Polytope of Type {600}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {600}*1200
Also Known As : 600-gon, {600}. if this polytope has another name.
Group : SmallGroup(1200,69)
Rank : 2
Schlafli Type : {600}
Number of vertices, edges, etc : 600, 600
Order of s₀s₁ : 600
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 : {300}*600
   3-fold quotients : {200}*400
   4-fold quotients : {150}*300
   5-fold quotients : {120}*240
   6-fold quotients : {100}*200
   8-fold quotients : {75}*150
   10-fold quotients : {60}*120
   12-fold quotients : {50}*100
   15-fold quotients : {40}*80
   20-fold quotients : {30}*60
   24-fold quotients : {25}*50
   25-fold quotients : {24}*48
   30-fold quotients : {20}*40
   40-fold quotients : {15}*30
   50-fold quotients : {12}*24
   60-fold quotients : {10}*20
   75-fold quotients : {8}*16
   100-fold quotients : {6}*12
   120-fold quotients : {5}*10
   150-fold quotients : {4}*8
   200-fold quotients : {3}*6
   300-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope