Polytope of Type {740}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {740}*1480
Also Known As : 740-gon, {740}. if this polytope has another name.
Group : SmallGroup(1480,30)
Rank : 2
Schlafli Type : {740}
Number of vertices, edges, etc : 740, 740
Order of s₀s₁ : 740
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 : {370}*740
   4-fold quotients : {185}*370
   5-fold quotients : {148}*296
   10-fold quotients : {74}*148
   20-fold quotients : {37}*74
   37-fold quotients : {20}*40
   74-fold quotients : {10}*20
   148-fold quotients : {5}*10
   185-fold quotients : {4}*8
   370-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope