Polytope of Type {26,13}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,13}*676
if this polytope has a name.
Group : SmallGroup(676,13)
Rank : 3
Schlafli Type : {26,13}
Number of vertices, edges, etc : 26, 169, 13
Order of s₀s₁s₂ : 26
Order of s₀s₁s₂s₁ : 26
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {26,13,2} of size 1352
Vertex Figure Of :
   {2,26,13} of size 1352
Quotients (Maximal Quotients in Boldface) :
   13-fold quotients : {2,13}*52
Covers (Minimal Covers in Boldface) :
   2-fold covers : {26,26}*1352b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope