Polytope of Type {726}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {726}*1452
Also Known As : 726-gon, {726}. if this polytope has another name.
Group : SmallGroup(1452,9)
Rank : 2
Schlafli Type : {726}
Number of vertices, edges, etc : 726, 726
Order of s₀s₁ : 726
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 : {363}*726
   3-fold quotients : {242}*484
   6-fold quotients : {121}*242
   11-fold quotients : {66}*132
   22-fold quotients : {33}*66
   33-fold quotients : {22}*44
   66-fold quotients : {11}*22
   121-fold quotients : {6}*12
   242-fold quotients : {3}*6
   363-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)( 12,112)( 13,111)( 14,121)
( 15,120)( 16,119)( 17,118)( 18,117)( 19,116)( 20,115)( 21,114)( 22,113)
( 23,101)( 24,100)( 25,110)( 26,109)( 27,108)( 28,107)( 29,106)( 30,105)
( 31,104)( 32,103)( 33,102)( 34, 90)( 35, 89)( 36, 99)( 37, 98)( 38, 97)
( 39, 96)( 40, 95)( 41, 94)( 42, 93)( 43, 92)( 44, 91)( 45, 79)( 46, 78)
( 47, 88)( 48, 87)( 49, 86)( 50, 85)( 51, 84)( 52, 83)( 53, 82)( 54, 81)
( 55, 80)( 56, 68)( 57, 67)( 58, 77)( 59, 76)( 60, 75)( 61, 74)( 62, 73)
( 63, 72)( 64, 71)( 65, 70)( 66, 69)(122,243)(123,253)(124,252)(125,251)
(126,250)(127,249)(128,248)(129,247)(130,246)(131,245)(132,244)(133,354)
(134,353)(135,363)(136,362)(137,361)(138,360)(139,359)(140,358)(141,357)
(142,356)(143,355)(144,343)(145,342)(146,352)(147,351)(148,350)(149,349)
(150,348)(151,347)(152,346)(153,345)(154,344)(155,332)(156,331)(157,341)
(158,340)(159,339)(160,338)(161,337)(162,336)(163,335)(164,334)(165,333)
(166,321)(167,320)(168,330)(169,329)(170,328)(171,327)(172,326)(173,325)
(174,324)(175,323)(176,322)(177,310)(178,309)(179,319)(180,318)(181,317)
(182,316)(183,315)(184,314)(185,313)(186,312)(187,311)(188,299)(189,298)
(190,308)(191,307)(192,306)(193,305)(194,304)(195,303)(196,302)(197,301)
(198,300)(199,288)(200,287)(201,297)(202,296)(203,295)(204,294)(205,293)
(206,292)(207,291)(208,290)(209,289)(210,277)(211,276)(212,286)(213,285)
(214,284)(215,283)(216,282)(217,281)(218,280)(219,279)(220,278)(221,266)
(222,265)(223,275)(224,274)(225,273)(226,272)(227,271)(228,270)(229,269)
(230,268)(231,267)(232,255)(233,254)(234,264)(235,263)(236,262)(237,261)
(238,260)(239,259)(240,258)(241,257)(242,256)(365,374)(366,373)(367,372)
(368,371)(369,370)(375,475)(376,474)(377,484)(378,483)(379,482)(380,481)
(381,480)(382,479)(383,478)(384,477)(385,476)(386,464)(387,463)(388,473)
(389,472)(390,471)(391,470)(392,469)(393,468)(394,467)(395,466)(396,465)
(397,453)(398,452)(399,462)(400,461)(401,460)(402,459)(403,458)(404,457)
(405,456)(406,455)(407,454)(408,442)(409,441)(410,451)(411,450)(412,449)
(413,448)(414,447)(415,446)(416,445)(417,444)(418,443)(419,431)(420,430)
(421,440)(422,439)(423,438)(424,437)(425,436)(426,435)(427,434)(428,433)
(429,432)(485,606)(486,616)(487,615)(488,614)(489,613)(490,612)(491,611)
(492,610)(493,609)(494,608)(495,607)(496,717)(497,716)(498,726)(499,725)
(500,724)(501,723)(502,722)(503,721)(504,720)(505,719)(506,718)(507,706)
(508,705)(509,715)(510,714)(511,713)(512,712)(513,711)(514,710)(515,709)
(516,708)(517,707)(518,695)(519,694)(520,704)(521,703)(522,702)(523,701)
(524,700)(525,699)(526,698)(527,697)(528,696)(529,684)(530,683)(531,693)
(532,692)(533,691)(534,690)(535,689)(536,688)(537,687)(538,686)(539,685)
(540,673)(541,672)(542,682)(543,681)(544,680)(545,679)(546,678)(547,677)
(548,676)(549,675)(550,674)(551,662)(552,661)(553,671)(554,670)(555,669)
(556,668)(557,667)(558,666)(559,665)(560,664)(561,663)(562,651)(563,650)
(564,660)(565,659)(566,658)(567,657)(568,656)(569,655)(570,654)(571,653)
(572,652)(573,640)(574,639)(575,649)(576,648)(577,647)(578,646)(579,645)
(580,644)(581,643)(582,642)(583,641)(584,629)(585,628)(586,638)(587,637)
(588,636)(589,635)(590,634)(591,633)(592,632)(593,631)(594,630)(595,618)
(596,617)(597,627)(598,626)(599,625)(600,624)(601,623)(602,622)(603,621)
(604,620)(605,619);;
s1 := (  1,496)(  2,506)(  3,505)(  4,504)(  5,503)(  6,502)(  7,501)(  8,500)
(  9,499)( 10,498)( 11,497)( 12,485)( 13,495)( 14,494)( 15,493)( 16,492)
( 17,491)( 18,490)( 19,489)( 20,488)( 21,487)( 22,486)( 23,596)( 24,595)
( 25,605)( 26,604)( 27,603)( 28,602)( 29,601)( 30,600)( 31,599)( 32,598)
( 33,597)( 34,585)( 35,584)( 36,594)( 37,593)( 38,592)( 39,591)( 40,590)
( 41,589)( 42,588)( 43,587)( 44,586)( 45,574)( 46,573)( 47,583)( 48,582)
( 49,581)( 50,580)( 51,579)( 52,578)( 53,577)( 54,576)( 55,575)( 56,563)
( 57,562)( 58,572)( 59,571)( 60,570)( 61,569)( 62,568)( 63,567)( 64,566)
( 65,565)( 66,564)( 67,552)( 68,551)( 69,561)( 70,560)( 71,559)( 72,558)
( 73,557)( 74,556)( 75,555)( 76,554)( 77,553)( 78,541)( 79,540)( 80,550)
( 81,549)( 82,548)( 83,547)( 84,546)( 85,545)( 86,544)( 87,543)( 88,542)
( 89,530)( 90,529)( 91,539)( 92,538)( 93,537)( 94,536)( 95,535)( 96,534)
( 97,533)( 98,532)( 99,531)(100,519)(101,518)(102,528)(103,527)(104,526)
(105,525)(106,524)(107,523)(108,522)(109,521)(110,520)(111,508)(112,507)
(113,517)(114,516)(115,515)(116,514)(117,513)(118,512)(119,511)(120,510)
(121,509)(122,375)(123,385)(124,384)(125,383)(126,382)(127,381)(128,380)
(129,379)(130,378)(131,377)(132,376)(133,364)(134,374)(135,373)(136,372)
(137,371)(138,370)(139,369)(140,368)(141,367)(142,366)(143,365)(144,475)
(145,474)(146,484)(147,483)(148,482)(149,481)(150,480)(151,479)(152,478)
(153,477)(154,476)(155,464)(156,463)(157,473)(158,472)(159,471)(160,470)
(161,469)(162,468)(163,467)(164,466)(165,465)(166,453)(167,452)(168,462)
(169,461)(170,460)(171,459)(172,458)(173,457)(174,456)(175,455)(176,454)
(177,442)(178,441)(179,451)(180,450)(181,449)(182,448)(183,447)(184,446)
(185,445)(186,444)(187,443)(188,431)(189,430)(190,440)(191,439)(192,438)
(193,437)(194,436)(195,435)(196,434)(197,433)(198,432)(199,420)(200,419)
(201,429)(202,428)(203,427)(204,426)(205,425)(206,424)(207,423)(208,422)
(209,421)(210,409)(211,408)(212,418)(213,417)(214,416)(215,415)(216,414)
(217,413)(218,412)(219,411)(220,410)(221,398)(222,397)(223,407)(224,406)
(225,405)(226,404)(227,403)(228,402)(229,401)(230,400)(231,399)(232,387)
(233,386)(234,396)(235,395)(236,394)(237,393)(238,392)(239,391)(240,390)
(241,389)(242,388)(243,617)(244,627)(245,626)(246,625)(247,624)(248,623)
(249,622)(250,621)(251,620)(252,619)(253,618)(254,606)(255,616)(256,615)
(257,614)(258,613)(259,612)(260,611)(261,610)(262,609)(263,608)(264,607)
(265,717)(266,716)(267,726)(268,725)(269,724)(270,723)(271,722)(272,721)
(273,720)(274,719)(275,718)(276,706)(277,705)(278,715)(279,714)(280,713)
(281,712)(282,711)(283,710)(284,709)(285,708)(286,707)(287,695)(288,694)
(289,704)(290,703)(291,702)(292,701)(293,700)(294,699)(295,698)(296,697)
(297,696)(298,684)(299,683)(300,693)(301,692)(302,691)(303,690)(304,689)
(305,688)(306,687)(307,686)(308,685)(309,673)(310,672)(311,682)(312,681)
(313,680)(314,679)(315,678)(316,677)(317,676)(318,675)(319,674)(320,662)
(321,661)(322,671)(323,670)(324,669)(325,668)(326,667)(327,666)(328,665)
(329,664)(330,663)(331,651)(332,650)(333,660)(334,659)(335,658)(336,657)
(337,656)(338,655)(339,654)(340,653)(341,652)(342,640)(343,639)(344,649)
(345,648)(346,647)(347,646)(348,645)(349,644)(350,643)(351,642)(352,641)
(353,629)(354,628)(355,638)(356,637)(357,636)(358,635)(359,634)(360,633)
(361,632)(362,631)(363,630);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope