Polytope of Type {246,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {246,4}*1968a
Also Known As : {246,4|2}. if this polytope has another name.
Group : SmallGroup(1968,175)
Rank : 3
Schlafli Type : {246,4}
Number of vertices, edges, etc : 246, 492, 4
Order of s₀s₁s₂ : 492
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 : {246,2}*984
   3-fold quotients : {82,4}*656
   4-fold quotients : {123,2}*492
   6-fold quotients : {82,2}*328
   12-fold quotients : {41,2}*164
   41-fold quotients : {6,4}*48a
   82-fold quotients : {6,2}*24
   123-fold quotients : {2,4}*16
   164-fold quotients : {3,2}*12
   246-fold quotients : {2,2}*8
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, 83)( 43,123)( 44,122)( 45,121)
( 46,120)( 47,119)( 48,118)( 49,117)( 50,116)( 51,115)( 52,114)( 53,113)
( 54,112)( 55,111)( 56,110)( 57,109)( 58,108)( 59,107)( 60,106)( 61,105)
( 62,104)( 63,103)( 64,102)( 65,101)( 66,100)( 67, 99)( 68, 98)( 69, 97)
( 70, 96)( 71, 95)( 72, 94)( 73, 93)( 74, 92)( 75, 91)( 76, 90)( 77, 89)
( 78, 88)( 79, 87)( 80, 86)( 81, 85)( 82, 84)(125,164)(126,163)(127,162)
(128,161)(129,160)(130,159)(131,158)(132,157)(133,156)(134,155)(135,154)
(136,153)(137,152)(138,151)(139,150)(140,149)(141,148)(142,147)(143,146)
(144,145)(165,206)(166,246)(167,245)(168,244)(169,243)(170,242)(171,241)
(172,240)(173,239)(174,238)(175,237)(176,236)(177,235)(178,234)(179,233)
(180,232)(181,231)(182,230)(183,229)(184,228)(185,227)(186,226)(187,225)
(188,224)(189,223)(190,222)(191,221)(192,220)(193,219)(194,218)(195,217)
(196,216)(197,215)(198,214)(199,213)(200,212)(201,211)(202,210)(203,209)
(204,208)(205,207)(248,287)(249,286)(250,285)(251,284)(252,283)(253,282)
(254,281)(255,280)(256,279)(257,278)(258,277)(259,276)(260,275)(261,274)
(262,273)(263,272)(264,271)(265,270)(266,269)(267,268)(288,329)(289,369)
(290,368)(291,367)(292,366)(293,365)(294,364)(295,363)(296,362)(297,361)
(298,360)(299,359)(300,358)(301,357)(302,356)(303,355)(304,354)(305,353)
(306,352)(307,351)(308,350)(309,349)(310,348)(311,347)(312,346)(313,345)
(314,344)(315,343)(316,342)(317,341)(318,340)(319,339)(320,338)(321,337)
(322,336)(323,335)(324,334)(325,333)(326,332)(327,331)(328,330)(371,410)
(372,409)(373,408)(374,407)(375,406)(376,405)(377,404)(378,403)(379,402)
(380,401)(381,400)(382,399)(383,398)(384,397)(385,396)(386,395)(387,394)
(388,393)(389,392)(390,391)(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, 43)(  2, 42)(  3, 82)(  4, 81)(  5, 80)(  6, 79)(  7, 78)(  8, 77)
(  9, 76)( 10, 75)( 11, 74)( 12, 73)( 13, 72)( 14, 71)( 15, 70)( 16, 69)
( 17, 68)( 18, 67)( 19, 66)( 20, 65)( 21, 64)( 22, 63)( 23, 62)( 24, 61)
( 25, 60)( 26, 59)( 27, 58)( 28, 57)( 29, 56)( 30, 55)( 31, 54)( 32, 53)
( 33, 52)( 34, 51)( 35, 50)( 36, 49)( 37, 48)( 38, 47)( 39, 46)( 40, 45)
( 41, 44)( 83, 84)( 85,123)( 86,122)( 87,121)( 88,120)( 89,119)( 90,118)
( 91,117)( 92,116)( 93,115)( 94,114)( 95,113)( 96,112)( 97,111)( 98,110)
( 99,109)(100,108)(101,107)(102,106)(103,105)(124,166)(125,165)(126,205)
(127,204)(128,203)(129,202)(130,201)(131,200)(132,199)(133,198)(134,197)
(135,196)(136,195)(137,194)(138,193)(139,192)(140,191)(141,190)(142,189)
(143,188)(144,187)(145,186)(146,185)(147,184)(148,183)(149,182)(150,181)
(151,180)(152,179)(153,178)(154,177)(155,176)(156,175)(157,174)(158,173)
(159,172)(160,171)(161,170)(162,169)(163,168)(164,167)(206,207)(208,246)
(209,245)(210,244)(211,243)(212,242)(213,241)(214,240)(215,239)(216,238)
(217,237)(218,236)(219,235)(220,234)(221,233)(222,232)(223,231)(224,230)
(225,229)(226,228)(247,412)(248,411)(249,451)(250,450)(251,449)(252,448)
(253,447)(254,446)(255,445)(256,444)(257,443)(258,442)(259,441)(260,440)
(261,439)(262,438)(263,437)(264,436)(265,435)(266,434)(267,433)(268,432)
(269,431)(270,430)(271,429)(272,428)(273,427)(274,426)(275,425)(276,424)
(277,423)(278,422)(279,421)(280,420)(281,419)(282,418)(283,417)(284,416)
(285,415)(286,414)(287,413)(288,371)(289,370)(290,410)(291,409)(292,408)
(293,407)(294,406)(295,405)(296,404)(297,403)(298,402)(299,401)(300,400)
(301,399)(302,398)(303,397)(304,396)(305,395)(306,394)(307,393)(308,392)
(309,391)(310,390)(311,389)(312,388)(313,387)(314,386)(315,385)(316,384)
(317,383)(318,382)(319,381)(320,380)(321,379)(322,378)(323,377)(324,376)
(325,375)(326,374)(327,373)(328,372)(329,453)(330,452)(331,492)(332,491)
(333,490)(334,489)(335,488)(336,487)(337,486)(338,485)(339,484)(340,483)
(341,482)(342,481)(343,480)(344,479)(345,478)(346,477)(347,476)(348,475)
(349,474)(350,473)(351,472)(352,471)(353,470)(354,469)(355,468)(356,467)
(357,466)(358,465)(359,464)(360,463)(361,462)(362,461)(363,460)(364,459)
(365,458)(366,457)(367,456)(368,455)(369,454);;
s2 := (  1,247)(  2,248)(  3,249)(  4,250)(  5,251)(  6,252)(  7,253)(  8,254)
(  9,255)( 10,256)( 11,257)( 12,258)( 13,259)( 14,260)( 15,261)( 16,262)
( 17,263)( 18,264)( 19,265)( 20,266)( 21,267)( 22,268)( 23,269)( 24,270)
( 25,271)( 26,272)( 27,273)( 28,274)( 29,275)( 30,276)( 31,277)( 32,278)
( 33,279)( 34,280)( 35,281)( 36,282)( 37,283)( 38,284)( 39,285)( 40,286)
( 41,287)( 42,288)( 43,289)( 44,290)( 45,291)( 46,292)( 47,293)( 48,294)
( 49,295)( 50,296)( 51,297)( 52,298)( 53,299)( 54,300)( 55,301)( 56,302)
( 57,303)( 58,304)( 59,305)( 60,306)( 61,307)( 62,308)( 63,309)( 64,310)
( 65,311)( 66,312)( 67,313)( 68,314)( 69,315)( 70,316)( 71,317)( 72,318)
( 73,319)( 74,320)( 75,321)( 76,322)( 77,323)( 78,324)( 79,325)( 80,326)
( 81,327)( 82,328)( 83,329)( 84,330)( 85,331)( 86,332)( 87,333)( 88,334)
( 89,335)( 90,336)( 91,337)( 92,338)( 93,339)( 94,340)( 95,341)( 96,342)
( 97,343)( 98,344)( 99,345)(100,346)(101,347)(102,348)(103,349)(104,350)
(105,351)(106,352)(107,353)(108,354)(109,355)(110,356)(111,357)(112,358)
(113,359)(114,360)(115,361)(116,362)(117,363)(118,364)(119,365)(120,366)
(121,367)(122,368)(123,369)(124,370)(125,371)(126,372)(127,373)(128,374)
(129,375)(130,376)(131,377)(132,378)(133,379)(134,380)(135,381)(136,382)
(137,383)(138,384)(139,385)(140,386)(141,387)(142,388)(143,389)(144,390)
(145,391)(146,392)(147,393)(148,394)(149,395)(150,396)(151,397)(152,398)
(153,399)(154,400)(155,401)(156,402)(157,403)(158,404)(159,405)(160,406)
(161,407)(162,408)(163,409)(164,410)(165,411)(166,412)(167,413)(168,414)
(169,415)(170,416)(171,417)(172,418)(173,419)(174,420)(175,421)(176,422)
(177,423)(178,424)(179,425)(180,426)(181,427)(182,428)(183,429)(184,430)
(185,431)(186,432)(187,433)(188,434)(189,435)(190,436)(191,437)(192,438)
(193,439)(194,440)(195,441)(196,442)(197,443)(198,444)(199,445)(200,446)
(201,447)(202,448)(203,449)(204,450)(205,451)(206,452)(207,453)(208,454)
(209,455)(210,456)(211,457)(212,458)(213,459)(214,460)(215,461)(216,462)
(217,463)(218,464)(219,465)(220,466)(221,467)(222,468)(223,469)(224,470)
(225,471)(226,472)(227,473)(228,474)(229,475)(230,476)(231,477)(232,478)
(233,479)(234,480)(235,481)(236,482)(237,483)(238,484)(239,485)(240,486)
(241,487)(242,488)(243,489)(244,490)(245,491)(246,492);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(492)!(  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, 83)( 43,123)( 44,122)
( 45,121)( 46,120)( 47,119)( 48,118)( 49,117)( 50,116)( 51,115)( 52,114)
( 53,113)( 54,112)( 55,111)( 56,110)( 57,109)( 58,108)( 59,107)( 60,106)
( 61,105)( 62,104)( 63,103)( 64,102)( 65,101)( 66,100)( 67, 99)( 68, 98)
( 69, 97)( 70, 96)( 71, 95)( 72, 94)( 73, 93)( 74, 92)( 75, 91)( 76, 90)
( 77, 89)( 78, 88)( 79, 87)( 80, 86)( 81, 85)( 82, 84)(125,164)(126,163)
(127,162)(128,161)(129,160)(130,159)(131,158)(132,157)(133,156)(134,155)
(135,154)(136,153)(137,152)(138,151)(139,150)(140,149)(141,148)(142,147)
(143,146)(144,145)(165,206)(166,246)(167,245)(168,244)(169,243)(170,242)
(171,241)(172,240)(173,239)(174,238)(175,237)(176,236)(177,235)(178,234)
(179,233)(180,232)(181,231)(182,230)(183,229)(184,228)(185,227)(186,226)
(187,225)(188,224)(189,223)(190,222)(191,221)(192,220)(193,219)(194,218)
(195,217)(196,216)(197,215)(198,214)(199,213)(200,212)(201,211)(202,210)
(203,209)(204,208)(205,207)(248,287)(249,286)(250,285)(251,284)(252,283)
(253,282)(254,281)(255,280)(256,279)(257,278)(258,277)(259,276)(260,275)
(261,274)(262,273)(263,272)(264,271)(265,270)(266,269)(267,268)(288,329)
(289,369)(290,368)(291,367)(292,366)(293,365)(294,364)(295,363)(296,362)
(297,361)(298,360)(299,359)(300,358)(301,357)(302,356)(303,355)(304,354)
(305,353)(306,352)(307,351)(308,350)(309,349)(310,348)(311,347)(312,346)
(313,345)(314,344)(315,343)(316,342)(317,341)(318,340)(319,339)(320,338)
(321,337)(322,336)(323,335)(324,334)(325,333)(326,332)(327,331)(328,330)
(371,410)(372,409)(373,408)(374,407)(375,406)(376,405)(377,404)(378,403)
(379,402)(380,401)(381,400)(382,399)(383,398)(384,397)(385,396)(386,395)
(387,394)(388,393)(389,392)(390,391)(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(492)!(  1, 43)(  2, 42)(  3, 82)(  4, 81)(  5, 80)(  6, 79)(  7, 78)
(  8, 77)(  9, 76)( 10, 75)( 11, 74)( 12, 73)( 13, 72)( 14, 71)( 15, 70)
( 16, 69)( 17, 68)( 18, 67)( 19, 66)( 20, 65)( 21, 64)( 22, 63)( 23, 62)
( 24, 61)( 25, 60)( 26, 59)( 27, 58)( 28, 57)( 29, 56)( 30, 55)( 31, 54)
( 32, 53)( 33, 52)( 34, 51)( 35, 50)( 36, 49)( 37, 48)( 38, 47)( 39, 46)
( 40, 45)( 41, 44)( 83, 84)( 85,123)( 86,122)( 87,121)( 88,120)( 89,119)
( 90,118)( 91,117)( 92,116)( 93,115)( 94,114)( 95,113)( 96,112)( 97,111)
( 98,110)( 99,109)(100,108)(101,107)(102,106)(103,105)(124,166)(125,165)
(126,205)(127,204)(128,203)(129,202)(130,201)(131,200)(132,199)(133,198)
(134,197)(135,196)(136,195)(137,194)(138,193)(139,192)(140,191)(141,190)
(142,189)(143,188)(144,187)(145,186)(146,185)(147,184)(148,183)(149,182)
(150,181)(151,180)(152,179)(153,178)(154,177)(155,176)(156,175)(157,174)
(158,173)(159,172)(160,171)(161,170)(162,169)(163,168)(164,167)(206,207)
(208,246)(209,245)(210,244)(211,243)(212,242)(213,241)(214,240)(215,239)
(216,238)(217,237)(218,236)(219,235)(220,234)(221,233)(222,232)(223,231)
(224,230)(225,229)(226,228)(247,412)(248,411)(249,451)(250,450)(251,449)
(252,448)(253,447)(254,446)(255,445)(256,444)(257,443)(258,442)(259,441)
(260,440)(261,439)(262,438)(263,437)(264,436)(265,435)(266,434)(267,433)
(268,432)(269,431)(270,430)(271,429)(272,428)(273,427)(274,426)(275,425)
(276,424)(277,423)(278,422)(279,421)(280,420)(281,419)(282,418)(283,417)
(284,416)(285,415)(286,414)(287,413)(288,371)(289,370)(290,410)(291,409)
(292,408)(293,407)(294,406)(295,405)(296,404)(297,403)(298,402)(299,401)
(300,400)(301,399)(302,398)(303,397)(304,396)(305,395)(306,394)(307,393)
(308,392)(309,391)(310,390)(311,389)(312,388)(313,387)(314,386)(315,385)
(316,384)(317,383)(318,382)(319,381)(320,380)(321,379)(322,378)(323,377)
(324,376)(325,375)(326,374)(327,373)(328,372)(329,453)(330,452)(331,492)
(332,491)(333,490)(334,489)(335,488)(336,487)(337,486)(338,485)(339,484)
(340,483)(341,482)(342,481)(343,480)(344,479)(345,478)(346,477)(347,476)
(348,475)(349,474)(350,473)(351,472)(352,471)(353,470)(354,469)(355,468)
(356,467)(357,466)(358,465)(359,464)(360,463)(361,462)(362,461)(363,460)
(364,459)(365,458)(366,457)(367,456)(368,455)(369,454);
s2 := Sym(492)!(  1,247)(  2,248)(  3,249)(  4,250)(  5,251)(  6,252)(  7,253)
(  8,254)(  9,255)( 10,256)( 11,257)( 12,258)( 13,259)( 14,260)( 15,261)
( 16,262)( 17,263)( 18,264)( 19,265)( 20,266)( 21,267)( 22,268)( 23,269)
( 24,270)( 25,271)( 26,272)( 27,273)( 28,274)( 29,275)( 30,276)( 31,277)
( 32,278)( 33,279)( 34,280)( 35,281)( 36,282)( 37,283)( 38,284)( 39,285)
( 40,286)( 41,287)( 42,288)( 43,289)( 44,290)( 45,291)( 46,292)( 47,293)
( 48,294)( 49,295)( 50,296)( 51,297)( 52,298)( 53,299)( 54,300)( 55,301)
( 56,302)( 57,303)( 58,304)( 59,305)( 60,306)( 61,307)( 62,308)( 63,309)
( 64,310)( 65,311)( 66,312)( 67,313)( 68,314)( 69,315)( 70,316)( 71,317)
( 72,318)( 73,319)( 74,320)( 75,321)( 76,322)( 77,323)( 78,324)( 79,325)
( 80,326)( 81,327)( 82,328)( 83,329)( 84,330)( 85,331)( 86,332)( 87,333)
( 88,334)( 89,335)( 90,336)( 91,337)( 92,338)( 93,339)( 94,340)( 95,341)
( 96,342)( 97,343)( 98,344)( 99,345)(100,346)(101,347)(102,348)(103,349)
(104,350)(105,351)(106,352)(107,353)(108,354)(109,355)(110,356)(111,357)
(112,358)(113,359)(114,360)(115,361)(116,362)(117,363)(118,364)(119,365)
(120,366)(121,367)(122,368)(123,369)(124,370)(125,371)(126,372)(127,373)
(128,374)(129,375)(130,376)(131,377)(132,378)(133,379)(134,380)(135,381)
(136,382)(137,383)(138,384)(139,385)(140,386)(141,387)(142,388)(143,389)
(144,390)(145,391)(146,392)(147,393)(148,394)(149,395)(150,396)(151,397)
(152,398)(153,399)(154,400)(155,401)(156,402)(157,403)(158,404)(159,405)
(160,406)(161,407)(162,408)(163,409)(164,410)(165,411)(166,412)(167,413)
(168,414)(169,415)(170,416)(171,417)(172,418)(173,419)(174,420)(175,421)
(176,422)(177,423)(178,424)(179,425)(180,426)(181,427)(182,428)(183,429)
(184,430)(185,431)(186,432)(187,433)(188,434)(189,435)(190,436)(191,437)
(192,438)(193,439)(194,440)(195,441)(196,442)(197,443)(198,444)(199,445)
(200,446)(201,447)(202,448)(203,449)(204,450)(205,451)(206,452)(207,453)
(208,454)(209,455)(210,456)(211,457)(212,458)(213,459)(214,460)(215,461)
(216,462)(217,463)(218,464)(219,465)(220,466)(221,467)(222,468)(223,469)
(224,470)(225,471)(226,472)(227,473)(228,474)(229,475)(230,476)(231,477)
(232,478)(233,479)(234,480)(235,481)(236,482)(237,483)(238,484)(239,485)
(240,486)(241,487)(242,488)(243,489)(244,490)(245,491)(246,492);
poly := sub<Sym(492)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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