Polytope of Type {730}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {730}*1460
Also Known As : 730-gon, {730}. if this polytope has another name.
Group : SmallGroup(1460,14)
Rank : 2
Schlafli Type : {730}
Number of vertices, edges, etc : 730, 730
Order of s₀s₁ : 730
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 : {365}*730
   5-fold quotients : {146}*292
   10-fold quotients : {73}*146
   73-fold quotients : {10}*20
   146-fold quotients : {5}*10
   365-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) :

s0 := (  2, 73)(  3, 72)(  4, 71)(  5, 70)(  6, 69)(  7, 68)(  8, 67)(  9, 66)( 10, 65)( 11, 64)( 12, 63)( 13, 62)( 14, 61)( 15, 60)( 16, 59)( 17, 58)( 18, 57)( 19, 56)( 20, 55)( 21, 54)( 22, 53)( 23, 52)( 24, 51)( 25, 50)( 26, 49)( 27, 48)( 28, 47)( 29, 46)( 30, 45)( 31, 44)( 32, 43)( 33, 42)( 34, 41)( 35, 40)( 36, 39)( 37, 38)( 74,293)( 75,365)( 76,364)( 77,363)( 78,362)( 79,361)( 80,360)( 81,359)( 82,358)( 83,357)( 84,356)( 85,355)( 86,354)( 87,353)( 88,352)( 89,351)( 90,350)( 91,349)( 92,348)( 93,347)( 94,346)( 95,345)( 96,344)( 97,343)( 98,342)( 99,341)(100,340)(101,339)(102,338)(103,337)(104,336)(105,335)(106,334)(107,333)(108,332)(109,331)(110,330)(111,329)(112,328)(113,327)(114,326)(115,325)(116,324)(117,323)(118,322)(119,321)(120,320)(121,319)(122,318)(123,317)(124,316)(125,315)(126,314)(127,313)(128,312)(129,311)(130,310)(131,309)(132,308)(133,307)(134,306)(135,305)(136,304)(137,303)(138,302)(139,301)(140,300)(141,299)(142,298)(143,297)(144,296)(145,295)(146,294)(147,220)(148,292)(149,291)(150,290)(151,289)(152,288)(153,287)(154,286)(155,285)(156,284)(157,283)(158,282)(159,281)(160,280)(161,279)(162,278)(163,277)(164,276)(165,275)(166,274)(167,273)(168,272)(169,271)(170,270)(171,269)(172,268)(173,267)(174,266)(175,265)(176,264)(177,263)(178,262)(179,261)(180,260)(181,259)(182,258)(183,257)(184,256)(185,255)(186,254)(187,253)(188,252)(189,251)(190,250)(191,249)(192,248)(193,247)(194,246)(195,245)(196,244)(197,243)(198,242)(199,241)(200,240)(201,239)(202,238)(203,237)(204,236)(205,235)(206,234)(207,233)(208,232)(209,231)(210,230)(211,229)(212,228)(213,227)(214,226)(215,225)(216,224)(217,223)(218,222)(219,221)(367,438)(368,437)(369,436)(370,435)(371,434)(372,433)(373,432)(374,431)(375,430)(376,429)(377,428)(378,427)(379,426)(380,425)(381,424)(382,423)(383,422)(384,421)(385,420)(386,419)(387,418)(388,417)(389,416)(390,415)(391,414)(392,413)(393,412)(394,411)(395,410)(396,409)(397,408)(398,407)(399,406)(400,405)(401,404)(402,403)(439,658)(440,730)(441,729)(442,728)(443,727)(444,726)(445,725)(446,724)(447,723)(448,722)(449,721)(450,720)(451,719)(452,718)(453,717)(454,716)(455,715)(456,714)(457,713)(458,712)(459,711)(460,710)(461,709)(462,708)(463,707)(464,706)(465,705)(466,704)(467,703)(468,702)(469,701)(470,700)(471,699)(472,698)(473,697)(474,696)(475,695)(476,694)(477,693)(478,692)(479,691)(480,690)(481,689)(482,688)(483,687)(484,686)(485,685)(486,684)(487,683)(488,682)(489,681)(490,680)(491,679)(492,678)(493,677)(494,676)(495,675)(496,674)(497,673)(498,672)(499,671)(500,670)(501,669)(502,668)(503,667)(504,666)(505,665)(506,664)(507,663)(508,662)(509,661)(510,660)(511,659)(512,585)(513,657)(514,656)(515,655)(516,654)(517,653)(518,652)(519,651)(520,650)(521,649)(522,648)(523,647)(524,646)(525,645)(526,644)(527,643)(528,642)(529,641)(530,640)(531,639)(532,638)(533,637)(534,636)(535,635)(536,634)(537,633)(538,632)(539,631)(540,630)(541,629)(542,628)(543,627)(544,626)(545,625)(546,624)(547,623)(548,622)(549,621)(550,620)(551,619)(552,618)(553,617)(554,616)(555,615)(556,614)(557,613)(558,612)(559,611)(560,610)(561,609)(562,608)(563,607)(564,606)(565,605)(566,604)(567,603)(568,602)(569,601)(570,600)(571,599)(572,598)(573,597)(574,596)(575,595)(576,594)(577,593)(578,592)(579,591)(580,590)(581,589)(582,588)(583,587)(584,586);;
s1 := (  1,440)(  2,439)(  3,511)(  4,510)(  5,509)(  6,508)(  7,507)(  8,506)(  9,505)( 10,504)( 11,503)( 12,502)( 13,501)( 14,500)( 15,499)( 16,498)( 17,497)( 18,496)( 19,495)( 20,494)( 21,493)( 22,492)( 23,491)( 24,490)( 25,489)( 26,488)( 27,487)( 28,486)( 29,485)( 30,484)( 31,483)( 32,482)( 33,481)( 34,480)( 35,479)( 36,478)( 37,477)( 38,476)( 39,475)( 40,474)( 41,473)( 42,472)( 43,471)( 44,470)( 45,469)( 46,468)( 47,467)( 48,466)( 49,465)( 50,464)( 51,463)( 52,462)( 53,461)( 54,460)( 55,459)( 56,458)( 57,457)( 58,456)( 59,455)( 60,454)( 61,453)( 62,452)( 63,451)( 64,450)( 65,449)( 66,448)( 67,447)( 68,446)( 69,445)( 70,444)( 71,443)( 72,442)( 73,441)( 74,367)( 75,366)( 76,438)( 77,437)( 78,436)( 79,435)( 80,434)( 81,433)( 82,432)( 83,431)( 84,430)( 85,429)( 86,428)( 87,427)( 88,426)( 89,425)( 90,424)( 91,423)( 92,422)( 93,421)( 94,420)( 95,419)( 96,418)( 97,417)( 98,416)( 99,415)(100,414)(101,413)(102,412)(103,411)(104,410)(105,409)(106,408)(107,407)(108,406)(109,405)(110,404)(111,403)(112,402)(113,401)(114,400)(115,399)(116,398)(117,397)(118,396)(119,395)(120,394)(121,393)(122,392)(123,391)(124,390)(125,389)(126,388)(127,387)(128,386)(129,385)(130,384)(131,383)(132,382)(133,381)(134,380)(135,379)(136,378)(137,377)(138,376)(139,375)(140,374)(141,373)(142,372)(143,371)(144,370)(145,369)(146,368)(147,659)(148,658)(149,730)(150,729)(151,728)(152,727)(153,726)(154,725)(155,724)(156,723)(157,722)(158,721)(159,720)(160,719)(161,718)(162,717)(163,716)(164,715)(165,714)(166,713)(167,712)(168,711)(169,710)(170,709)(171,708)(172,707)(173,706)(174,705)(175,704)(176,703)(177,702)(178,701)(179,700)(180,699)(181,698)(182,697)(183,696)(184,695)(185,694)(186,693)(187,692)(188,691)(189,690)(190,689)(191,688)(192,687)(193,686)(194,685)(195,684)(196,683)(197,682)(198,681)(199,680)(200,679)(201,678)(202,677)(203,676)(204,675)(205,674)(206,673)(207,672)(208,671)(209,670)(210,669)(211,668)(212,667)(213,666)(214,665)(215,664)(216,663)(217,662)(218,661)(219,660)(220,586)(221,585)(222,657)(223,656)(224,655)(225,654)(226,653)(227,652)(228,651)(229,650)(230,649)(231,648)(232,647)(233,646)(234,645)(235,644)(236,643)(237,642)(238,641)(239,640)(240,639)(241,638)(242,637)(243,636)(244,635)(245,634)(246,633)(247,632)(248,631)(249,630)(250,629)(251,628)(252,627)(253,626)(254,625)(255,624)(256,623)(257,622)(258,621)(259,620)(260,619)(261,618)(262,617)(263,616)(264,615)(265,614)(266,613)(267,612)(268,611)(269,610)(270,609)(271,608)(272,607)(273,606)(274,605)(275,604)(276,603)(277,602)(278,601)(279,600)(280,599)(281,598)(282,597)(283,596)(284,595)(285,594)(286,593)(287,592)(288,591)(289,590)(290,589)(291,588)(292,587)(293,513)(294,512)(295,584)(296,583)(297,582)(298,581)(299,580)(300,579)(301,578)(302,577)(303,576)(304,575)(305,574)(306,573)(307,572)(308,571)(309,570)(310,569)(311,568)(312,567)(313,566)(314,565)(315,564)(316,563)(317,562)(318,561)(319,560)(320,559)(321,558)(322,557)(323,556)(324,555)(325,554)(326,553)(327,552)(328,551)(329,550)(330,549)(331,548)(332,547)(333,546)(334,545)(335,544)(336,543)(337,542)(338,541)(339,540)(340,539)(341,538)(342,537)(343,536)(344,535)(345,534)(346,533)(347,532)(348,531)(349,530)(350,529)(351,528)(352,527)(353,526)(354,525)(355,524)(356,523)(357,522)(358,521)(359,520)(360,519)(361,518)(362,517)(363,516)(364,515)(365,514);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(730)!(  2, 73)(  3, 72)(  4, 71)(  5, 70)(  6, 69)(  7, 68)(  8, 67)(  9, 66)( 10, 65)( 11, 64)( 12, 63)( 13, 62)( 14, 61)( 15, 60)( 16, 59)( 17, 58)( 18, 57)( 19, 56)( 20, 55)( 21, 54)( 22, 53)( 23, 52)( 24, 51)( 25, 50)( 26, 49)( 27, 48)( 28, 47)( 29, 46)( 30, 45)( 31, 44)( 32, 43)( 33, 42)( 34, 41)( 35, 40)( 36, 39)( 37, 38)( 74,293)( 75,365)( 76,364)( 77,363)( 78,362)( 79,361)( 80,360)( 81,359)( 82,358)( 83,357)( 84,356)( 85,355)( 86,354)( 87,353)( 88,352)( 89,351)( 90,350)( 91,349)( 92,348)( 93,347)( 94,346)( 95,345)( 96,344)( 97,343)( 98,342)( 99,341)(100,340)(101,339)(102,338)(103,337)(104,336)(105,335)(106,334)(107,333)(108,332)(109,331)(110,330)(111,329)(112,328)(113,327)(114,326)(115,325)(116,324)(117,323)(118,322)(119,321)(120,320)(121,319)(122,318)(123,317)(124,316)(125,315)(126,314)(127,313)(128,312)(129,311)(130,310)(131,309)(132,308)(133,307)(134,306)(135,305)(136,304)(137,303)(138,302)(139,301)(140,300)(141,299)(142,298)(143,297)(144,296)(145,295)(146,294)(147,220)(148,292)(149,291)(150,290)(151,289)(152,288)(153,287)(154,286)(155,285)(156,284)(157,283)(158,282)(159,281)(160,280)(161,279)(162,278)(163,277)(164,276)(165,275)(166,274)(167,273)(168,272)(169,271)(170,270)(171,269)(172,268)(173,267)(174,266)(175,265)(176,264)(177,263)(178,262)(179,261)(180,260)(181,259)(182,258)(183,257)(184,256)(185,255)(186,254)(187,253)(188,252)(189,251)(190,250)(191,249)(192,248)(193,247)(194,246)(195,245)(196,244)(197,243)(198,242)(199,241)(200,240)(201,239)(202,238)(203,237)(204,236)(205,235)(206,234)(207,233)(208,232)(209,231)(210,230)(211,229)(212,228)(213,227)(214,226)(215,225)(216,224)(217,223)(218,222)(219,221)(367,438)(368,437)(369,436)(370,435)(371,434)(372,433)(373,432)(374,431)(375,430)(376,429)(377,428)(378,427)(379,426)(380,425)(381,424)(382,423)(383,422)(384,421)(385,420)(386,419)(387,418)(388,417)(389,416)(390,415)(391,414)(392,413)(393,412)(394,411)(395,410)(396,409)(397,408)(398,407)(399,406)(400,405)(401,404)(402,403)(439,658)(440,730)(441,729)(442,728)(443,727)(444,726)(445,725)(446,724)(447,723)(448,722)(449,721)(450,720)(451,719)(452,718)(453,717)(454,716)(455,715)(456,714)(457,713)(458,712)(459,711)(460,710)(461,709)(462,708)(463,707)(464,706)(465,705)(466,704)(467,703)(468,702)(469,701)(470,700)(471,699)(472,698)(473,697)(474,696)(475,695)(476,694)(477,693)(478,692)(479,691)(480,690)(481,689)(482,688)(483,687)(484,686)(485,685)(486,684)(487,683)(488,682)(489,681)(490,680)(491,679)(492,678)(493,677)(494,676)(495,675)(496,674)(497,673)(498,672)(499,671)(500,670)(501,669)(502,668)(503,667)(504,666)(505,665)(506,664)(507,663)(508,662)(509,661)(510,660)(511,659)(512,585)(513,657)(514,656)(515,655)(516,654)(517,653)(518,652)(519,651)(520,650)(521,649)(522,648)(523,647)(524,646)(525,645)(526,644)(527,643)(528,642)(529,641)(530,640)(531,639)(532,638)(533,637)(534,636)(535,635)(536,634)(537,633)(538,632)(539,631)(540,630)(541,629)(542,628)(543,627)(544,626)(545,625)(546,624)(547,623)(548,622)(549,621)(550,620)(551,619)(552,618)(553,617)(554,616)(555,615)(556,614)(557,613)(558,612)(559,611)(560,610)(561,609)(562,608)(563,607)(564,606)(565,605)(566,604)(567,603)(568,602)(569,601)(570,600)(571,599)(572,598)(573,597)(574,596)(575,595)(576,594)(577,593)(578,592)(579,591)(580,590)(581,589)(582,588)(583,587)(584,586);
s1 := Sym(730)!(  1,440)(  2,439)(  3,511)(  4,510)(  5,509)(  6,508)(  7,507)(  8,506)(  9,505)( 10,504)( 11,503)( 12,502)( 13,501)( 14,500)( 15,499)( 16,498)( 17,497)( 18,496)( 19,495)( 20,494)( 21,493)( 22,492)( 23,491)( 24,490)( 25,489)( 26,488)( 27,487)( 28,486)( 29,485)( 30,484)( 31,483)( 32,482)( 33,481)( 34,480)( 35,479)( 36,478)( 37,477)( 38,476)( 39,475)( 40,474)( 41,473)( 42,472)( 43,471)( 44,470)( 45,469)( 46,468)( 47,467)( 48,466)( 49,465)( 50,464)( 51,463)( 52,462)( 53,461)( 54,460)( 55,459)( 56,458)( 57,457)( 58,456)( 59,455)( 60,454)( 61,453)( 62,452)( 63,451)( 64,450)( 65,449)( 66,448)( 67,447)( 68,446)( 69,445)( 70,444)( 71,443)( 72,442)( 73,441)( 74,367)( 75,366)( 76,438)( 77,437)( 78,436)( 79,435)( 80,434)( 81,433)( 82,432)( 83,431)( 84,430)( 85,429)( 86,428)( 87,427)( 88,426)( 89,425)( 90,424)( 91,423)( 92,422)( 93,421)( 94,420)( 95,419)( 96,418)( 97,417)( 98,416)( 99,415)(100,414)(101,413)(102,412)(103,411)(104,410)(105,409)(106,408)(107,407)(108,406)(109,405)(110,404)(111,403)(112,402)(113,401)(114,400)(115,399)(116,398)(117,397)(118,396)(119,395)(120,394)(121,393)(122,392)(123,391)(124,390)(125,389)(126,388)(127,387)(128,386)(129,385)(130,384)(131,383)(132,382)(133,381)(134,380)(135,379)(136,378)(137,377)(138,376)(139,375)(140,374)(141,373)(142,372)(143,371)(144,370)(145,369)(146,368)(147,659)(148,658)(149,730)(150,729)(151,728)(152,727)(153,726)(154,725)(155,724)(156,723)(157,722)(158,721)(159,720)(160,719)(161,718)(162,717)(163,716)(164,715)(165,714)(166,713)(167,712)(168,711)(169,710)(170,709)(171,708)(172,707)(173,706)(174,705)(175,704)(176,703)(177,702)(178,701)(179,700)(180,699)(181,698)(182,697)(183,696)(184,695)(185,694)(186,693)(187,692)(188,691)(189,690)(190,689)(191,688)(192,687)(193,686)(194,685)(195,684)(196,683)(197,682)(198,681)(199,680)(200,679)(201,678)(202,677)(203,676)(204,675)(205,674)(206,673)(207,672)(208,671)(209,670)(210,669)(211,668)(212,667)(213,666)(214,665)(215,664)(216,663)(217,662)(218,661)(219,660)(220,586)(221,585)(222,657)(223,656)(224,655)(225,654)(226,653)(227,652)(228,651)(229,650)(230,649)(231,648)(232,647)(233,646)(234,645)(235,644)(236,643)(237,642)(238,641)(239,640)(240,639)(241,638)(242,637)(243,636)(244,635)(245,634)(246,633)(247,632)(248,631)(249,630)(250,629)(251,628)(252,627)(253,626)(254,625)(255,624)(256,623)(257,622)(258,621)(259,620)(260,619)(261,618)(262,617)(263,616)(264,615)(265,614)(266,613)(267,612)(268,611)(269,610)(270,609)(271,608)(272,607)(273,606)(274,605)(275,604)(276,603)(277,602)(278,601)(279,600)(280,599)(281,598)(282,597)(283,596)(284,595)(285,594)(286,593)(287,592)(288,591)(289,590)(290,589)(291,588)(292,587)(293,513)(294,512)(295,584)(296,583)(297,582)(298,581)(299,580)(300,579)(301,578)(302,577)(303,576)(304,575)(305,574)(306,573)(307,572)(308,571)(309,570)(310,569)(311,568)(312,567)(313,566)(314,565)(315,564)(316,563)(317,562)(318,561)(319,560)(320,559)(321,558)(322,557)(323,556)(324,555)(325,554)(326,553)(327,552)(328,551)(329,550)(330,549)(331,548)(332,547)(333,546)(334,545)(335,544)(336,543)(337,542)(338,541)(339,540)(340,539)(341,538)(342,537)(343,536)(344,535)(345,534)(346,533)(347,532)(348,531)(349,530)(350,529)(351,528)(352,527)(353,526)(354,525)(355,524)(356,523)(357,522)(358,521)(359,520)(360,519)(361,518)(362,517)(363,516)(364,515)(365,514);
poly := sub<Sym(730)|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 >;

References : None.
to this polytope