Polytope of Type {142,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {142,4}*1136
Also Known As : {142,4|2}. if this polytope has another name.
Group : SmallGroup(1136,34)
Rank : 3
Schlafli Type : {142,4}
Number of vertices, edges, etc : 142, 284, 4
Order of s₀s₁s₂ : 284
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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 : {142,2}*568
   4-fold quotients : {71,2}*284
   71-fold quotients : {2,4}*16
   142-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,143)(  2,213)(  3,212)(  4,211)(  5,210)(  6,209)(  7,208)(  8,207)
(  9,206)( 10,205)( 11,204)( 12,203)( 13,202)( 14,201)( 15,200)( 16,199)
( 17,198)( 18,197)( 19,196)( 20,195)( 21,194)( 22,193)( 23,192)( 24,191)
( 25,190)( 26,189)( 27,188)( 28,187)( 29,186)( 30,185)( 31,184)( 32,183)
( 33,182)( 34,181)( 35,180)( 36,179)( 37,178)( 38,177)( 39,176)( 40,175)
( 41,174)( 42,173)( 43,172)( 44,171)( 45,170)( 46,169)( 47,168)( 48,167)
( 49,166)( 50,165)( 51,164)( 52,163)( 53,162)( 54,161)( 55,160)( 56,159)
( 57,158)( 58,157)( 59,156)( 60,155)( 61,154)( 62,153)( 63,152)( 64,151)
( 65,150)( 66,149)( 67,148)( 68,147)( 69,146)( 70,145)( 71,144)( 72,214)
( 73,284)( 74,283)( 75,282)( 76,281)( 77,280)( 78,279)( 79,278)( 80,277)
( 81,276)( 82,275)( 83,274)( 84,273)( 85,272)( 86,271)( 87,270)( 88,269)
( 89,268)( 90,267)( 91,266)( 92,265)( 93,264)( 94,263)( 95,262)( 96,261)
( 97,260)( 98,259)( 99,258)(100,257)(101,256)(102,255)(103,254)(104,253)
(105,252)(106,251)(107,250)(108,249)(109,248)(110,247)(111,246)(112,245)
(113,244)(114,243)(115,242)(116,241)(117,240)(118,239)(119,238)(120,237)
(121,236)(122,235)(123,234)(124,233)(125,232)(126,231)(127,230)(128,229)
(129,228)(130,227)(131,226)(132,225)(133,224)(134,223)(135,222)(136,221)
(137,220)(138,219)(139,218)(140,217)(141,216)(142,215)(285,427)(286,497)
(287,496)(288,495)(289,494)(290,493)(291,492)(292,491)(293,490)(294,489)
(295,488)(296,487)(297,486)(298,485)(299,484)(300,483)(301,482)(302,481)
(303,480)(304,479)(305,478)(306,477)(307,476)(308,475)(309,474)(310,473)
(311,472)(312,471)(313,470)(314,469)(315,468)(316,467)(317,466)(318,465)
(319,464)(320,463)(321,462)(322,461)(323,460)(324,459)(325,458)(326,457)
(327,456)(328,455)(329,454)(330,453)(331,452)(332,451)(333,450)(334,449)
(335,448)(336,447)(337,446)(338,445)(339,444)(340,443)(341,442)(342,441)
(343,440)(344,439)(345,438)(346,437)(347,436)(348,435)(349,434)(350,433)
(351,432)(352,431)(353,430)(354,429)(355,428)(356,498)(357,568)(358,567)
(359,566)(360,565)(361,564)(362,563)(363,562)(364,561)(365,560)(366,559)
(367,558)(368,557)(369,556)(370,555)(371,554)(372,553)(373,552)(374,551)
(375,550)(376,549)(377,548)(378,547)(379,546)(380,545)(381,544)(382,543)
(383,542)(384,541)(385,540)(386,539)(387,538)(388,537)(389,536)(390,535)
(391,534)(392,533)(393,532)(394,531)(395,530)(396,529)(397,528)(398,527)
(399,526)(400,525)(401,524)(402,523)(403,522)(404,521)(405,520)(406,519)
(407,518)(408,517)(409,516)(410,515)(411,514)(412,513)(413,512)(414,511)
(415,510)(416,509)(417,508)(418,507)(419,506)(420,505)(421,504)(422,503)
(423,502)(424,501)(425,500)(426,499);;
s1 := (  1,144)(  2,143)(  3,213)(  4,212)(  5,211)(  6,210)(  7,209)(  8,208)
(  9,207)( 10,206)( 11,205)( 12,204)( 13,203)( 14,202)( 15,201)( 16,200)
( 17,199)( 18,198)( 19,197)( 20,196)( 21,195)( 22,194)( 23,193)( 24,192)
( 25,191)( 26,190)( 27,189)( 28,188)( 29,187)( 30,186)( 31,185)( 32,184)
( 33,183)( 34,182)( 35,181)( 36,180)( 37,179)( 38,178)( 39,177)( 40,176)
( 41,175)( 42,174)( 43,173)( 44,172)( 45,171)( 46,170)( 47,169)( 48,168)
( 49,167)( 50,166)( 51,165)( 52,164)( 53,163)( 54,162)( 55,161)( 56,160)
( 57,159)( 58,158)( 59,157)( 60,156)( 61,155)( 62,154)( 63,153)( 64,152)
( 65,151)( 66,150)( 67,149)( 68,148)( 69,147)( 70,146)( 71,145)( 72,215)
( 73,214)( 74,284)( 75,283)( 76,282)( 77,281)( 78,280)( 79,279)( 80,278)
( 81,277)( 82,276)( 83,275)( 84,274)( 85,273)( 86,272)( 87,271)( 88,270)
( 89,269)( 90,268)( 91,267)( 92,266)( 93,265)( 94,264)( 95,263)( 96,262)
( 97,261)( 98,260)( 99,259)(100,258)(101,257)(102,256)(103,255)(104,254)
(105,253)(106,252)(107,251)(108,250)(109,249)(110,248)(111,247)(112,246)
(113,245)(114,244)(115,243)(116,242)(117,241)(118,240)(119,239)(120,238)
(121,237)(122,236)(123,235)(124,234)(125,233)(126,232)(127,231)(128,230)
(129,229)(130,228)(131,227)(132,226)(133,225)(134,224)(135,223)(136,222)
(137,221)(138,220)(139,219)(140,218)(141,217)(142,216)(285,499)(286,498)
(287,568)(288,567)(289,566)(290,565)(291,564)(292,563)(293,562)(294,561)
(295,560)(296,559)(297,558)(298,557)(299,556)(300,555)(301,554)(302,553)
(303,552)(304,551)(305,550)(306,549)(307,548)(308,547)(309,546)(310,545)
(311,544)(312,543)(313,542)(314,541)(315,540)(316,539)(317,538)(318,537)
(319,536)(320,535)(321,534)(322,533)(323,532)(324,531)(325,530)(326,529)
(327,528)(328,527)(329,526)(330,525)(331,524)(332,523)(333,522)(334,521)
(335,520)(336,519)(337,518)(338,517)(339,516)(340,515)(341,514)(342,513)
(343,512)(344,511)(345,510)(346,509)(347,508)(348,507)(349,506)(350,505)
(351,504)(352,503)(353,502)(354,501)(355,500)(356,428)(357,427)(358,497)
(359,496)(360,495)(361,494)(362,493)(363,492)(364,491)(365,490)(366,489)
(367,488)(368,487)(369,486)(370,485)(371,484)(372,483)(373,482)(374,481)
(375,480)(376,479)(377,478)(378,477)(379,476)(380,475)(381,474)(382,473)
(383,472)(384,471)(385,470)(386,469)(387,468)(388,467)(389,466)(390,465)
(391,464)(392,463)(393,462)(394,461)(395,460)(396,459)(397,458)(398,457)
(399,456)(400,455)(401,454)(402,453)(403,452)(404,451)(405,450)(406,449)
(407,448)(408,447)(409,446)(410,445)(411,444)(412,443)(413,442)(414,441)
(415,440)(416,439)(417,438)(418,437)(419,436)(420,435)(421,434)(422,433)
(423,432)(424,431)(425,430)(426,429);;
s2 := (  1,285)(  2,286)(  3,287)(  4,288)(  5,289)(  6,290)(  7,291)(  8,292)
(  9,293)( 10,294)( 11,295)( 12,296)( 13,297)( 14,298)( 15,299)( 16,300)
( 17,301)( 18,302)( 19,303)( 20,304)( 21,305)( 22,306)( 23,307)( 24,308)
( 25,309)( 26,310)( 27,311)( 28,312)( 29,313)( 30,314)( 31,315)( 32,316)
( 33,317)( 34,318)( 35,319)( 36,320)( 37,321)( 38,322)( 39,323)( 40,324)
( 41,325)( 42,326)( 43,327)( 44,328)( 45,329)( 46,330)( 47,331)( 48,332)
( 49,333)( 50,334)( 51,335)( 52,336)( 53,337)( 54,338)( 55,339)( 56,340)
( 57,341)( 58,342)( 59,343)( 60,344)( 61,345)( 62,346)( 63,347)( 64,348)
( 65,349)( 66,350)( 67,351)( 68,352)( 69,353)( 70,354)( 71,355)( 72,356)
( 73,357)( 74,358)( 75,359)( 76,360)( 77,361)( 78,362)( 79,363)( 80,364)
( 81,365)( 82,366)( 83,367)( 84,368)( 85,369)( 86,370)( 87,371)( 88,372)
( 89,373)( 90,374)( 91,375)( 92,376)( 93,377)( 94,378)( 95,379)( 96,380)
( 97,381)( 98,382)( 99,383)(100,384)(101,385)(102,386)(103,387)(104,388)
(105,389)(106,390)(107,391)(108,392)(109,393)(110,394)(111,395)(112,396)
(113,397)(114,398)(115,399)(116,400)(117,401)(118,402)(119,403)(120,404)
(121,405)(122,406)(123,407)(124,408)(125,409)(126,410)(127,411)(128,412)
(129,413)(130,414)(131,415)(132,416)(133,417)(134,418)(135,419)(136,420)
(137,421)(138,422)(139,423)(140,424)(141,425)(142,426)(143,427)(144,428)
(145,429)(146,430)(147,431)(148,432)(149,433)(150,434)(151,435)(152,436)
(153,437)(154,438)(155,439)(156,440)(157,441)(158,442)(159,443)(160,444)
(161,445)(162,446)(163,447)(164,448)(165,449)(166,450)(167,451)(168,452)
(169,453)(170,454)(171,455)(172,456)(173,457)(174,458)(175,459)(176,460)
(177,461)(178,462)(179,463)(180,464)(181,465)(182,466)(183,467)(184,468)
(185,469)(186,470)(187,471)(188,472)(189,473)(190,474)(191,475)(192,476)
(193,477)(194,478)(195,479)(196,480)(197,481)(198,482)(199,483)(200,484)
(201,485)(202,486)(203,487)(204,488)(205,489)(206,490)(207,491)(208,492)
(209,493)(210,494)(211,495)(212,496)(213,497)(214,498)(215,499)(216,500)
(217,501)(218,502)(219,503)(220,504)(221,505)(222,506)(223,507)(224,508)
(225,509)(226,510)(227,511)(228,512)(229,513)(230,514)(231,515)(232,516)
(233,517)(234,518)(235,519)(236,520)(237,521)(238,522)(239,523)(240,524)
(241,525)(242,526)(243,527)(244,528)(245,529)(246,530)(247,531)(248,532)
(249,533)(250,534)(251,535)(252,536)(253,537)(254,538)(255,539)(256,540)
(257,541)(258,542)(259,543)(260,544)(261,545)(262,546)(263,547)(264,548)
(265,549)(266,550)(267,551)(268,552)(269,553)(270,554)(271,555)(272,556)
(273,557)(274,558)(275,559)(276,560)(277,561)(278,562)(279,563)(280,564)
(281,565)(282,566)(283,567)(284,568);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(568)!(  1,143)(  2,213)(  3,212)(  4,211)(  5,210)(  6,209)(  7,208)
(  8,207)(  9,206)( 10,205)( 11,204)( 12,203)( 13,202)( 14,201)( 15,200)
( 16,199)( 17,198)( 18,197)( 19,196)( 20,195)( 21,194)( 22,193)( 23,192)
( 24,191)( 25,190)( 26,189)( 27,188)( 28,187)( 29,186)( 30,185)( 31,184)
( 32,183)( 33,182)( 34,181)( 35,180)( 36,179)( 37,178)( 38,177)( 39,176)
( 40,175)( 41,174)( 42,173)( 43,172)( 44,171)( 45,170)( 46,169)( 47,168)
( 48,167)( 49,166)( 50,165)( 51,164)( 52,163)( 53,162)( 54,161)( 55,160)
( 56,159)( 57,158)( 58,157)( 59,156)( 60,155)( 61,154)( 62,153)( 63,152)
( 64,151)( 65,150)( 66,149)( 67,148)( 68,147)( 69,146)( 70,145)( 71,144)
( 72,214)( 73,284)( 74,283)( 75,282)( 76,281)( 77,280)( 78,279)( 79,278)
( 80,277)( 81,276)( 82,275)( 83,274)( 84,273)( 85,272)( 86,271)( 87,270)
( 88,269)( 89,268)( 90,267)( 91,266)( 92,265)( 93,264)( 94,263)( 95,262)
( 96,261)( 97,260)( 98,259)( 99,258)(100,257)(101,256)(102,255)(103,254)
(104,253)(105,252)(106,251)(107,250)(108,249)(109,248)(110,247)(111,246)
(112,245)(113,244)(114,243)(115,242)(116,241)(117,240)(118,239)(119,238)
(120,237)(121,236)(122,235)(123,234)(124,233)(125,232)(126,231)(127,230)
(128,229)(129,228)(130,227)(131,226)(132,225)(133,224)(134,223)(135,222)
(136,221)(137,220)(138,219)(139,218)(140,217)(141,216)(142,215)(285,427)
(286,497)(287,496)(288,495)(289,494)(290,493)(291,492)(292,491)(293,490)
(294,489)(295,488)(296,487)(297,486)(298,485)(299,484)(300,483)(301,482)
(302,481)(303,480)(304,479)(305,478)(306,477)(307,476)(308,475)(309,474)
(310,473)(311,472)(312,471)(313,470)(314,469)(315,468)(316,467)(317,466)
(318,465)(319,464)(320,463)(321,462)(322,461)(323,460)(324,459)(325,458)
(326,457)(327,456)(328,455)(329,454)(330,453)(331,452)(332,451)(333,450)
(334,449)(335,448)(336,447)(337,446)(338,445)(339,444)(340,443)(341,442)
(342,441)(343,440)(344,439)(345,438)(346,437)(347,436)(348,435)(349,434)
(350,433)(351,432)(352,431)(353,430)(354,429)(355,428)(356,498)(357,568)
(358,567)(359,566)(360,565)(361,564)(362,563)(363,562)(364,561)(365,560)
(366,559)(367,558)(368,557)(369,556)(370,555)(371,554)(372,553)(373,552)
(374,551)(375,550)(376,549)(377,548)(378,547)(379,546)(380,545)(381,544)
(382,543)(383,542)(384,541)(385,540)(386,539)(387,538)(388,537)(389,536)
(390,535)(391,534)(392,533)(393,532)(394,531)(395,530)(396,529)(397,528)
(398,527)(399,526)(400,525)(401,524)(402,523)(403,522)(404,521)(405,520)
(406,519)(407,518)(408,517)(409,516)(410,515)(411,514)(412,513)(413,512)
(414,511)(415,510)(416,509)(417,508)(418,507)(419,506)(420,505)(421,504)
(422,503)(423,502)(424,501)(425,500)(426,499);
s1 := Sym(568)!(  1,144)(  2,143)(  3,213)(  4,212)(  5,211)(  6,210)(  7,209)
(  8,208)(  9,207)( 10,206)( 11,205)( 12,204)( 13,203)( 14,202)( 15,201)
( 16,200)( 17,199)( 18,198)( 19,197)( 20,196)( 21,195)( 22,194)( 23,193)
( 24,192)( 25,191)( 26,190)( 27,189)( 28,188)( 29,187)( 30,186)( 31,185)
( 32,184)( 33,183)( 34,182)( 35,181)( 36,180)( 37,179)( 38,178)( 39,177)
( 40,176)( 41,175)( 42,174)( 43,173)( 44,172)( 45,171)( 46,170)( 47,169)
( 48,168)( 49,167)( 50,166)( 51,165)( 52,164)( 53,163)( 54,162)( 55,161)
( 56,160)( 57,159)( 58,158)( 59,157)( 60,156)( 61,155)( 62,154)( 63,153)
( 64,152)( 65,151)( 66,150)( 67,149)( 68,148)( 69,147)( 70,146)( 71,145)
( 72,215)( 73,214)( 74,284)( 75,283)( 76,282)( 77,281)( 78,280)( 79,279)
( 80,278)( 81,277)( 82,276)( 83,275)( 84,274)( 85,273)( 86,272)( 87,271)
( 88,270)( 89,269)( 90,268)( 91,267)( 92,266)( 93,265)( 94,264)( 95,263)
( 96,262)( 97,261)( 98,260)( 99,259)(100,258)(101,257)(102,256)(103,255)
(104,254)(105,253)(106,252)(107,251)(108,250)(109,249)(110,248)(111,247)
(112,246)(113,245)(114,244)(115,243)(116,242)(117,241)(118,240)(119,239)
(120,238)(121,237)(122,236)(123,235)(124,234)(125,233)(126,232)(127,231)
(128,230)(129,229)(130,228)(131,227)(132,226)(133,225)(134,224)(135,223)
(136,222)(137,221)(138,220)(139,219)(140,218)(141,217)(142,216)(285,499)
(286,498)(287,568)(288,567)(289,566)(290,565)(291,564)(292,563)(293,562)
(294,561)(295,560)(296,559)(297,558)(298,557)(299,556)(300,555)(301,554)
(302,553)(303,552)(304,551)(305,550)(306,549)(307,548)(308,547)(309,546)
(310,545)(311,544)(312,543)(313,542)(314,541)(315,540)(316,539)(317,538)
(318,537)(319,536)(320,535)(321,534)(322,533)(323,532)(324,531)(325,530)
(326,529)(327,528)(328,527)(329,526)(330,525)(331,524)(332,523)(333,522)
(334,521)(335,520)(336,519)(337,518)(338,517)(339,516)(340,515)(341,514)
(342,513)(343,512)(344,511)(345,510)(346,509)(347,508)(348,507)(349,506)
(350,505)(351,504)(352,503)(353,502)(354,501)(355,500)(356,428)(357,427)
(358,497)(359,496)(360,495)(361,494)(362,493)(363,492)(364,491)(365,490)
(366,489)(367,488)(368,487)(369,486)(370,485)(371,484)(372,483)(373,482)
(374,481)(375,480)(376,479)(377,478)(378,477)(379,476)(380,475)(381,474)
(382,473)(383,472)(384,471)(385,470)(386,469)(387,468)(388,467)(389,466)
(390,465)(391,464)(392,463)(393,462)(394,461)(395,460)(396,459)(397,458)
(398,457)(399,456)(400,455)(401,454)(402,453)(403,452)(404,451)(405,450)
(406,449)(407,448)(408,447)(409,446)(410,445)(411,444)(412,443)(413,442)
(414,441)(415,440)(416,439)(417,438)(418,437)(419,436)(420,435)(421,434)
(422,433)(423,432)(424,431)(425,430)(426,429);
s2 := Sym(568)!(  1,285)(  2,286)(  3,287)(  4,288)(  5,289)(  6,290)(  7,291)
(  8,292)(  9,293)( 10,294)( 11,295)( 12,296)( 13,297)( 14,298)( 15,299)
( 16,300)( 17,301)( 18,302)( 19,303)( 20,304)( 21,305)( 22,306)( 23,307)
( 24,308)( 25,309)( 26,310)( 27,311)( 28,312)( 29,313)( 30,314)( 31,315)
( 32,316)( 33,317)( 34,318)( 35,319)( 36,320)( 37,321)( 38,322)( 39,323)
( 40,324)( 41,325)( 42,326)( 43,327)( 44,328)( 45,329)( 46,330)( 47,331)
( 48,332)( 49,333)( 50,334)( 51,335)( 52,336)( 53,337)( 54,338)( 55,339)
( 56,340)( 57,341)( 58,342)( 59,343)( 60,344)( 61,345)( 62,346)( 63,347)
( 64,348)( 65,349)( 66,350)( 67,351)( 68,352)( 69,353)( 70,354)( 71,355)
( 72,356)( 73,357)( 74,358)( 75,359)( 76,360)( 77,361)( 78,362)( 79,363)
( 80,364)( 81,365)( 82,366)( 83,367)( 84,368)( 85,369)( 86,370)( 87,371)
( 88,372)( 89,373)( 90,374)( 91,375)( 92,376)( 93,377)( 94,378)( 95,379)
( 96,380)( 97,381)( 98,382)( 99,383)(100,384)(101,385)(102,386)(103,387)
(104,388)(105,389)(106,390)(107,391)(108,392)(109,393)(110,394)(111,395)
(112,396)(113,397)(114,398)(115,399)(116,400)(117,401)(118,402)(119,403)
(120,404)(121,405)(122,406)(123,407)(124,408)(125,409)(126,410)(127,411)
(128,412)(129,413)(130,414)(131,415)(132,416)(133,417)(134,418)(135,419)
(136,420)(137,421)(138,422)(139,423)(140,424)(141,425)(142,426)(143,427)
(144,428)(145,429)(146,430)(147,431)(148,432)(149,433)(150,434)(151,435)
(152,436)(153,437)(154,438)(155,439)(156,440)(157,441)(158,442)(159,443)
(160,444)(161,445)(162,446)(163,447)(164,448)(165,449)(166,450)(167,451)
(168,452)(169,453)(170,454)(171,455)(172,456)(173,457)(174,458)(175,459)
(176,460)(177,461)(178,462)(179,463)(180,464)(181,465)(182,466)(183,467)
(184,468)(185,469)(186,470)(187,471)(188,472)(189,473)(190,474)(191,475)
(192,476)(193,477)(194,478)(195,479)(196,480)(197,481)(198,482)(199,483)
(200,484)(201,485)(202,486)(203,487)(204,488)(205,489)(206,490)(207,491)
(208,492)(209,493)(210,494)(211,495)(212,496)(213,497)(214,498)(215,499)
(216,500)(217,501)(218,502)(219,503)(220,504)(221,505)(222,506)(223,507)
(224,508)(225,509)(226,510)(227,511)(228,512)(229,513)(230,514)(231,515)
(232,516)(233,517)(234,518)(235,519)(236,520)(237,521)(238,522)(239,523)
(240,524)(241,525)(242,526)(243,527)(244,528)(245,529)(246,530)(247,531)
(248,532)(249,533)(250,534)(251,535)(252,536)(253,537)(254,538)(255,539)
(256,540)(257,541)(258,542)(259,543)(260,544)(261,545)(262,546)(263,547)
(264,548)(265,549)(266,550)(267,551)(268,552)(269,553)(270,554)(271,555)
(272,556)(273,557)(274,558)(275,559)(276,560)(277,561)(278,562)(279,563)
(280,564)(281,565)(282,566)(283,567)(284,568);
poly := sub<Sym(568)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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