 61)( 46, 60)( 47, 59)
( 48, 58)( 49, 57)( 50, 56)( 51, 55)( 52, 54)( 93,104)( 94,103)( 95,102)
( 96,101)( 97,100)( 98, 99)(105,170)(106,182)(107,181)(108,180)(109,179)
(110,178)(111,177)(112,176)(113,175)(114,174)(115,173)(116,172)(117,171)
(118,157)(119,169)(120,168)(121,167)(122,166)(123,165)(124,164)(125,163)
(126,162)(127,161)(128,160)(129,159)(130,158)(131,144)(132,156)(133,155)
(134,154)(135,153)(136,152)(137,151)(138,150)(139,149)(140,148)(141,147)
(142,146)(143,145)(183,274)(184,286)(185,285)(186,284)(187,283)(188,282)
(189,281)(190,280)(191,279)(192,278)(193,277)(194,276)(195,275)(196,352)
(197,364)(198,363)(199,362)(200,361)(201,360)(202,359)(203,358)(204,357)
(205,356)(206,355)(207,354)(208,353)(209,339)(210,351)(211,350)(212,349)
(213,348)(214,347)(215,346)(216,345)(217,344)(218,343)(219,342)(220,341)
(221,340)(222,326)(223,338)(224,337)(225,336)(226,335)(227,334)(228,333)
(229,332)(230,331)(231,330)(232,329)(233,328)(234,327)(235,313)(236,325)
(237,324)(238,323)(239,322)(240,321)(241,320)(242,319)(243,318)(244,317)
(245,316)(246,315)(247,314)(248,300)(249,312)(250,311)(251,310)(252,309)
(253,308)(254,307)(255,306)(256,305)(257,304)(258,303)(259,302)(260,301)
(261,287)(262,299)(263,298)(264,297)(265,296)(266,295)(267,294)(268,293)
(269,292)(270,291)(271,290)(272,289)(273,288)(365,547)(366,559)(367,558)
(368,557)(369,556)(370,555)(371,554)(372,553)(373,552)(374,551)(375,550)
(376,549)(377,548)(378,625)(379,637)(380,636)(381,635)(382,634)(383,633)
(384,632)(385,631)(386,630)(387,629)(388,628)(389,627)(390,626)(391,612)
(392,624)(393,623)(394,622)(395,621)(396,620)(397,619)(398,618)(399,617)
(400,616)(401,615)(402,614)(403,613)(404,599)(405,611)(406,610)(407,609)
(408,608)(409,607)(410,606)(411,605)(412,604)(413,603)(414,602)(415,601)
(416,600)(417,586)(418,598)(419,597)(420,596)(421,595)(422,594)(423,593)
(424,592)(425,591)(426,590)(427,589)(428,588)(429,587)(430,573)(431,585)
(432,584)(433,583)(434,582)(435,581)(436,580)(437,579)(438,578)(439,577)
(440,576)(441,575)(442,574)(443,560)(444,572)(445,571)(446,570)(447,569)
(448,568)(449,567)(450,566)(451,565)(452,564)(453,563)(454,562)(455,561)
(456,638)(457,650)(458,649)(459,648)(460,647)(461,646)(462,645)(463,644)
(464,643)(465,642)(466,641)(467,640)(468,639)(469,716)(470,728)(471,727)
(472,726)(473,725)(474,724)(475,723)(476,722)(477,721)(478,720)(479,719)
(480,718)(481,717)(482,703)(483,715)(484,714)(485,713)(486,712)(487,711)
(488,710)(489,709)(490,708)(491,707)(492,706)(493,705)(494,704)(495,690)
(496,702)(497,701)(498,700)(499,699)(500,698)(501,697)(502,696)(503,695)
(504,694)(505,693)(506,692)(507,691)(508,677)(509,689)(510,688)(511,687)
(512,686)(513,685)(514,684)(515,683)(516,682)(517,681)(518,680)(519,679)
(520,678)(521,664)(522,676)(523,675)(524,674)(525,673)(526,672)(527,671)
(528,670)(529,669)(530,668)(531,667)(532,666)(533,665)(534,651)(535,663)
(536,662)(537,661)(538,660)(539,659)(540,658)(541,657)(542,656)(543,655)
(544,654)(545,653)(546,652);;
s1 := (  1,379)(  2,378)(  3,390)(  4,389)(  5,388)(  6,387)(  7,386)(  8,385)
(  9,384)( 10,383)( 11,382)( 12,381)( 13,380)( 14,366)( 15,365)( 16,377)
( 17,376)( 18,375)( 19,374)( 20,373)( 21,372)( 22,371)( 23,370)( 24,369)
( 25,368)( 26,367)( 27,444)( 28,443)( 29,455)( 30,454)( 31,453)( 32,452)
( 33,451)( 34,450)( 35,449)( 36,448)( 37,447)( 38,446)( 39,445)( 40,431)
( 41,430)( 42,442)( 43,441)( 44,440)( 45,439)( 46,438)( 47,437)( 48,436)
( 49,435)( 50,434)( 51,433)( 52,432)( 53,418)( 54,417)( 55,429)( 56,428)
( 57,427)( 58,426)( 59,425)( 60,424)( 61,423)( 62,422)( 63,421)( 64,420)
( 65,419)( 66,405)( 67,404)( 68,416)( 69,415)( 70,414)( 71,413)( 72,412)
( 73,411)( 74,410)( 75,409)( 76,408)( 77,407)( 78,406)( 79,392)( 80,391)
( 81,403)( 82,402)( 83,401)( 84,400)( 85,399)( 86,398)( 87,397)( 88,396)
( 89,395)( 90,394)( 91,393)( 92,470)( 93,469)( 94,481)( 95,480)( 96,479)
( 97,478)( 98,477)( 99,476)(100,475)(101,474)(102,473)(103,472)(104,471)
(105,457)(106,456)(107,468)(108,467)(109,466)(110,465)(111,464)(112,463)
(113,462)(114,461)(115,460)(116,459)(117,458)(118,535)(119,534)(120,546)
(121,545)(122,544)(123,543)(124,542)(125,541)(126,540)(127,539)(128,538)
(129,537)(130,536)(131,522)(132,521)(133,533)(134,532)(135,531)(136,530)
(137,529)(138,528)(139,527)(140,526)(141,525)(142,524)(143,523)(144,509)
(145,508)(146,520)(147,519)(148,518)(149,517)(150,516)(151,515)(152,514)
(153,513)(154,512)(155,511)(156,510)(157,496)(158,495)(159,507)(160,506)
(161,505)(162,504)(163,503)(164,502)(165,501)(166,500)(167,499)(168,498)
(169,497)(170,483)(171,482)(172,494)(173,493)(174,492)(175,491)(176,490)
(177,489)(178,488)(179,487)(180,486)(181,485)(182,484)(183,652)(184,651)
(185,663)(186,662)(187,661)(188,660)(189,659)(190,658)(191,657)(192,656)
(193,655)(194,654)(195,653)(196,639)(197,638)(198,650)(199,649)(200,648)
(201,647)(202,646)(203,645)(204,644)(205,643)(206,642)(207,641)(208,640)
(209,717)(210,716)(211,728)(212,727)(213,726)(214,725)(215,724)(216,723)
(217,722)(218,721)(219,720)(220,719)(221,718)(222,704)(223,703)(224,715)
(225,714)(226,713)(227,712)(228,711)(229,710)(230,709)(231,708)(232,707)
(233,706)(234,705)(235,691)(236,690)(237,702)(238,701)(239,700)(240,699)
(241,698)(242,697)(243,696)(244,695)(245,694)(246,693)(247,692)(248,678)
(249,677)(250,689)(251,688)(252,687)(253,686)(254,685)(255,684)(256,683)
(257,682)(258,681)(259,680)(260,679)(261,665)(262,664)(263,676)(264,675)
(265,674)(266,673)(267,672)(268,671)(269,670)(270,669)(271,668)(272,667)
(273,666)(274,561)(275,560)(276,572)(277,571)(278,570)(279,569)(280,568)
(281,567)(282,566)(283,565)(284,564)(285,563)(286,562)(287,548)(288,547)
(289,559)(290,558)(291,557)(292,556)(293,555)(294,554)(295,553)(296,552)
(297,551)(298,550)(299,549)(300,626)(301,625)(302,637)(303,636)(304,635)
(305,634)(306,633)(307,632)(308,631)(309,630)(310,629)(311,628)(312,627)
(313,613)(314,612)(315,624)(316,623)(317,622)(318,621)(319,620)(320,619)
(321,618)(322,617)(323,616)(324,615)(325,614)(326,600)(327,599)(328,611)
(329,610)(330,609)(331,608)(332,607)(333,606)(334,605)(335,604)(336,603)
(337,602)(338,601)(339,587)(340,586)(341,598)(342,597)(343,596)(344,595)
(345,594)(346,593)(347,592)(348,591)(349,590)(350,589)(351,588)(352,574)
(353,573)(354,585)(355,584)(356,583)(357,582)(358,581)(359,580)(360,579)
(361,578)(362,577)(363,576)(364,575);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(728)!(  2, 13)(  3, 12)(  4, 11)(  5, 10)(  6,  9)(  7,  8)( 14, 79)
( 15, 91)( 16, 90)( 17, 89)( 18, 88)( 19, 87)( 20, 86)( 21, 85)( 22, 84)
( 23, 83)( 24, 82)( 25, 81)( 26, 80)( 27, 66)( 28, 78)( 29, 77)( 30, 76)
( 31, 75)( 32, 74)( 33, 73)( 34, 72)( 35, 71)( 36, 70)( 37, 69)( 38, 68)
( 39, 67)( 40, 53)( 41, 65)( 42, 64)( 43, 63)( 44, 62)( 45, 61)( 46, 60)
( 47, 59)( 48, 58)( 49, 57)( 50, 56)( 51, 55)( 52, 54)( 93,104)( 94,103)
( 95,102)( 96,101)( 97,100)( 98, 99)(105,170)(106,182)(107,181)(108,180)
(109,179)(110,178)(111,177)(112,176)(113,175)(114,174)(115,173)(116,172)
(117,171)(118,157)(119,169)(120,168)(121,167)(122,166)(123,165)(124,164)
(125,163)(126,162)(127,161)(128,160)(129,159)(130,158)(131,144)(132,156)
(133,155)(134,154)(135,153)(136,152)(137,151)(138,150)(139,149)(140,148)
(141,147)(142,146)(143,145)(183,274)(184,286)(185,285)(186,284)(187,283)
(188,282)(189,281)(190,280)(191,279)(192,278)(193,277)(194,276)(195,275)
(196,352)(197,364)(198,363)(199,362)(200,361)(201,360)(202,359)(203,358)
(204,357)(205,356)(206,355)(207,354)(208,353)(209,339)(210,351)(211,350)
(212,349)(213,348)(214,347)(215,346)(216,345)(217,344)(218,343)(219,342)
(220,341)(221,340)(222,326)(223,338)(224,337)(225,336)(226,335)(227,334)
(228,333)(229,332)(230,331)(231,330)(232,329)(233,328)(234,327)(235,313)
(236,325)(237,324)(238,323)(239,322)(240,321)(241,320)(242,319)(243,318)
(244,317)(245,316)(246,315)(247,314)(248,300)(249,312)(250,311)(251,310)
(252,309)(253,308)(254,307)(255,306)(256,305)(257,304)(258,303)(259,302)
(260,301)(261,287)(262,299)(263,298)(264,297)(265,296)(266,295)(267,294)
(268,293)(269,292)(270,291)(271,290)(272,289)(273,288)(365,547)(366,559)
(367,558)(368,557)(369,556)(370,555)(371,554)(372,553)(373,552)(374,551)
(375,550)(376,549)(377,548)(378,625)(379,637)(380,636)(381,635)(382,634)
(383,633)(384,632)(385,631)(386,630)(387,629)(388,628)(389,627)(390,626)
(391,612)(392,624)(393,623)(394,622)(395,621)(396,620)(397,619)(398,618)
(399,617)(400,616)(401,615)(402,614)(403,613)(404,599)(405,611)(406,610)
(407,609)(408,608)(409,607)(410,606)(411,605)(412,604)(413,603)(414,602)
(415,601)(416,600)(417,586)(418,598)(419,597)(420,596)(421,595)(422,594)
(423,593)(424,592)(425,591)(426,590)(427,589)(428,588)(429,587)(430,573)
(431,585)(432,584)(433,583)(434,582)(435,581)(436,580)(437,579)(438,578)
(439,577)(440,576)(441,575)(442,574)(443,560)(444,572)(445,571)(446,570)
(447,569)(448,568)(449,567)(450,566)(451,565)(452,564)(453,563)(454,562)
(455,561)(456,638)(457,650)(458,649)(459,648)(460,647)(461,646)(462,645)
(463,644)(464,643)(465,642)(466,641)(467,640)(468,639)(469,716)(470,728)
(471,727)(472,726)(473,725)(474,724)(475,723)(476,722)(477,721)(478,720)
(479,719)(480,718)(481,717)(482,703)(483,715)(484,714)(485,713)(486,712)
(487,711)(488,710)(489,709)(490,708)(491,707)(492,706)(493,705)(494,704)
(495,690)(496,702)(497,701)(498,700)(499,699)(500,698)(501,697)(502,696)
(503,695)(504,694)(505,693)(506,692)(507,691)(508,677)(509,689)(510,688)
(511,687)(512,686)(513,685)(514,684)(515,683)(516,682)(517,681)(518,680)
(519,679)(520,678)(521,664)(522,676)(523,675)(524,674)(525,673)(526,672)
(527,671)(528,670)(529,669)(530,668)(531,667)(532,666)(533,665)(534,651)
(535,663)(536,662)(537,661)(538,660)(539,659)(540,658)(541,657)(542,656)
(543,655)(544,654)(545,653)(546,652);
s1 := Sym(728)!(  1,379)(  2,378)(  3,390)(  4,389)(  5,388)(  6,387)(  7,386)
(  8,385)(  9,384)( 10,383)( 11,382)( 12,381)( 13,380)( 14,366)( 15,365)
( 16,377)( 17,376)( 18,375)( 19,374)( 20,373)( 21,372)( 22,371)( 23,370)
( 24,369)( 25,368)( 26,367)( 27,444)( 28,443)( 29,455)( 30,454)( 31,453)
( 32,452)( 33,451)( 34,450)( 35,449)( 36,448)( 37,447)( 38,446)( 39,445)
( 40,431)( 41,430)( 42,442)( 43,441)( 44,440)( 45,439)( 46,438)( 47,437)
( 48,436)( 49,435)( 50,434)( 51,433)( 52,432)( 53,418)( 54,417)( 55,429)
( 56,428)( 57,427)( 58,426)( 59,425)( 60,424)( 61,423)( 62,422)( 63,421)
( 64,420)( 65,419)( 66,405)( 67,404)( 68,416)( 69,415)( 70,414)( 71,413)
( 72,412)( 73,411)( 74,410)( 75,409)( 76,408)( 77,407)( 78,406)( 79,392)
( 80,391)( 81,403)( 82,402)( 83,401)( 84,400)( 85,399)( 86,398)( 87,397)
( 88,396)( 89,395)( 90,394)( 91,393)( 92,470)( 93,469)( 94,481)( 95,480)
( 96,479)( 97,478)( 98,477)( 99,476)(100,475)(101,474)(102,473)(103,472)
(104,471)(105,457)(106,456)(107,468)(108,467)(109,466)(110,465)(111,464)
(112,463)(113,462)(114,461)(115,460)(116,459)(117,458)(118,535)(119,534)
(120,546)(121,545)(122,544)(123,543)(124,542)(125,541)(126,540)(127,539)
(128,538)(129,537)(130,536)(131,522)(132,521)(133,533)(134,532)(135,531)
(136,530)(137,529)(138,528)(139,527)(140,526)(141,525)(142,524)(143,523)
(144,509)(145,508)(146,520)(147,519)(148,518)(149,517)(150,516)(151,515)
(152,514)(153,513)(154,512)(155,511)(156,510)(157,496)(158,495)(159,507)
(160,506)(161,505)(162,504)(163,503)(164,502)(165,501)(166,500)(167,499)
(168,498)(169,497)(170,483)(171,482)(172,494)(173,493)(174,492)(175,491)
(176,490)(177,489)(178,488)(179,487)(180,486)(181,485)(182,484)(183,652)
(184,651)(185,663)(186,662)(187,661)(188,660)(189,659)(190,658)(191,657)
(192,656)(193,655)(194,654)(195,653)(196,639)(197,638)(198,650)(199,649)
(200,648)(201,647)(202,646)(203,645)(204,644)(205,643)(206,642)(207,641)
(208,640)(209,717)(210,716)(211,728)(212,727)(213,726)(214,725)(215,724)
(216,723)(217,722)(218,721)(219,720)(220,719)(221,718)(222,704)(223,703)
(224,715)(225,714)(226,713)(227,712)(228,711)(229,710)(230,709)(231,708)
(232,707)(233,706)(234,705)(235,691)(236,690)(237,702)(238,701)(239,700)
(240,699)(241,698)(242,697)(243,696)(244,695)(245,694)(246,693)(247,692)
(248,678)(249,677)(250,689)(251,688)(252,687)(253,686)(254,685)(255,684)
(256,683)(257,682)(258,681)(259,680)(260,679)(261,665)(262,664)(263,676)
(264,675)(265,674)(266,673)(267,672)(268,671)(269,670)(270,669)(271,668)
(272,667)(273,666)(274,561)(275,560)(276,572)(277,571)(278,570)(279,569)
(280,568)(281,567)(282,566)(283,565)(284,564)(285,563)(286,562)(287,548)
(288,547)(289,559)(290,558)(291,557)(292,556)(293,555)(294,554)(295,553)
(296,552)(297,551)(298,550)(299,549)(300,626)(301,625)(302,637)(303,636)
(304,635)(305,634)(306,633)(307,632)(308,631)(309,630)(310,629)(311,628)
(312,627)(313,613)(314,612)(315,624)(316,623)(317,622)(318,621)(319,620)
(320,619)(321,618)(322,617)(323,616)(324,615)(325,614)(326,600)(327,599)
(328,611)(329,610)(330,609)(331,608)(332,607)(333,606)(334,605)(335,604)
(336,603)(337,602)(338,601)(339,587)(340,586)(341,598)(342,597)(343,596)
(344,595)(345,594)(346,593)(347,592)(348,591)(349,590)(350,589)(351,588)
(352,574)(353,573)(354,585)(355,584)(356,583)(357,582)(358,581)(359,580)
(360,579)(361,578)(362,577)(363,576)(364,575);
poly := sub<Sym(728)|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 >;

References : None.
to this polytope