Polytope of Type {26,38}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,38}*1976
Also Known As : {26,38|2}. if this polytope has another name.
Group : SmallGroup(1976,35)
Rank : 3
Schlafli Type : {26,38}
Number of vertices, edges, etc : 26, 494, 38
Order of s₀s₁s₂ : 494
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) :
   13-fold quotients : {2,38}*152
   19-fold quotients : {26,2}*104
   26-fold quotients : {2,19}*76
   38-fold quotients : {13,2}*52
   247-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope