Polytope of Type {760}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {760}*1520
Also Known As : 760-gon, {760}. if this polytope has another name.
Group : SmallGroup(1520,67)
Rank : 2
Schlafli Type : {760}
Number of vertices, edges, etc : 760, 760
Order of s₀s₁ : 760
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 : {380}*760
   4-fold quotients : {190}*380
   5-fold quotients : {152}*304
   8-fold quotients : {95}*190
   10-fold quotients : {76}*152
   19-fold quotients : {40}*80
   20-fold quotients : {38}*76
   38-fold quotients : {20}*40
   40-fold quotients : {19}*38
   76-fold quotients : {10}*20
   95-fold quotients : {8}*16
   152-fold quotients : {5}*10
   190-fold quotients : {4}*8
   380-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, 77)( 21, 95)( 22, 94)( 23, 93)( 24, 92)( 25, 91)( 26, 90)
( 27, 89)( 28, 88)( 29, 87)( 30, 86)( 31, 85)( 32, 84)( 33, 83)( 34, 82)
( 35, 81)( 36, 80)( 37, 79)( 38, 78)( 39, 58)( 40, 76)( 41, 75)( 42, 74)
( 43, 73)( 44, 72)( 45, 71)( 46, 70)( 47, 69)( 48, 68)( 49, 67)( 50, 66)
( 51, 65)( 52, 64)( 53, 63)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 97,114)
( 98,113)( 99,112)(100,111)(101,110)(102,109)(103,108)(104,107)(105,106)
(115,172)(116,190)(117,189)(118,188)(119,187)(120,186)(121,185)(122,184)
(123,183)(124,182)(125,181)(126,180)(127,179)(128,178)(129,177)(130,176)
(131,175)(132,174)(133,173)(134,153)(135,171)(136,170)(137,169)(138,168)
(139,167)(140,166)(141,165)(142,164)(143,163)(144,162)(145,161)(146,160)
(147,159)(148,158)(149,157)(150,156)(151,155)(152,154)(191,286)(192,304)
(193,303)(194,302)(195,301)(196,300)(197,299)(198,298)(199,297)(200,296)
(201,295)(202,294)(203,293)(204,292)(205,291)(206,290)(207,289)(208,288)
(209,287)(210,362)(211,380)(212,379)(213,378)(214,377)(215,376)(216,375)
(217,374)(218,373)(219,372)(220,371)(221,370)(222,369)(223,368)(224,367)
(225,366)(226,365)(227,364)(228,363)(229,343)(230,361)(231,360)(232,359)
(233,358)(234,357)(235,356)(236,355)(237,354)(238,353)(239,352)(240,351)
(241,350)(242,349)(243,348)(244,347)(245,346)(246,345)(247,344)(248,324)
(249,342)(250,341)(251,340)(252,339)(253,338)(254,337)(255,336)(256,335)
(257,334)(258,333)(259,332)(260,331)(261,330)(262,329)(263,328)(264,327)
(265,326)(266,325)(267,305)(268,323)(269,322)(270,321)(271,320)(272,319)
(273,318)(274,317)(275,316)(276,315)(277,314)(278,313)(279,312)(280,311)
(281,310)(282,309)(283,308)(284,307)(285,306)(381,571)(382,589)(383,588)
(384,587)(385,586)(386,585)(387,584)(388,583)(389,582)(390,581)(391,580)
(392,579)(393,578)(394,577)(395,576)(396,575)(397,574)(398,573)(399,572)
(400,647)(401,665)(402,664)(403,663)(404,662)(405,661)(406,660)(407,659)
(408,658)(409,657)(410,656)(411,655)(412,654)(413,653)(414,652)(415,651)
(416,650)(417,649)(418,648)(419,628)(420,646)(421,645)(422,644)(423,643)
(424,642)(425,641)(426,640)(427,639)(428,638)(429,637)(430,636)(431,635)
(432,634)(433,633)(434,632)(435,631)(436,630)(437,629)(438,609)(439,627)
(440,626)(441,625)(442,624)(443,623)(444,622)(445,621)(446,620)(447,619)
(448,618)(449,617)(450,616)(451,615)(452,614)(453,613)(454,612)(455,611)
(456,610)(457,590)(458,608)(459,607)(460,606)(461,605)(462,604)(463,603)
(464,602)(465,601)(466,600)(467,599)(468,598)(469,597)(470,596)(471,595)
(472,594)(473,593)(474,592)(475,591)(476,666)(477,684)(478,683)(479,682)
(480,681)(481,680)(482,679)(483,678)(484,677)(485,676)(486,675)(487,674)
(488,673)(489,672)(490,671)(491,670)(492,669)(493,668)(494,667)(495,742)
(496,760)(497,759)(498,758)(499,757)(500,756)(501,755)(502,754)(503,753)
(504,752)(505,751)(506,750)(507,749)(508,748)(509,747)(510,746)(511,745)
(512,744)(513,743)(514,723)(515,741)(516,740)(517,739)(518,738)(519,737)
(520,736)(521,735)(522,734)(523,733)(524,732)(525,731)(526,730)(527,729)
(528,728)(529,727)(530,726)(531,725)(532,724)(533,704)(534,722)(535,721)
(536,720)(537,719)(538,718)(539,717)(540,716)(541,715)(542,714)(543,713)
(544,712)(545,711)(546,710)(547,709)(548,708)(549,707)(550,706)(551,705)
(552,685)(553,703)(554,702)(555,701)(556,700)(557,699)(558,698)(559,697)
(560,696)(561,695)(562,694)(563,693)(564,692)(565,691)(566,690)(567,689)
(568,688)(569,687)(570,686);;
s1 := (  1,401)(  2,400)(  3,418)(  4,417)(  5,416)(  6,415)(  7,414)(  8,413)
(  9,412)( 10,411)( 11,410)( 12,409)( 13,408)( 14,407)( 15,406)( 16,405)
( 17,404)( 18,403)( 19,402)( 20,382)( 21,381)( 22,399)( 23,398)( 24,397)
( 25,396)( 26,395)( 27,394)( 28,393)( 29,392)( 30,391)( 31,390)( 32,389)
( 33,388)( 34,387)( 35,386)( 36,385)( 37,384)( 38,383)( 39,458)( 40,457)
( 41,475)( 42,474)( 43,473)( 44,472)( 45,471)( 46,470)( 47,469)( 48,468)
( 49,467)( 50,466)( 51,465)( 52,464)( 53,463)( 54,462)( 55,461)( 56,460)
( 57,459)( 58,439)( 59,438)( 60,456)( 61,455)( 62,454)( 63,453)( 64,452)
( 65,451)( 66,450)( 67,449)( 68,448)( 69,447)( 70,446)( 71,445)( 72,444)
( 73,443)( 74,442)( 75,441)( 76,440)( 77,420)( 78,419)( 79,437)( 80,436)
( 81,435)( 82,434)( 83,433)( 84,432)( 85,431)( 86,430)( 87,429)( 88,428)
( 89,427)( 90,426)( 91,425)( 92,424)( 93,423)( 94,422)( 95,421)( 96,496)
( 97,495)( 98,513)( 99,512)(100,511)(101,510)(102,509)(103,508)(104,507)
(105,506)(106,505)(107,504)(108,503)(109,502)(110,501)(111,500)(112,499)
(113,498)(114,497)(115,477)(116,476)(117,494)(118,493)(119,492)(120,491)
(121,490)(122,489)(123,488)(124,487)(125,486)(126,485)(127,484)(128,483)
(129,482)(130,481)(131,480)(132,479)(133,478)(134,553)(135,552)(136,570)
(137,569)(138,568)(139,567)(140,566)(141,565)(142,564)(143,563)(144,562)
(145,561)(146,560)(147,559)(148,558)(149,557)(150,556)(151,555)(152,554)
(153,534)(154,533)(155,551)(156,550)(157,549)(158,548)(159,547)(160,546)
(161,545)(162,544)(163,543)(164,542)(165,541)(166,540)(167,539)(168,538)
(169,537)(170,536)(171,535)(172,515)(173,514)(174,532)(175,531)(176,530)
(177,529)(178,528)(179,527)(180,526)(181,525)(182,524)(183,523)(184,522)
(185,521)(186,520)(187,519)(188,518)(189,517)(190,516)(191,686)(192,685)
(193,703)(194,702)(195,701)(196,700)(197,699)(198,698)(199,697)(200,696)
(201,695)(202,694)(203,693)(204,692)(205,691)(206,690)(207,689)(208,688)
(209,687)(210,667)(211,666)(212,684)(213,683)(214,682)(215,681)(216,680)
(217,679)(218,678)(219,677)(220,676)(221,675)(222,674)(223,673)(224,672)
(225,671)(226,670)(227,669)(228,668)(229,743)(230,742)(231,760)(232,759)
(233,758)(234,757)(235,756)(236,755)(237,754)(238,753)(239,752)(240,751)
(241,750)(242,749)(243,748)(244,747)(245,746)(246,745)(247,744)(248,724)
(249,723)(250,741)(251,740)(252,739)(253,738)(254,737)(255,736)(256,735)
(257,734)(258,733)(259,732)(260,731)(261,730)(262,729)(263,728)(264,727)
(265,726)(266,725)(267,705)(268,704)(269,722)(270,721)(271,720)(272,719)
(273,718)(274,717)(275,716)(276,715)(277,714)(278,713)(279,712)(280,711)
(281,710)(282,709)(283,708)(284,707)(285,706)(286,591)(287,590)(288,608)
(289,607)(290,606)(291,605)(292,604)(293,603)(294,602)(295,601)(296,600)
(297,599)(298,598)(299,597)(300,596)(301,595)(302,594)(303,593)(304,592)
(305,572)(306,571)(307,589)(308,588)(309,587)(310,586)(311,585)(312,584)
(313,583)(314,582)(315,581)(316,580)(317,579)(318,578)(319,577)(320,576)
(321,575)(322,574)(323,573)(324,648)(325,647)(326,665)(327,664)(328,663)
(329,662)(330,661)(331,660)(332,659)(333,658)(334,657)(335,656)(336,655)
(337,654)(338,653)(339,652)(340,651)(341,650)(342,649)(343,629)(344,628)
(345,646)(346,645)(347,644)(348,643)(349,642)(350,641)(351,640)(352,639)
(353,638)(354,637)(355,636)(356,635)(357,634)(358,633)(359,632)(360,631)
(361,630)(362,610)(363,609)(364,627)(365,626)(366,625)(367,624)(368,623)
(369,622)(370,621)(371,620)(372,619)(373,618)(374,617)(375,616)(376,615)
(377,614)(378,613)(379,612)(380,611);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope