Polytope of Type {642}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {642}*1284
Also Known As : 642-gon, {642}. if this polytope has another name.
Group : SmallGroup(1284,9)
Rank : 2
Schlafli Type : {642}
Number of vertices, edges, etc : 642, 642
Order of s₀s₁ : 642
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 : {321}*642
   3-fold quotients : {214}*428
   6-fold quotients : {107}*214
   107-fold quotients : {6}*12
   214-fold quotients : {3}*6
   321-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope