Polytope of Type {780}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {780}*1560
Also Known As : 780-gon, {780}. if this polytope has another name.
Group : SmallGroup(1560,140)
Rank : 2
Schlafli Type : {780}
Number of vertices, edges, etc : 780, 780
Order of s₀s₁ : 780
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 : {390}*780
   3-fold quotients : {260}*520
   4-fold quotients : {195}*390
   5-fold quotients : {156}*312
   6-fold quotients : {130}*260
   10-fold quotients : {78}*156
   12-fold quotients : {65}*130
   13-fold quotients : {60}*120
   15-fold quotients : {52}*104
   20-fold quotients : {39}*78
   26-fold quotients : {30}*60
   30-fold quotients : {26}*52
   39-fold quotients : {20}*40
   52-fold quotients : {15}*30
   60-fold quotients : {13}*26
   65-fold quotients : {12}*24
   78-fold quotients : {10}*20
   130-fold quotients : {6}*12
   156-fold quotients : {5}*10
   195-fold quotients : {4}*8
   260-fold quotients : {3}*6
   390-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, 53)( 15, 65)
( 16, 64)( 17, 63)( 18, 62)( 19, 61)( 20, 60)( 21, 59)( 22, 58)( 23, 57)
( 24, 56)( 25, 55)( 26, 54)( 27, 40)( 28, 52)( 29, 51)( 30, 50)( 31, 49)
( 32, 48)( 33, 47)( 34, 46)( 35, 45)( 36, 44)( 37, 43)( 38, 42)( 39, 41)
( 66,131)( 67,143)( 68,142)( 69,141)( 70,140)( 71,139)( 72,138)( 73,137)
( 74,136)( 75,135)( 76,134)( 77,133)( 78,132)( 79,183)( 80,195)( 81,194)
( 82,193)( 83,192)( 84,191)( 85,190)( 86,189)( 87,188)( 88,187)( 89,186)
( 90,185)( 91,184)( 92,170)( 93,182)( 94,181)( 95,180)( 96,179)( 97,178)
( 98,177)( 99,176)(100,175)(101,174)(102,173)(103,172)(104,171)(105,157)
(106,169)(107,168)(108,167)(109,166)(110,165)(111,164)(112,163)(113,162)
(114,161)(115,160)(116,159)(117,158)(118,144)(119,156)(120,155)(121,154)
(122,153)(123,152)(124,151)(125,150)(126,149)(127,148)(128,147)(129,146)
(130,145)(197,208)(198,207)(199,206)(200,205)(201,204)(202,203)(209,248)
(210,260)(211,259)(212,258)(213,257)(214,256)(215,255)(216,254)(217,253)
(218,252)(219,251)(220,250)(221,249)(222,235)(223,247)(224,246)(225,245)
(226,244)(227,243)(228,242)(229,241)(230,240)(231,239)(232,238)(233,237)
(234,236)(261,326)(262,338)(263,337)(264,336)(265,335)(266,334)(267,333)
(268,332)(269,331)(270,330)(271,329)(272,328)(273,327)(274,378)(275,390)
(276,389)(277,388)(278,387)(279,386)(280,385)(281,384)(282,383)(283,382)
(284,381)(285,380)(286,379)(287,365)(288,377)(289,376)(290,375)(291,374)
(292,373)(293,372)(294,371)(295,370)(296,369)(297,368)(298,367)(299,366)
(300,352)(301,364)(302,363)(303,362)(304,361)(305,360)(306,359)(307,358)
(308,357)(309,356)(310,355)(311,354)(312,353)(313,339)(314,351)(315,350)
(316,349)(317,348)(318,347)(319,346)(320,345)(321,344)(322,343)(323,342)
(324,341)(325,340)(391,586)(392,598)(393,597)(394,596)(395,595)(396,594)
(397,593)(398,592)(399,591)(400,590)(401,589)(402,588)(403,587)(404,638)
(405,650)(406,649)(407,648)(408,647)(409,646)(410,645)(411,644)(412,643)
(413,642)(414,641)(415,640)(416,639)(417,625)(418,637)(419,636)(420,635)
(421,634)(422,633)(423,632)(424,631)(425,630)(426,629)(427,628)(428,627)
(429,626)(430,612)(431,624)(432,623)(433,622)(434,621)(435,620)(436,619)
(437,618)(438,617)(439,616)(440,615)(441,614)(442,613)(443,599)(444,611)
(445,610)(446,609)(447,608)(448,607)(449,606)(450,605)(451,604)(452,603)
(453,602)(454,601)(455,600)(456,716)(457,728)(458,727)(459,726)(460,725)
(461,724)(462,723)(463,722)(464,721)(465,720)(466,719)(467,718)(468,717)
(469,768)(470,780)(471,779)(472,778)(473,777)(474,776)(475,775)(476,774)
(477,773)(478,772)(479,771)(480,770)(481,769)(482,755)(483,767)(484,766)
(485,765)(486,764)(487,763)(488,762)(489,761)(490,760)(491,759)(492,758)
(493,757)(494,756)(495,742)(496,754)(497,753)(498,752)(499,751)(500,750)
(501,749)(502,748)(503,747)(504,746)(505,745)(506,744)(507,743)(508,729)
(509,741)(510,740)(511,739)(512,738)(513,737)(514,736)(515,735)(516,734)
(517,733)(518,732)(519,731)(520,730)(521,651)(522,663)(523,662)(524,661)
(525,660)(526,659)(527,658)(528,657)(529,656)(530,655)(531,654)(532,653)
(533,652)(534,703)(535,715)(536,714)(537,713)(538,712)(539,711)(540,710)
(541,709)(542,708)(543,707)(544,706)(545,705)(546,704)(547,690)(548,702)
(549,701)(550,700)(551,699)(552,698)(553,697)(554,696)(555,695)(556,694)
(557,693)(558,692)(559,691)(560,677)(561,689)(562,688)(563,687)(564,686)
(565,685)(566,684)(567,683)(568,682)(569,681)(570,680)(571,679)(572,678)
(573,664)(574,676)(575,675)(576,674)(577,673)(578,672)(579,671)(580,670)
(581,669)(582,668)(583,667)(584,666)(585,665);;
s1 := (  1,470)(  2,469)(  3,481)(  4,480)(  5,479)(  6,478)(  7,477)(  8,476)
(  9,475)( 10,474)( 11,473)( 12,472)( 13,471)( 14,457)( 15,456)( 16,468)
( 17,467)( 18,466)( 19,465)( 20,464)( 21,463)( 22,462)( 23,461)( 24,460)
( 25,459)( 26,458)( 27,509)( 28,508)( 29,520)( 30,519)( 31,518)( 32,517)
( 33,516)( 34,515)( 35,514)( 36,513)( 37,512)( 38,511)( 39,510)( 40,496)
( 41,495)( 42,507)( 43,506)( 44,505)( 45,504)( 46,503)( 47,502)( 48,501)
( 49,500)( 50,499)( 51,498)( 52,497)( 53,483)( 54,482)( 55,494)( 56,493)
( 57,492)( 58,491)( 59,490)( 60,489)( 61,488)( 62,487)( 63,486)( 64,485)
( 65,484)( 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)( 92,444)( 93,443)( 94,455)( 95,454)( 96,453)
( 97,452)( 98,451)( 99,450)(100,449)(101,448)(102,447)(103,446)(104,445)
(105,431)(106,430)(107,442)(108,441)(109,440)(110,439)(111,438)(112,437)
(113,436)(114,435)(115,434)(116,433)(117,432)(118,418)(119,417)(120,429)
(121,428)(122,427)(123,426)(124,425)(125,424)(126,423)(127,422)(128,421)
(129,420)(130,419)(131,535)(132,534)(133,546)(134,545)(135,544)(136,543)
(137,542)(138,541)(139,540)(140,539)(141,538)(142,537)(143,536)(144,522)
(145,521)(146,533)(147,532)(148,531)(149,530)(150,529)(151,528)(152,527)
(153,526)(154,525)(155,524)(156,523)(157,574)(158,573)(159,585)(160,584)
(161,583)(162,582)(163,581)(164,580)(165,579)(166,578)(167,577)(168,576)
(169,575)(170,561)(171,560)(172,572)(173,571)(174,570)(175,569)(176,568)
(177,567)(178,566)(179,565)(180,564)(181,563)(182,562)(183,548)(184,547)
(185,559)(186,558)(187,557)(188,556)(189,555)(190,554)(191,553)(192,552)
(193,551)(194,550)(195,549)(196,665)(197,664)(198,676)(199,675)(200,674)
(201,673)(202,672)(203,671)(204,670)(205,669)(206,668)(207,667)(208,666)
(209,652)(210,651)(211,663)(212,662)(213,661)(214,660)(215,659)(216,658)
(217,657)(218,656)(219,655)(220,654)(221,653)(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)(261,600)(262,599)(263,611)(264,610)
(265,609)(266,608)(267,607)(268,606)(269,605)(270,604)(271,603)(272,602)
(273,601)(274,587)(275,586)(276,598)(277,597)(278,596)(279,595)(280,594)
(281,593)(282,592)(283,591)(284,590)(285,589)(286,588)(287,639)(288,638)
(289,650)(290,649)(291,648)(292,647)(293,646)(294,645)(295,644)(296,643)
(297,642)(298,641)(299,640)(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)(326,730)(327,729)(328,741)
(329,740)(330,739)(331,738)(332,737)(333,736)(334,735)(335,734)(336,733)
(337,732)(338,731)(339,717)(340,716)(341,728)(342,727)(343,726)(344,725)
(345,724)(346,723)(347,722)(348,721)(349,720)(350,719)(351,718)(352,769)
(353,768)(354,780)(355,779)(356,778)(357,777)(358,776)(359,775)(360,774)
(361,773)(362,772)(363,771)(364,770)(365,756)(366,755)(367,767)(368,766)
(369,765)(370,764)(371,763)(372,762)(373,761)(374,760)(375,759)(376,758)
(377,757)(378,743)(379,742)(380,754)(381,753)(382,752)(383,751)(384,750)
(385,749)(386,748)(387,747)(388,746)(389,745)(390,744);;
poly := Group([s0,s1]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(780)!(  2, 13)(  3, 12)(  4, 11)(  5, 10)(  6,  9)(  7,  8)( 14, 53)
( 15, 65)( 16, 64)( 17, 63)( 18, 62)( 19, 61)( 20, 60)( 21, 59)( 22, 58)
( 23, 57)( 24, 56)( 25, 55)( 26, 54)( 27, 40)( 28, 52)( 29, 51)( 30, 50)
( 31, 49)( 32, 48)( 33, 47)( 34, 46)( 35, 45)( 36, 44)( 37, 43)( 38, 42)
( 39, 41)( 66,131)( 67,143)( 68,142)( 69,141)( 70,140)( 71,139)( 72,138)
( 73,137)( 74,136)( 75,135)( 76,134)( 77,133)( 78,132)( 79,183)( 80,195)
( 81,194)( 82,193)( 83,192)( 84,191)( 85,190)( 86,189)( 87,188)( 88,187)
( 89,186)( 90,185)( 91,184)( 92,170)( 93,182)( 94,181)( 95,180)( 96,179)
( 97,178)( 98,177)( 99,176)(100,175)(101,174)(102,173)(103,172)(104,171)
(105,157)(106,169)(107,168)(108,167)(109,166)(110,165)(111,164)(112,163)
(113,162)(114,161)(115,160)(116,159)(117,158)(118,144)(119,156)(120,155)
(121,154)(122,153)(123,152)(124,151)(125,150)(126,149)(127,148)(128,147)
(129,146)(130,145)(197,208)(198,207)(199,206)(200,205)(201,204)(202,203)
(209,248)(210,260)(211,259)(212,258)(213,257)(214,256)(215,255)(216,254)
(217,253)(218,252)(219,251)(220,250)(221,249)(222,235)(223,247)(224,246)
(225,245)(226,244)(227,243)(228,242)(229,241)(230,240)(231,239)(232,238)
(233,237)(234,236)(261,326)(262,338)(263,337)(264,336)(265,335)(266,334)
(267,333)(268,332)(269,331)(270,330)(271,329)(272,328)(273,327)(274,378)
(275,390)(276,389)(277,388)(278,387)(279,386)(280,385)(281,384)(282,383)
(283,382)(284,381)(285,380)(286,379)(287,365)(288,377)(289,376)(290,375)
(291,374)(292,373)(293,372)(294,371)(295,370)(296,369)(297,368)(298,367)
(299,366)(300,352)(301,364)(302,363)(303,362)(304,361)(305,360)(306,359)
(307,358)(308,357)(309,356)(310,355)(311,354)(312,353)(313,339)(314,351)
(315,350)(316,349)(317,348)(318,347)(319,346)(320,345)(321,344)(322,343)
(323,342)(324,341)(325,340)(391,586)(392,598)(393,597)(394,596)(395,595)
(396,594)(397,593)(398,592)(399,591)(400,590)(401,589)(402,588)(403,587)
(404,638)(405,650)(406,649)(407,648)(408,647)(409,646)(410,645)(411,644)
(412,643)(413,642)(414,641)(415,640)(416,639)(417,625)(418,637)(419,636)
(420,635)(421,634)(422,633)(423,632)(424,631)(425,630)(426,629)(427,628)
(428,627)(429,626)(430,612)(431,624)(432,623)(433,622)(434,621)(435,620)
(436,619)(437,618)(438,617)(439,616)(440,615)(441,614)(442,613)(443,599)
(444,611)(445,610)(446,609)(447,608)(448,607)(449,606)(450,605)(451,604)
(452,603)(453,602)(454,601)(455,600)(456,716)(457,728)(458,727)(459,726)
(460,725)(461,724)(462,723)(463,722)(464,721)(465,720)(466,719)(467,718)
(468,717)(469,768)(470,780)(471,779)(472,778)(473,777)(474,776)(475,775)
(476,774)(477,773)(478,772)(479,771)(480,770)(481,769)(482,755)(483,767)
(484,766)(485,765)(486,764)(487,763)(488,762)(489,761)(490,760)(491,759)
(492,758)(493,757)(494,756)(495,742)(496,754)(497,753)(498,752)(499,751)
(500,750)(501,749)(502,748)(503,747)(504,746)(505,745)(506,744)(507,743)
(508,729)(509,741)(510,740)(511,739)(512,738)(513,737)(514,736)(515,735)
(516,734)(517,733)(518,732)(519,731)(520,730)(521,651)(522,663)(523,662)
(524,661)(525,660)(526,659)(527,658)(528,657)(529,656)(530,655)(531,654)
(532,653)(533,652)(534,703)(535,715)(536,714)(537,713)(538,712)(539,711)
(540,710)(541,709)(542,708)(543,707)(544,706)(545,705)(546,704)(547,690)
(548,702)(549,701)(550,700)(551,699)(552,698)(553,697)(554,696)(555,695)
(556,694)(557,693)(558,692)(559,691)(560,677)(561,689)(562,688)(563,687)
(564,686)(565,685)(566,684)(567,683)(568,682)(569,681)(570,680)(571,679)
(572,678)(573,664)(574,676)(575,675)(576,674)(577,673)(578,672)(579,671)
(580,670)(581,669)(582,668)(583,667)(584,666)(585,665);
s1 := Sym(780)!(  1,470)(  2,469)(  3,481)(  4,480)(  5,479)(  6,478)(  7,477)
(  8,476)(  9,475)( 10,474)( 11,473)( 12,472)( 13,471)( 14,457)( 15,456)
( 16,468)( 17,467)( 18,466)( 19,465)( 20,464)( 21,463)( 22,462)( 23,461)
( 24,460)( 25,459)( 26,458)( 27,509)( 28,508)( 29,520)( 30,519)( 31,518)
( 32,517)( 33,516)( 34,515)( 35,514)( 36,513)( 37,512)( 38,511)( 39,510)
( 40,496)( 41,495)( 42,507)( 43,506)( 44,505)( 45,504)( 46,503)( 47,502)
( 48,501)( 49,500)( 50,499)( 51,498)( 52,497)( 53,483)( 54,482)( 55,494)
( 56,493)( 57,492)( 58,491)( 59,490)( 60,489)( 61,488)( 62,487)( 63,486)
( 64,485)( 65,484)( 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)( 92,444)( 93,443)( 94,455)( 95,454)
( 96,453)( 97,452)( 98,451)( 99,450)(100,449)(101,448)(102,447)(103,446)
(104,445)(105,431)(106,430)(107,442)(108,441)(109,440)(110,439)(111,438)
(112,437)(113,436)(114,435)(115,434)(116,433)(117,432)(118,418)(119,417)
(120,429)(121,428)(122,427)(123,426)(124,425)(125,424)(126,423)(127,422)
(128,421)(129,420)(130,419)(131,535)(132,534)(133,546)(134,545)(135,544)
(136,543)(137,542)(138,541)(139,540)(140,539)(141,538)(142,537)(143,536)
(144,522)(145,521)(146,533)(147,532)(148,531)(149,530)(150,529)(151,528)
(152,527)(153,526)(154,525)(155,524)(156,523)(157,574)(158,573)(159,585)
(160,584)(161,583)(162,582)(163,581)(164,580)(165,579)(166,578)(167,577)
(168,576)(169,575)(170,561)(171,560)(172,572)(173,571)(174,570)(175,569)
(176,568)(177,567)(178,566)(179,565)(180,564)(181,563)(182,562)(183,548)
(184,547)(185,559)(186,558)(187,557)(188,556)(189,555)(190,554)(191,553)
(192,552)(193,551)(194,550)(195,549)(196,665)(197,664)(198,676)(199,675)
(200,674)(201,673)(202,672)(203,671)(204,670)(205,669)(206,668)(207,667)
(208,666)(209,652)(210,651)(211,663)(212,662)(213,661)(214,660)(215,659)
(216,658)(217,657)(218,656)(219,655)(220,654)(221,653)(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)(261,600)(262,599)(263,611)
(264,610)(265,609)(266,608)(267,607)(268,606)(269,605)(270,604)(271,603)
(272,602)(273,601)(274,587)(275,586)(276,598)(277,597)(278,596)(279,595)
(280,594)(281,593)(282,592)(283,591)(284,590)(285,589)(286,588)(287,639)
(288,638)(289,650)(290,649)(291,648)(292,647)(293,646)(294,645)(295,644)
(296,643)(297,642)(298,641)(299,640)(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)(326,730)(327,729)
(328,741)(329,740)(330,739)(331,738)(332,737)(333,736)(334,735)(335,734)
(336,733)(337,732)(338,731)(339,717)(340,716)(341,728)(342,727)(343,726)
(344,725)(345,724)(346,723)(347,722)(348,721)(349,720)(350,719)(351,718)
(352,769)(353,768)(354,780)(355,779)(356,778)(357,777)(358,776)(359,775)
(360,774)(361,773)(362,772)(363,771)(364,770)(365,756)(366,755)(367,767)
(368,766)(369,765)(370,764)(371,763)(372,762)(373,761)(374,760)(375,759)
(376,758)(377,757)(378,743)(379,742)(380,754)(381,753)(382,752)(383,751)
(384,750)(385,749)(386,748)(387,747)(388,746)(389,745)(390,744);
poly := sub<Sym(780)|s0,s1>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope