Polytope of Type {632}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {632}*1264
Also Known As : 632-gon, {632}. if this polytope has another name.
Group : SmallGroup(1264,26)
Rank : 2
Schlafli Type : {632}
Number of vertices, edges, etc : 632, 632
Order of s₀s₁ : 632
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 : {316}*632
   4-fold quotients : {158}*316
   8-fold quotients : {79}*158
   79-fold quotients : {8}*16
   158-fold quotients : {4}*8
   316-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope