Polytope of Type {574}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {574}*1148
Also Known As : 574-gon, {574}. if this polytope has another name.
Group : SmallGroup(1148,10)
Rank : 2
Schlafli Type : {574}
Number of vertices, edges, etc : 574, 574
Order of s₀s₁ : 574
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 : {287}*574
   7-fold quotients : {82}*164
   14-fold quotients : {41}*82
   41-fold quotients : {14}*28
   82-fold quotients : {7}*14
   287-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope