Polytope of Type {13,26}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {13,26}*676
if this polytope has a name.
Group : SmallGroup(676,13)
Rank : 3
Schlafli Type : {13,26}
Number of vertices, edges, etc : 13, 169, 26
Order of s₀s₁s₂ : 26
Order of s₀s₁s₂s₁ : 26
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {13,26,2} of size 1352
Vertex Figure Of :
   {2,13,26} of size 1352
Quotients (Maximal Quotients in Boldface) :
   13-fold quotients : {13,2}*52
Covers (Minimal Covers in Boldface) :
   2-fold covers : {26,26}*1352c
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)(  2, 14)(  3, 26)(  4, 25)(  5, 24)(  6, 23)(  7, 22)(  8, 21)
(  9, 20)( 10, 19)( 11, 18)( 12, 17)( 13, 16)( 27,158)( 28,157)( 29,169)
( 30,168)( 31,167)( 32,166)( 33,165)( 34,164)( 35,163)( 36,162)( 37,161)
( 38,160)( 39,159)( 40,145)( 41,144)( 42,156)( 43,155)( 44,154)( 45,153)
( 46,152)( 47,151)( 48,150)( 49,149)( 50,148)( 51,147)( 52,146)( 53,132)
( 54,131)( 55,143)( 56,142)( 57,141)( 58,140)( 59,139)( 60,138)( 61,137)
( 62,136)( 63,135)( 64,134)( 65,133)( 66,119)( 67,118)( 68,130)( 69,129)
( 70,128)( 71,127)( 72,126)( 73,125)( 74,124)( 75,123)( 76,122)( 77,121)
( 78,120)( 79,106)( 80,105)( 81,117)( 82,116)( 83,115)( 84,114)( 85,113)
( 86,112)( 87,111)( 88,110)( 89,109)( 90,108)( 91,107)( 92, 93)( 94,104)
( 95,103)( 96,102)( 97,101)( 98,100);;
s2 := (  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);;
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*s2*s1*s2*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 ];;
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)(  2, 14)(  3, 26)(  4, 25)(  5, 24)(  6, 23)(  7, 22)
(  8, 21)(  9, 20)( 10, 19)( 11, 18)( 12, 17)( 13, 16)( 27,158)( 28,157)
( 29,169)( 30,168)( 31,167)( 32,166)( 33,165)( 34,164)( 35,163)( 36,162)
( 37,161)( 38,160)( 39,159)( 40,145)( 41,144)( 42,156)( 43,155)( 44,154)
( 45,153)( 46,152)( 47,151)( 48,150)( 49,149)( 50,148)( 51,147)( 52,146)
( 53,132)( 54,131)( 55,143)( 56,142)( 57,141)( 58,140)( 59,139)( 60,138)
( 61,137)( 62,136)( 63,135)( 64,134)( 65,133)( 66,119)( 67,118)( 68,130)
( 69,129)( 70,128)( 71,127)( 72,126)( 73,125)( 74,124)( 75,123)( 76,122)
( 77,121)( 78,120)( 79,106)( 80,105)( 81,117)( 82,116)( 83,115)( 84,114)
( 85,113)( 86,112)( 87,111)( 88,110)( 89,109)( 90,108)( 91,107)( 92, 93)
( 94,104)( 95,103)( 96,102)( 97,101)( 98,100);
s2 := 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);
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*s2*s1*s2*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 >;

References : None.
to this polytope