Polytope of Type {578}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {578}*1156
Also Known As : 578-gon, {578}. if this polytope has another name.
Group : SmallGroup(1156,4)
Rank : 2
Schlafli Type : {578}
Number of vertices, edges, etc : 578, 578
Order of s₀s₁ : 578
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 : {289}*578
   17-fold quotients : {34}*68
   34-fold quotients : {17}*34
   289-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope