Polytope of Type {636}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {636}*1272
Also Known As : 636-gon, {636}. if this polytope has another name.
Group : SmallGroup(1272,27)
Rank : 2
Schlafli Type : {636}
Number of vertices, edges, etc : 636, 636
Order of s₀s₁ : 636
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 : {318}*636
   3-fold quotients : {212}*424
   4-fold quotients : {159}*318
   6-fold quotients : {106}*212
   12-fold quotients : {53}*106
   53-fold quotients : {12}*24
   106-fold quotients : {6}*12
   159-fold quotients : {4}*8
   212-fold quotients : {3}*6
   318-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope