Polytope of Type {26,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,4}*1352
if this polytope has a name.
Group : SmallGroup(1352,43)
Rank : 3
Schlafli Type : {26,4}
Number of vertices, edges, etc : 169, 338, 26
Order of s₀s₁s₂ : 4
Order of s₀s₁s₂s₁ : 26
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
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)( 14,157)( 15,169)
( 16,168)( 17,167)( 18,166)( 19,165)( 20,164)( 21,163)( 22,162)( 23,161)
( 24,160)( 25,159)( 26,158)( 27,144)( 28,156)( 29,155)( 30,154)( 31,153)
( 32,152)( 33,151)( 34,150)( 35,149)( 36,148)( 37,147)( 38,146)( 39,145)
( 40,131)( 41,143)( 42,142)( 43,141)( 44,140)( 45,139)( 46,138)( 47,137)
( 48,136)( 49,135)( 50,134)( 51,133)( 52,132)( 53,118)( 54,130)( 55,129)
( 56,128)( 57,127)( 58,126)( 59,125)( 60,124)( 61,123)( 62,122)( 63,121)
( 64,120)( 65,119)( 66,105)( 67,117)( 68,116)( 69,115)( 70,114)( 71,113)
( 72,112)( 73,111)( 74,110)( 75,109)( 76,108)( 77,107)( 78,106)( 79, 92)
( 80,104)( 81,103)( 82,102)( 83,101)( 84,100)( 85, 99)( 86, 98)( 87, 97)
( 88, 96)( 89, 95)( 90, 94)( 91, 93);;
s1 := (  1, 15)(  3,158)(  4,145)(  5,132)(  6,119)(  7,106)(  8, 93)(  9, 80)
( 10, 67)( 11, 54)( 12, 41)( 13, 28)( 16,157)( 17,144)( 18,131)( 19,118)
( 20,105)( 21, 92)( 22, 79)( 23, 66)( 24, 53)( 25, 40)( 26, 27)( 29,169)
( 30,156)( 31,143)( 32,130)( 33,117)( 34,104)( 35, 91)( 36, 78)( 37, 65)
( 38, 52)( 42,168)( 43,155)( 44,142)( 45,129)( 46,116)( 47,103)( 48, 90)
( 49, 77)( 50, 64)( 55,167)( 56,154)( 57,141)( 58,128)( 59,115)( 60,102)
( 61, 89)( 62, 76)( 68,166)( 69,153)( 70,140)( 71,127)( 72,114)( 73,101)
( 74, 88)( 81,165)( 82,152)( 83,139)( 84,126)( 85,113)( 86,100)( 94,164)
( 95,151)( 96,138)( 97,125)( 98,112)(107,163)(108,150)(109,137)(110,124)
(120,162)(121,149)(122,136)(133,161)(134,148)(146,160);;
s2 := (  2,105)(  3, 40)(  4,144)(  5, 79)(  6, 14)(  7,118)(  8, 53)(  9,157)
( 10, 92)( 11, 27)( 12,131)( 13, 66)( 15,110)( 16, 45)( 17,149)( 18, 84)
( 20,123)( 21, 58)( 22,162)( 23, 97)( 24, 32)( 25,136)( 26, 71)( 28,115)
( 29, 50)( 30,154)( 31, 89)( 33,128)( 34, 63)( 35,167)( 36,102)( 38,141)
( 39, 76)( 41,107)( 43,146)( 44, 81)( 46,120)( 47, 55)( 48,159)( 49, 94)
( 51,133)( 52, 68)( 54,112)( 56,151)( 57, 86)( 59,125)( 61,164)( 62, 99)
( 64,138)( 65, 73)( 67,117)( 69,156)( 70, 91)( 72,130)( 74,169)( 75,104)
( 77,143)( 80,109)( 82,148)( 85,122)( 87,161)( 88, 96)( 90,135)( 93,114)
( 95,153)( 98,127)(100,166)(103,140)(108,145)(111,119)(113,158)(116,132)
(121,150)(126,163)(129,137)(134,155)(139,168)(152,160);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*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*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*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(169)!(  2, 13)(  3, 12)(  4, 11)(  5, 10)(  6,  9)(  7,  8)( 14,157)
( 15,169)( 16,168)( 17,167)( 18,166)( 19,165)( 20,164)( 21,163)( 22,162)
( 23,161)( 24,160)( 25,159)( 26,158)( 27,144)( 28,156)( 29,155)( 30,154)
( 31,153)( 32,152)( 33,151)( 34,150)( 35,149)( 36,148)( 37,147)( 38,146)
( 39,145)( 40,131)( 41,143)( 42,142)( 43,141)( 44,140)( 45,139)( 46,138)
( 47,137)( 48,136)( 49,135)( 50,134)( 51,133)( 52,132)( 53,118)( 54,130)
( 55,129)( 56,128)( 57,127)( 58,126)( 59,125)( 60,124)( 61,123)( 62,122)
( 63,121)( 64,120)( 65,119)( 66,105)( 67,117)( 68,116)( 69,115)( 70,114)
( 71,113)( 72,112)( 73,111)( 74,110)( 75,109)( 76,108)( 77,107)( 78,106)
( 79, 92)( 80,104)( 81,103)( 82,102)( 83,101)( 84,100)( 85, 99)( 86, 98)
( 87, 97)( 88, 96)( 89, 95)( 90, 94)( 91, 93);
s1 := Sym(169)!(  1, 15)(  3,158)(  4,145)(  5,132)(  6,119)(  7,106)(  8, 93)
(  9, 80)( 10, 67)( 11, 54)( 12, 41)( 13, 28)( 16,157)( 17,144)( 18,131)
( 19,118)( 20,105)( 21, 92)( 22, 79)( 23, 66)( 24, 53)( 25, 40)( 26, 27)
( 29,169)( 30,156)( 31,143)( 32,130)( 33,117)( 34,104)( 35, 91)( 36, 78)
( 37, 65)( 38, 52)( 42,168)( 43,155)( 44,142)( 45,129)( 46,116)( 47,103)
( 48, 90)( 49, 77)( 50, 64)( 55,167)( 56,154)( 57,141)( 58,128)( 59,115)
( 60,102)( 61, 89)( 62, 76)( 68,166)( 69,153)( 70,140)( 71,127)( 72,114)
( 73,101)( 74, 88)( 81,165)( 82,152)( 83,139)( 84,126)( 85,113)( 86,100)
( 94,164)( 95,151)( 96,138)( 97,125)( 98,112)(107,163)(108,150)(109,137)
(110,124)(120,162)(121,149)(122,136)(133,161)(134,148)(146,160);
s2 := Sym(169)!(  2,105)(  3, 40)(  4,144)(  5, 79)(  6, 14)(  7,118)(  8, 53)
(  9,157)( 10, 92)( 11, 27)( 12,131)( 13, 66)( 15,110)( 16, 45)( 17,149)
( 18, 84)( 20,123)( 21, 58)( 22,162)( 23, 97)( 24, 32)( 25,136)( 26, 71)
( 28,115)( 29, 50)( 30,154)( 31, 89)( 33,128)( 34, 63)( 35,167)( 36,102)
( 38,141)( 39, 76)( 41,107)( 43,146)( 44, 81)( 46,120)( 47, 55)( 48,159)
( 49, 94)( 51,133)( 52, 68)( 54,112)( 56,151)( 57, 86)( 59,125)( 61,164)
( 62, 99)( 64,138)( 65, 73)( 67,117)( 69,156)( 70, 91)( 72,130)( 74,169)
( 75,104)( 77,143)( 80,109)( 82,148)( 85,122)( 87,161)( 88, 96)( 90,135)
( 93,114)( 95,153)( 98,127)(100,166)(103,140)(108,145)(111,119)(113,158)
(116,132)(121,150)(126,163)(129,137)(134,155)(139,168)(152,160);
poly := sub<Sym(169)|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, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*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*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*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 >;

References : None.
to this polytope