Polytope of Type {572}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {572}*1144
Also Known As : 572-gon, {572}. if this polytope has another name.
Group : SmallGroup(1144,26)
Rank : 2
Schlafli Type : {572}
Number of vertices, edges, etc : 572, 572
Order of s₀s₁ : 572
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 : {286}*572
   4-fold quotients : {143}*286
   11-fold quotients : {52}*104
   13-fold quotients : {44}*88
   22-fold quotients : {26}*52
   26-fold quotients : {22}*44
   44-fold quotients : {13}*26
   52-fold quotients : {11}*22
   143-fold quotients : {4}*8
   286-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope