Polytope of Type {576}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {576}*1152
Also Known As : 576-gon, {576}. if this polytope has another name.
Group : SmallGroup(1152,7120)
Rank : 2
Schlafli Type : {576}
Number of vertices, edges, etc : 576, 576
Order of s₀s₁ : 576
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 : {288}*576
   3-fold quotients : {192}*384
   4-fold quotients : {144}*288
   6-fold quotients : {96}*192
   8-fold quotients : {72}*144
   9-fold quotients : {64}*128
   12-fold quotients : {48}*96
   16-fold quotients : {36}*72
   18-fold quotients : {32}*64
   24-fold quotients : {24}*48
   32-fold quotients : {18}*36
   36-fold quotients : {16}*32
   48-fold quotients : {12}*24
   64-fold quotients : {9}*18
   72-fold quotients : {8}*16
   96-fold quotients : {6}*12
   144-fold quotients : {4}*8
   192-fold quotients : {3}*6
   288-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope