Polytope of Type {134,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {134,4}*1072
Also Known As : {134,4|2}. if this polytope has another name.
Group : SmallGroup(1072,34)
Rank : 3
Schlafli Type : {134,4}
Number of vertices, edges, etc : 134, 268, 4
Order of s0s1s2 : 268
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 : {134,2}*536
4-fold quotients : {67,2}*268
67-fold quotients : {2,4}*16
134-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,135)( 2,201)( 3,200)( 4,199)( 5,198)( 6,197)( 7,196)( 8,195)
( 9,194)( 10,193)( 11,192)( 12,191)( 13,190)( 14,189)( 15,188)( 16,187)
( 17,186)( 18,185)( 19,184)( 20,183)( 21,182)( 22,181)( 23,180)( 24,179)
( 25,178)( 26,177)( 27,176)( 28,175)( 29,174)( 30,173)( 31,172)( 32,171)
( 33,170)( 34,169)( 35,168)( 36,167)( 37,166)( 38,165)( 39,164)( 40,163)
( 41,162)( 42,161)( 43,160)( 44,159)( 45,158)( 46,157)( 47,156)( 48,155)
( 49,154)( 50,153)( 51,152)( 52,151)( 53,150)( 54,149)( 55,148)( 56,147)
( 57,146)( 58,145)( 59,144)( 60,143)( 61,142)( 62,141)( 63,140)( 64,139)
( 65,138)( 66,137)( 67,136)( 68,202)( 69,268)( 70,267)( 71,266)( 72,265)
( 73,264)( 74,263)( 75,262)( 76,261)( 77,260)( 78,259)( 79,258)( 80,257)
( 81,256)( 82,255)( 83,254)( 84,253)( 85,252)( 86,251)( 87,250)( 88,249)
( 89,248)( 90,247)( 91,246)( 92,245)( 93,244)( 94,243)( 95,242)( 96,241)
( 97,240)( 98,239)( 99,238)(100,237)(101,236)(102,235)(103,234)(104,233)
(105,232)(106,231)(107,230)(108,229)(109,228)(110,227)(111,226)(112,225)
(113,224)(114,223)(115,222)(116,221)(117,220)(118,219)(119,218)(120,217)
(121,216)(122,215)(123,214)(124,213)(125,212)(126,211)(127,210)(128,209)
(129,208)(130,207)(131,206)(132,205)(133,204)(134,203)(269,403)(270,469)
(271,468)(272,467)(273,466)(274,465)(275,464)(276,463)(277,462)(278,461)
(279,460)(280,459)(281,458)(282,457)(283,456)(284,455)(285,454)(286,453)
(287,452)(288,451)(289,450)(290,449)(291,448)(292,447)(293,446)(294,445)
(295,444)(296,443)(297,442)(298,441)(299,440)(300,439)(301,438)(302,437)
(303,436)(304,435)(305,434)(306,433)(307,432)(308,431)(309,430)(310,429)
(311,428)(312,427)(313,426)(314,425)(315,424)(316,423)(317,422)(318,421)
(319,420)(320,419)(321,418)(322,417)(323,416)(324,415)(325,414)(326,413)
(327,412)(328,411)(329,410)(330,409)(331,408)(332,407)(333,406)(334,405)
(335,404)(336,470)(337,536)(338,535)(339,534)(340,533)(341,532)(342,531)
(343,530)(344,529)(345,528)(346,527)(347,526)(348,525)(349,524)(350,523)
(351,522)(352,521)(353,520)(354,519)(355,518)(356,517)(357,516)(358,515)
(359,514)(360,513)(361,512)(362,511)(363,510)(364,509)(365,508)(366,507)
(367,506)(368,505)(369,504)(370,503)(371,502)(372,501)(373,500)(374,499)
(375,498)(376,497)(377,496)(378,495)(379,494)(380,493)(381,492)(382,491)
(383,490)(384,489)(385,488)(386,487)(387,486)(388,485)(389,484)(390,483)
(391,482)(392,481)(393,480)(394,479)(395,478)(396,477)(397,476)(398,475)
(399,474)(400,473)(401,472)(402,471);;
s1 := ( 1,136)( 2,135)( 3,201)( 4,200)( 5,199)( 6,198)( 7,197)( 8,196)
( 9,195)( 10,194)( 11,193)( 12,192)( 13,191)( 14,190)( 15,189)( 16,188)
( 17,187)( 18,186)( 19,185)( 20,184)( 21,183)( 22,182)( 23,181)( 24,180)
( 25,179)( 26,178)( 27,177)( 28,176)( 29,175)( 30,174)( 31,173)( 32,172)
( 33,171)( 34,170)( 35,169)( 36,168)( 37,167)( 38,166)( 39,165)( 40,164)
( 41,163)( 42,162)( 43,161)( 44,160)( 45,159)( 46,158)( 47,157)( 48,156)
( 49,155)( 50,154)( 51,153)( 52,152)( 53,151)( 54,150)( 55,149)( 56,148)
( 57,147)( 58,146)( 59,145)( 60,144)( 61,143)( 62,142)( 63,141)( 64,140)
( 65,139)( 66,138)( 67,137)( 68,203)( 69,202)( 70,268)( 71,267)( 72,266)
( 73,265)( 74,264)( 75,263)( 76,262)( 77,261)( 78,260)( 79,259)( 80,258)
( 81,257)( 82,256)( 83,255)( 84,254)( 85,253)( 86,252)( 87,251)( 88,250)
( 89,249)( 90,248)( 91,247)( 92,246)( 93,245)( 94,244)( 95,243)( 96,242)
( 97,241)( 98,240)( 99,239)(100,238)(101,237)(102,236)(103,235)(104,234)
(105,233)(106,232)(107,231)(108,230)(109,229)(110,228)(111,227)(112,226)
(113,225)(114,224)(115,223)(116,222)(117,221)(118,220)(119,219)(120,218)
(121,217)(122,216)(123,215)(124,214)(125,213)(126,212)(127,211)(128,210)
(129,209)(130,208)(131,207)(132,206)(133,205)(134,204)(269,471)(270,470)
(271,536)(272,535)(273,534)(274,533)(275,532)(276,531)(277,530)(278,529)
(279,528)(280,527)(281,526)(282,525)(283,524)(284,523)(285,522)(286,521)
(287,520)(288,519)(289,518)(290,517)(291,516)(292,515)(293,514)(294,513)
(295,512)(296,511)(297,510)(298,509)(299,508)(300,507)(301,506)(302,505)
(303,504)(304,503)(305,502)(306,501)(307,500)(308,499)(309,498)(310,497)
(311,496)(312,495)(313,494)(314,493)(315,492)(316,491)(317,490)(318,489)
(319,488)(320,487)(321,486)(322,485)(323,484)(324,483)(325,482)(326,481)
(327,480)(328,479)(329,478)(330,477)(331,476)(332,475)(333,474)(334,473)
(335,472)(336,404)(337,403)(338,469)(339,468)(340,467)(341,466)(342,465)
(343,464)(344,463)(345,462)(346,461)(347,460)(348,459)(349,458)(350,457)
(351,456)(352,455)(353,454)(354,453)(355,452)(356,451)(357,450)(358,449)
(359,448)(360,447)(361,446)(362,445)(363,444)(364,443)(365,442)(366,441)
(367,440)(368,439)(369,438)(370,437)(371,436)(372,435)(373,434)(374,433)
(375,432)(376,431)(377,430)(378,429)(379,428)(380,427)(381,426)(382,425)
(383,424)(384,423)(385,422)(386,421)(387,420)(388,419)(389,418)(390,417)
(391,416)(392,415)(393,414)(394,413)(395,412)(396,411)(397,410)(398,409)
(399,408)(400,407)(401,406)(402,405);;
s2 := ( 1,269)( 2,270)( 3,271)( 4,272)( 5,273)( 6,274)( 7,275)( 8,276)
( 9,277)( 10,278)( 11,279)( 12,280)( 13,281)( 14,282)( 15,283)( 16,284)
( 17,285)( 18,286)( 19,287)( 20,288)( 21,289)( 22,290)( 23,291)( 24,292)
( 25,293)( 26,294)( 27,295)( 28,296)( 29,297)( 30,298)( 31,299)( 32,300)
( 33,301)( 34,302)( 35,303)( 36,304)( 37,305)( 38,306)( 39,307)( 40,308)
( 41,309)( 42,310)( 43,311)( 44,312)( 45,313)( 46,314)( 47,315)( 48,316)
( 49,317)( 50,318)( 51,319)( 52,320)( 53,321)( 54,322)( 55,323)( 56,324)
( 57,325)( 58,326)( 59,327)( 60,328)( 61,329)( 62,330)( 63,331)( 64,332)
( 65,333)( 66,334)( 67,335)( 68,336)( 69,337)( 70,338)( 71,339)( 72,340)
( 73,341)( 74,342)( 75,343)( 76,344)( 77,345)( 78,346)( 79,347)( 80,348)
( 81,349)( 82,350)( 83,351)( 84,352)( 85,353)( 86,354)( 87,355)( 88,356)
( 89,357)( 90,358)( 91,359)( 92,360)( 93,361)( 94,362)( 95,363)( 96,364)
( 97,365)( 98,366)( 99,367)(100,368)(101,369)(102,370)(103,371)(104,372)
(105,373)(106,374)(107,375)(108,376)(109,377)(110,378)(111,379)(112,380)
(113,381)(114,382)(115,383)(116,384)(117,385)(118,386)(119,387)(120,388)
(121,389)(122,390)(123,391)(124,392)(125,393)(126,394)(127,395)(128,396)
(129,397)(130,398)(131,399)(132,400)(133,401)(134,402)(135,403)(136,404)
(137,405)(138,406)(139,407)(140,408)(141,409)(142,410)(143,411)(144,412)
(145,413)(146,414)(147,415)(148,416)(149,417)(150,418)(151,419)(152,420)
(153,421)(154,422)(155,423)(156,424)(157,425)(158,426)(159,427)(160,428)
(161,429)(162,430)(163,431)(164,432)(165,433)(166,434)(167,435)(168,436)
(169,437)(170,438)(171,439)(172,440)(173,441)(174,442)(175,443)(176,444)
(177,445)(178,446)(179,447)(180,448)(181,449)(182,450)(183,451)(184,452)
(185,453)(186,454)(187,455)(188,456)(189,457)(190,458)(191,459)(192,460)
(193,461)(194,462)(195,463)(196,464)(197,465)(198,466)(199,467)(200,468)
(201,469)(202,470)(203,471)(204,472)(205,473)(206,474)(207,475)(208,476)
(209,477)(210,478)(211,479)(212,480)(213,481)(214,482)(215,483)(216,484)
(217,485)(218,486)(219,487)(220,488)(221,489)(222,490)(223,491)(224,492)
(225,493)(226,494)(227,495)(228,496)(229,497)(230,498)(231,499)(232,500)
(233,501)(234,502)(235,503)(236,504)(237,505)(238,506)(239,507)(240,508)
(241,509)(242,510)(243,511)(244,512)(245,513)(246,514)(247,515)(248,516)
(249,517)(250,518)(251,519)(252,520)(253,521)(254,522)(255,523)(256,524)
(257,525)(258,526)(259,527)(260,528)(261,529)(262,530)(263,531)(264,532)
(265,533)(266,534)(267,535)(268,536);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(536)!( 1,135)( 2,201)( 3,200)( 4,199)( 5,198)( 6,197)( 7,196)
( 8,195)( 9,194)( 10,193)( 11,192)( 12,191)( 13,190)( 14,189)( 15,188)
( 16,187)( 17,186)( 18,185)( 19,184)( 20,183)( 21,182)( 22,181)( 23,180)
( 24,179)( 25,178)( 26,177)( 27,176)( 28,175)( 29,174)( 30,173)( 31,172)
( 32,171)( 33,170)( 34,169)( 35,168)( 36,167)( 37,166)( 38,165)( 39,164)
( 40,163)( 41,162)( 42,161)( 43,160)( 44,159)( 45,158)( 46,157)( 47,156)
( 48,155)( 49,154)( 50,153)( 51,152)( 52,151)( 53,150)( 54,149)( 55,148)
( 56,147)( 57,146)( 58,145)( 59,144)( 60,143)( 61,142)( 62,141)( 63,140)
( 64,139)( 65,138)( 66,137)( 67,136)( 68,202)( 69,268)( 70,267)( 71,266)
( 72,265)( 73,264)( 74,263)( 75,262)( 76,261)( 77,260)( 78,259)( 79,258)
( 80,257)( 81,256)( 82,255)( 83,254)( 84,253)( 85,252)( 86,251)( 87,250)
( 88,249)( 89,248)( 90,247)( 91,246)( 92,245)( 93,244)( 94,243)( 95,242)
( 96,241)( 97,240)( 98,239)( 99,238)(100,237)(101,236)(102,235)(103,234)
(104,233)(105,232)(106,231)(107,230)(108,229)(109,228)(110,227)(111,226)
(112,225)(113,224)(114,223)(115,222)(116,221)(117,220)(118,219)(119,218)
(120,217)(121,216)(122,215)(123,214)(124,213)(125,212)(126,211)(127,210)
(128,209)(129,208)(130,207)(131,206)(132,205)(133,204)(134,203)(269,403)
(270,469)(271,468)(272,467)(273,466)(274,465)(275,464)(276,463)(277,462)
(278,461)(279,460)(280,459)(281,458)(282,457)(283,456)(284,455)(285,454)
(286,453)(287,452)(288,451)(289,450)(290,449)(291,448)(292,447)(293,446)
(294,445)(295,444)(296,443)(297,442)(298,441)(299,440)(300,439)(301,438)
(302,437)(303,436)(304,435)(305,434)(306,433)(307,432)(308,431)(309,430)
(310,429)(311,428)(312,427)(313,426)(314,425)(315,424)(316,423)(317,422)
(318,421)(319,420)(320,419)(321,418)(322,417)(323,416)(324,415)(325,414)
(326,413)(327,412)(328,411)(329,410)(330,409)(331,408)(332,407)(333,406)
(334,405)(335,404)(336,470)(337,536)(338,535)(339,534)(340,533)(341,532)
(342,531)(343,530)(344,529)(345,528)(346,527)(347,526)(348,525)(349,524)
(350,523)(351,522)(352,521)(353,520)(354,519)(355,518)(356,517)(357,516)
(358,515)(359,514)(360,513)(361,512)(362,511)(363,510)(364,509)(365,508)
(366,507)(367,506)(368,505)(369,504)(370,503)(371,502)(372,501)(373,500)
(374,499)(375,498)(376,497)(377,496)(378,495)(379,494)(380,493)(381,492)
(382,491)(383,490)(384,489)(385,488)(386,487)(387,486)(388,485)(389,484)
(390,483)(391,482)(392,481)(393,480)(394,479)(395,478)(396,477)(397,476)
(398,475)(399,474)(400,473)(401,472)(402,471);
s1 := Sym(536)!( 1,136)( 2,135)( 3,201)( 4,200)( 5,199)( 6,198)( 7,197)
( 8,196)( 9,195)( 10,194)( 11,193)( 12,192)( 13,191)( 14,190)( 15,189)
( 16,188)( 17,187)( 18,186)( 19,185)( 20,184)( 21,183)( 22,182)( 23,181)
( 24,180)( 25,179)( 26,178)( 27,177)( 28,176)( 29,175)( 30,174)( 31,173)
( 32,172)( 33,171)( 34,170)( 35,169)( 36,168)( 37,167)( 38,166)( 39,165)
( 40,164)( 41,163)( 42,162)( 43,161)( 44,160)( 45,159)( 46,158)( 47,157)
( 48,156)( 49,155)( 50,154)( 51,153)( 52,152)( 53,151)( 54,150)( 55,149)
( 56,148)( 57,147)( 58,146)( 59,145)( 60,144)( 61,143)( 62,142)( 63,141)
( 64,140)( 65,139)( 66,138)( 67,137)( 68,203)( 69,202)( 70,268)( 71,267)
( 72,266)( 73,265)( 74,264)( 75,263)( 76,262)( 77,261)( 78,260)( 79,259)
( 80,258)( 81,257)( 82,256)( 83,255)( 84,254)( 85,253)( 86,252)( 87,251)
( 88,250)( 89,249)( 90,248)( 91,247)( 92,246)( 93,245)( 94,244)( 95,243)
( 96,242)( 97,241)( 98,240)( 99,239)(100,238)(101,237)(102,236)(103,235)
(104,234)(105,233)(106,232)(107,231)(108,230)(109,229)(110,228)(111,227)
(112,226)(113,225)(114,224)(115,223)(116,222)(117,221)(118,220)(119,219)
(120,218)(121,217)(122,216)(123,215)(124,214)(125,213)(126,212)(127,211)
(128,210)(129,209)(130,208)(131,207)(132,206)(133,205)(134,204)(269,471)
(270,470)(271,536)(272,535)(273,534)(274,533)(275,532)(276,531)(277,530)
(278,529)(279,528)(280,527)(281,526)(282,525)(283,524)(284,523)(285,522)
(286,521)(287,520)(288,519)(289,518)(290,517)(291,516)(292,515)(293,514)
(294,513)(295,512)(296,511)(297,510)(298,509)(299,508)(300,507)(301,506)
(302,505)(303,504)(304,503)(305,502)(306,501)(307,500)(308,499)(309,498)
(310,497)(311,496)(312,495)(313,494)(314,493)(315,492)(316,491)(317,490)
(318,489)(319,488)(320,487)(321,486)(322,485)(323,484)(324,483)(325,482)
(326,481)(327,480)(328,479)(329,478)(330,477)(331,476)(332,475)(333,474)
(334,473)(335,472)(336,404)(337,403)(338,469)(339,468)(340,467)(341,466)
(342,465)(343,464)(344,463)(345,462)(346,461)(347,460)(348,459)(349,458)
(350,457)(351,456)(352,455)(353,454)(354,453)(355,452)(356,451)(357,450)
(358,449)(359,448)(360,447)(361,446)(362,445)(363,444)(364,443)(365,442)
(366,441)(367,440)(368,439)(369,438)(370,437)(371,436)(372,435)(373,434)
(374,433)(375,432)(376,431)(377,430)(378,429)(379,428)(380,427)(381,426)
(382,425)(383,424)(384,423)(385,422)(386,421)(387,420)(388,419)(389,418)
(390,417)(391,416)(392,415)(393,414)(394,413)(395,412)(396,411)(397,410)
(398,409)(399,408)(400,407)(401,406)(402,405);
s2 := Sym(536)!( 1,269)( 2,270)( 3,271)( 4,272)( 5,273)( 6,274)( 7,275)
( 8,276)( 9,277)( 10,278)( 11,279)( 12,280)( 13,281)( 14,282)( 15,283)
( 16,284)( 17,285)( 18,286)( 19,287)( 20,288)( 21,289)( 22,290)( 23,291)
( 24,292)( 25,293)( 26,294)( 27,295)( 28,296)( 29,297)( 30,298)( 31,299)
( 32,300)( 33,301)( 34,302)( 35,303)( 36,304)( 37,305)( 38,306)( 39,307)
( 40,308)( 41,309)( 42,310)( 43,311)( 44,312)( 45,313)( 46,314)( 47,315)
( 48,316)( 49,317)( 50,318)( 51,319)( 52,320)( 53,321)( 54,322)( 55,323)
( 56,324)( 57,325)( 58,326)( 59,327)( 60,328)( 61,329)( 62,330)( 63,331)
( 64,332)( 65,333)( 66,334)( 67,335)( 68,336)( 69,337)( 70,338)( 71,339)
( 72,340)( 73,341)( 74,342)( 75,343)( 76,344)( 77,345)( 78,346)( 79,347)
( 80,348)( 81,349)( 82,350)( 83,351)( 84,352)( 85,353)( 86,354)( 87,355)
( 88,356)( 89,357)( 90,358)( 91,359)( 92,360)( 93,361)( 94,362)( 95,363)
( 96,364)( 97,365)( 98,366)( 99,367)(100,368)(101,369)(102,370)(103,371)
(104,372)(105,373)(106,374)(107,375)(108,376)(109,377)(110,378)(111,379)
(112,380)(113,381)(114,382)(115,383)(116,384)(117,385)(118,386)(119,387)
(120,388)(121,389)(122,390)(123,391)(124,392)(125,393)(126,394)(127,395)
(128,396)(129,397)(130,398)(131,399)(132,400)(133,401)(134,402)(135,403)
(136,404)(137,405)(138,406)(139,407)(140,408)(141,409)(142,410)(143,411)
(144,412)(145,413)(146,414)(147,415)(148,416)(149,417)(150,418)(151,419)
(152,420)(153,421)(154,422)(155,423)(156,424)(157,425)(158,426)(159,427)
(160,428)(161,429)(162,430)(163,431)(164,432)(165,433)(166,434)(167,435)
(168,436)(169,437)(170,438)(171,439)(172,440)(173,441)(174,442)(175,443)
(176,444)(177,445)(178,446)(179,447)(180,448)(181,449)(182,450)(183,451)
(184,452)(185,453)(186,454)(187,455)(188,456)(189,457)(190,458)(191,459)
(192,460)(193,461)(194,462)(195,463)(196,464)(197,465)(198,466)(199,467)
(200,468)(201,469)(202,470)(203,471)(204,472)(205,473)(206,474)(207,475)
(208,476)(209,477)(210,478)(211,479)(212,480)(213,481)(214,482)(215,483)
(216,484)(217,485)(218,486)(219,487)(220,488)(221,489)(222,490)(223,491)
(224,492)(225,493)(226,494)(227,495)(228,496)(229,497)(230,498)(231,499)
(232,500)(233,501)(234,502)(235,503)(236,504)(237,505)(238,506)(239,507)
(240,508)(241,509)(242,510)(243,511)(244,512)(245,513)(246,514)(247,515)
(248,516)(249,517)(250,518)(251,519)(252,520)(253,521)(254,522)(255,523)
(256,524)(257,525)(258,526)(259,527)(260,528)(261,529)(262,530)(263,531)
(264,532)(265,533)(266,534)(267,535)(268,536);
poly := sub<Sym(536)|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 >;
References : None.
to this polytope