Polytope of Type {620}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {620}*1240
Also Known As : 620-gon, {620}. if this polytope has another name.
Group : SmallGroup(1240,36)
Rank : 2
Schlafli Type : {620}
Number of vertices, edges, etc : 620, 620
Order of s₀s₁ : 620
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 : {310}*620
   4-fold quotients : {155}*310
   5-fold quotients : {124}*248
   10-fold quotients : {62}*124
   20-fold quotients : {31}*62
   31-fold quotients : {20}*40
   62-fold quotients : {10}*20
   124-fold quotients : {5}*10
   155-fold quotients : {4}*8
   310-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope