Polytope of Type {722}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {722}*1444
Also Known As : 722-gon, {722}. if this polytope has another name.
Group : SmallGroup(1444,3)
Rank : 2
Schlafli Type : {722}
Number of vertices, edges, etc : 722, 722
Order of s₀s₁ : 722
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 : {361}*722
   19-fold quotients : {38}*76
   38-fold quotients : {19}*38
   361-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope