Polytope of Type {2,26,13}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,26,13}*1352
if this polytope has a name.
Group : SmallGroup(1352,49)
Rank : 4
Schlafli Type : {2,26,13}
Number of vertices, edges, etc : 2, 26, 169, 13
Order of s₀s₁s₂s₃ : 26
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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 : {2,2,13}*104
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)(  9, 10)( 17, 28)( 18, 27)
( 19, 26)( 20, 25)( 21, 24)( 22, 23)( 30, 41)( 31, 40)( 32, 39)( 33, 38)
( 34, 37)( 35, 36)( 43, 54)( 44, 53)( 45, 52)( 46, 51)( 47, 50)( 48, 49)
( 56, 67)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 69, 80)( 70, 79)
( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 82, 93)( 83, 92)( 84, 91)( 85, 90)
( 86, 89)( 87, 88)( 95,106)( 96,105)( 97,104)( 98,103)( 99,102)(100,101)
(108,119)(109,118)(110,117)(111,116)(112,115)(113,114)(121,132)(122,131)
(123,130)(124,129)(125,128)(126,127)(134,145)(135,144)(136,143)(137,142)
(138,141)(139,140)(147,158)(148,157)(149,156)(150,155)(151,154)(152,153)
(160,171)(161,170)(162,169)(163,168)(164,167)(165,166);;
s2 := (  3,  4)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)( 16,160)( 17,159)
( 18,171)( 19,170)( 20,169)( 21,168)( 22,167)( 23,166)( 24,165)( 25,164)
( 26,163)( 27,162)( 28,161)( 29,147)( 30,146)( 31,158)( 32,157)( 33,156)
( 34,155)( 35,154)( 36,153)( 37,152)( 38,151)( 39,150)( 40,149)( 41,148)
( 42,134)( 43,133)( 44,145)( 45,144)( 46,143)( 47,142)( 48,141)( 49,140)
( 50,139)( 51,138)( 52,137)( 53,136)( 54,135)( 55,121)( 56,120)( 57,132)
( 58,131)( 59,130)( 60,129)( 61,128)( 62,127)( 63,126)( 64,125)( 65,124)
( 66,123)( 67,122)( 68,108)( 69,107)( 70,119)( 71,118)( 72,117)( 73,116)
( 74,115)( 75,114)( 76,113)( 77,112)( 78,111)( 79,110)( 80,109)( 81, 95)
( 82, 94)( 83,106)( 84,105)( 85,104)( 86,103)( 87,102)( 88,101)( 89,100)
( 90, 99)( 91, 98)( 92, 97)( 93, 96);;
s3 := (  3, 16)(  4, 28)(  5, 27)(  6, 26)(  7, 25)(  8, 24)(  9, 23)( 10, 22)
( 11, 21)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 29,159)( 30,171)( 31,170)
( 32,169)( 33,168)( 34,167)( 35,166)( 36,165)( 37,164)( 38,163)( 39,162)
( 40,161)( 41,160)( 42,146)( 43,158)( 44,157)( 45,156)( 46,155)( 47,154)
( 48,153)( 49,152)( 50,151)( 51,150)( 52,149)( 53,148)( 54,147)( 55,133)
( 56,145)( 57,144)( 58,143)( 59,142)( 60,141)( 61,140)( 62,139)( 63,138)
( 64,137)( 65,136)( 66,135)( 67,134)( 68,120)( 69,132)( 70,131)( 71,130)
( 72,129)( 73,128)( 74,127)( 75,126)( 76,125)( 77,124)( 78,123)( 79,122)
( 80,121)( 81,107)( 82,119)( 83,118)( 84,117)( 85,116)( 86,115)( 87,114)
( 88,113)( 89,112)( 90,111)( 91,110)( 92,109)( 93,108)( 95,106)( 96,105)
( 97,104)( 98,103)( 99,102)(100,101);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(171)!(1,2);
s1 := Sym(171)!(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)(  9, 10)( 17, 28)
( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 22, 23)( 30, 41)( 31, 40)( 32, 39)
( 33, 38)( 34, 37)( 35, 36)( 43, 54)( 44, 53)( 45, 52)( 46, 51)( 47, 50)
( 48, 49)( 56, 67)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 69, 80)
( 70, 79)( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 82, 93)( 83, 92)( 84, 91)
( 85, 90)( 86, 89)( 87, 88)( 95,106)( 96,105)( 97,104)( 98,103)( 99,102)
(100,101)(108,119)(109,118)(110,117)(111,116)(112,115)(113,114)(121,132)
(122,131)(123,130)(124,129)(125,128)(126,127)(134,145)(135,144)(136,143)
(137,142)(138,141)(139,140)(147,158)(148,157)(149,156)(150,155)(151,154)
(152,153)(160,171)(161,170)(162,169)(163,168)(164,167)(165,166);
s2 := Sym(171)!(  3,  4)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)( 16,160)
( 17,159)( 18,171)( 19,170)( 20,169)( 21,168)( 22,167)( 23,166)( 24,165)
( 25,164)( 26,163)( 27,162)( 28,161)( 29,147)( 30,146)( 31,158)( 32,157)
( 33,156)( 34,155)( 35,154)( 36,153)( 37,152)( 38,151)( 39,150)( 40,149)
( 41,148)( 42,134)( 43,133)( 44,145)( 45,144)( 46,143)( 47,142)( 48,141)
( 49,140)( 50,139)( 51,138)( 52,137)( 53,136)( 54,135)( 55,121)( 56,120)
( 57,132)( 58,131)( 59,130)( 60,129)( 61,128)( 62,127)( 63,126)( 64,125)
( 65,124)( 66,123)( 67,122)( 68,108)( 69,107)( 70,119)( 71,118)( 72,117)
( 73,116)( 74,115)( 75,114)( 76,113)( 77,112)( 78,111)( 79,110)( 80,109)
( 81, 95)( 82, 94)( 83,106)( 84,105)( 85,104)( 86,103)( 87,102)( 88,101)
( 89,100)( 90, 99)( 91, 98)( 92, 97)( 93, 96);
s3 := Sym(171)!(  3, 16)(  4, 28)(  5, 27)(  6, 26)(  7, 25)(  8, 24)(  9, 23)
( 10, 22)( 11, 21)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 29,159)( 30,171)
( 31,170)( 32,169)( 33,168)( 34,167)( 35,166)( 36,165)( 37,164)( 38,163)
( 39,162)( 40,161)( 41,160)( 42,146)( 43,158)( 44,157)( 45,156)( 46,155)
( 47,154)( 48,153)( 49,152)( 50,151)( 51,150)( 52,149)( 53,148)( 54,147)
( 55,133)( 56,145)( 57,144)( 58,143)( 59,142)( 60,141)( 61,140)( 62,139)
( 63,138)( 64,137)( 65,136)( 66,135)( 67,134)( 68,120)( 69,132)( 70,131)
( 71,130)( 72,129)( 73,128)( 74,127)( 75,126)( 76,125)( 77,124)( 78,123)
( 79,122)( 80,121)( 81,107)( 82,119)( 83,118)( 84,117)( 85,116)( 86,115)
( 87,114)( 88,113)( 89,112)( 90,111)( 91,110)( 92,109)( 93,108)( 95,106)
( 96,105)( 97,104)( 98,103)( 99,102)(100,101);
poly := sub<Sym(171)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope