Polytope of Type {2,13,26}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,13,26}*1352
if this polytope has a name.
Group : SmallGroup(1352,49)
Rank : 4
Schlafli Type : {2,13,26}
Number of vertices, edges, etc : 2, 13, 169, 26
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 : {2,13,2}*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)( 16,159)( 17,171)
( 18,170)( 19,169)( 20,168)( 21,167)( 22,166)( 23,165)( 24,164)( 25,163)
( 26,162)( 27,161)( 28,160)( 29,146)( 30,158)( 31,157)( 32,156)( 33,155)
( 34,154)( 35,153)( 36,152)( 37,151)( 38,150)( 39,149)( 40,148)( 41,147)
( 42,133)( 43,145)( 44,144)( 45,143)( 46,142)( 47,141)( 48,140)( 49,139)
( 50,138)( 51,137)( 52,136)( 53,135)( 54,134)( 55,120)( 56,132)( 57,131)
( 58,130)( 59,129)( 60,128)( 61,127)( 62,126)( 63,125)( 64,124)( 65,123)
( 66,122)( 67,121)( 68,107)( 69,119)( 70,118)( 71,117)( 72,116)( 73,115)
( 74,114)( 75,113)( 76,112)( 77,111)( 78,110)( 79,109)( 80,108)( 81, 94)
( 82,106)( 83,105)( 84,104)( 85,103)( 86,102)( 87,101)( 88,100)( 89, 99)
( 90, 98)( 91, 97)( 92, 96)( 93, 95);;
s2 := (  3, 17)(  4, 16)(  5, 28)(  6, 27)(  7, 26)(  8, 25)(  9, 24)( 10, 23)
( 11, 22)( 12, 21)( 13, 20)( 14, 19)( 15, 18)( 29,160)( 30,159)( 31,171)
( 32,170)( 33,169)( 34,168)( 35,167)( 36,166)( 37,165)( 38,164)( 39,163)
( 40,162)( 41,161)( 42,147)( 43,146)( 44,158)( 45,157)( 46,156)( 47,155)
( 48,154)( 49,153)( 50,152)( 51,151)( 52,150)( 53,149)( 54,148)( 55,134)
( 56,133)( 57,145)( 58,144)( 59,143)( 60,142)( 61,141)( 62,140)( 63,139)
( 64,138)( 65,137)( 66,136)( 67,135)( 68,121)( 69,120)( 70,132)( 71,131)
( 72,130)( 73,129)( 74,128)( 75,127)( 76,126)( 77,125)( 78,124)( 79,123)
( 80,122)( 81,108)( 82,107)( 83,119)( 84,118)( 85,117)( 86,116)( 87,115)
( 88,114)( 89,113)( 90,112)( 91,111)( 92,110)( 93,109)( 94, 95)( 96,106)
( 97,105)( 98,104)( 99,103)(100,102);;
s3 := (  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);;
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*s3*s2*s3*s1*s2*s3*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(171)!(1,2);
s1 := Sym(171)!(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)(  9, 10)( 16,159)
( 17,171)( 18,170)( 19,169)( 20,168)( 21,167)( 22,166)( 23,165)( 24,164)
( 25,163)( 26,162)( 27,161)( 28,160)( 29,146)( 30,158)( 31,157)( 32,156)
( 33,155)( 34,154)( 35,153)( 36,152)( 37,151)( 38,150)( 39,149)( 40,148)
( 41,147)( 42,133)( 43,145)( 44,144)( 45,143)( 46,142)( 47,141)( 48,140)
( 49,139)( 50,138)( 51,137)( 52,136)( 53,135)( 54,134)( 55,120)( 56,132)
( 57,131)( 58,130)( 59,129)( 60,128)( 61,127)( 62,126)( 63,125)( 64,124)
( 65,123)( 66,122)( 67,121)( 68,107)( 69,119)( 70,118)( 71,117)( 72,116)
( 73,115)( 74,114)( 75,113)( 76,112)( 77,111)( 78,110)( 79,109)( 80,108)
( 81, 94)( 82,106)( 83,105)( 84,104)( 85,103)( 86,102)( 87,101)( 88,100)
( 89, 99)( 90, 98)( 91, 97)( 92, 96)( 93, 95);
s2 := Sym(171)!(  3, 17)(  4, 16)(  5, 28)(  6, 27)(  7, 26)(  8, 25)(  9, 24)
( 10, 23)( 11, 22)( 12, 21)( 13, 20)( 14, 19)( 15, 18)( 29,160)( 30,159)
( 31,171)( 32,170)( 33,169)( 34,168)( 35,167)( 36,166)( 37,165)( 38,164)
( 39,163)( 40,162)( 41,161)( 42,147)( 43,146)( 44,158)( 45,157)( 46,156)
( 47,155)( 48,154)( 49,153)( 50,152)( 51,151)( 52,150)( 53,149)( 54,148)
( 55,134)( 56,133)( 57,145)( 58,144)( 59,143)( 60,142)( 61,141)( 62,140)
( 63,139)( 64,138)( 65,137)( 66,136)( 67,135)( 68,121)( 69,120)( 70,132)
( 71,131)( 72,130)( 73,129)( 74,128)( 75,127)( 76,126)( 77,125)( 78,124)
( 79,123)( 80,122)( 81,108)( 82,107)( 83,119)( 84,118)( 85,117)( 86,116)
( 87,115)( 88,114)( 89,113)( 90,112)( 91,111)( 92,110)( 93,109)( 94, 95)
( 96,106)( 97,105)( 98,104)( 99,103)(100,102);
s3 := 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);
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*s3*s2*s3*s1*s2*s3*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 >;

to this polytope