Polytope of Type {640}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {640}*1280
Also Known As : 640-gon, {640}. if this polytope has another name.
Group : SmallGroup(1280,57481)
Rank : 2
Schlafli Type : {640}
Number of vertices, edges, etc : 640, 640
Order of s₀s₁ : 640
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 : {320}*640
   4-fold quotients : {160}*320
   5-fold quotients : {128}*256
   8-fold quotients : {80}*160
   10-fold quotients : {64}*128
   16-fold quotients : {40}*80
   20-fold quotients : {32}*64
   32-fold quotients : {20}*40
   40-fold quotients : {16}*32
   64-fold quotients : {10}*20
   80-fold quotients : {8}*16
   128-fold quotients : {5}*10
   160-fold quotients : {4}*8
   320-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope