Polytope of Type {2,26,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,26,8}*832
if this polytope has a name.
Group : SmallGroup(832,1425)
Rank : 4
Schlafli Type : {2,26,8}
Number of vertices, edges, etc : 2, 26, 104, 8
Order of s₀s₁s₂s₃ : 104
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,26,8,2} of size 1664
Vertex Figure Of :
   {2,2,26,8} of size 1664
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,26,4}*416
   4-fold quotients : {2,26,2}*208
   8-fold quotients : {2,13,2}*104
   13-fold quotients : {2,2,8}*64
   26-fold quotients : {2,2,4}*32
   52-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,52,8}*1664a, {4,26,8}*1664, {2,26,16}*1664
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);;
s2 := (  3,  4)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)( 16, 17)( 18, 28)
( 19, 27)( 20, 26)( 21, 25)( 22, 24)( 29, 43)( 30, 42)( 31, 54)( 32, 53)
( 33, 52)( 34, 51)( 35, 50)( 36, 49)( 37, 48)( 38, 47)( 39, 46)( 40, 45)
( 41, 44)( 55, 82)( 56, 81)( 57, 93)( 58, 92)( 59, 91)( 60, 90)( 61, 89)
( 62, 88)( 63, 87)( 64, 86)( 65, 85)( 66, 84)( 67, 83)( 68, 95)( 69, 94)
( 70,106)( 71,105)( 72,104)( 73,103)( 74,102)( 75,101)( 76,100)( 77, 99)
( 78, 98)( 79, 97)( 80, 96);;
s3 := (  3, 55)(  4, 56)(  5, 57)(  6, 58)(  7, 59)(  8, 60)(  9, 61)( 10, 62)
( 11, 63)( 12, 64)( 13, 65)( 14, 66)( 15, 67)( 16, 68)( 17, 69)( 18, 70)
( 19, 71)( 20, 72)( 21, 73)( 22, 74)( 23, 75)( 24, 76)( 25, 77)( 26, 78)
( 27, 79)( 28, 80)( 29, 94)( 30, 95)( 31, 96)( 32, 97)( 33, 98)( 34, 99)
( 35,100)( 36,101)( 37,102)( 38,103)( 39,104)( 40,105)( 41,106)( 42, 81)
( 43, 82)( 44, 83)( 45, 84)( 46, 85)( 47, 86)( 48, 87)( 49, 88)( 50, 89)
( 51, 90)( 52, 91)( 53, 92)( 54, 93);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*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(106)!(1,2);
s1 := Sym(106)!(  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);
s2 := Sym(106)!(  3,  4)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)( 16, 17)
( 18, 28)( 19, 27)( 20, 26)( 21, 25)( 22, 24)( 29, 43)( 30, 42)( 31, 54)
( 32, 53)( 33, 52)( 34, 51)( 35, 50)( 36, 49)( 37, 48)( 38, 47)( 39, 46)
( 40, 45)( 41, 44)( 55, 82)( 56, 81)( 57, 93)( 58, 92)( 59, 91)( 60, 90)
( 61, 89)( 62, 88)( 63, 87)( 64, 86)( 65, 85)( 66, 84)( 67, 83)( 68, 95)
( 69, 94)( 70,106)( 71,105)( 72,104)( 73,103)( 74,102)( 75,101)( 76,100)
( 77, 99)( 78, 98)( 79, 97)( 80, 96);
s3 := Sym(106)!(  3, 55)(  4, 56)(  5, 57)(  6, 58)(  7, 59)(  8, 60)(  9, 61)
( 10, 62)( 11, 63)( 12, 64)( 13, 65)( 14, 66)( 15, 67)( 16, 68)( 17, 69)
( 18, 70)( 19, 71)( 20, 72)( 21, 73)( 22, 74)( 23, 75)( 24, 76)( 25, 77)
( 26, 78)( 27, 79)( 28, 80)( 29, 94)( 30, 95)( 31, 96)( 32, 97)( 33, 98)
( 34, 99)( 35,100)( 36,101)( 37,102)( 38,103)( 39,104)( 40,105)( 41,106)
( 42, 81)( 43, 82)( 44, 83)( 45, 84)( 46, 85)( 47, 86)( 48, 87)( 49, 88)
( 50, 89)( 51, 90)( 52, 91)( 53, 92)( 54, 93);
poly := sub<Sym(106)|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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*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