Polytope of Type {2,106,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,106,2,2}*1696
if this polytope has a name.
Group : SmallGroup(1696,195)
Rank : 5
Schlafli Type : {2,106,2,2}
Number of vertices, edges, etc : 2, 106, 106, 2, 2
Order of s₀s₁s₂s₃s₄ : 106
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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) :
   2-fold quotients : {2,53,2,2}*848
   53-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 55)(  5, 54)(  6, 53)(  7, 52)(  8, 51)(  9, 50)( 10, 49)( 11, 48)
( 12, 47)( 13, 46)( 14, 45)( 15, 44)( 16, 43)( 17, 42)( 18, 41)( 19, 40)
( 20, 39)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)( 27, 32)
( 28, 31)( 29, 30)( 57,108)( 58,107)( 59,106)( 60,105)( 61,104)( 62,103)
( 63,102)( 64,101)( 65,100)( 66, 99)( 67, 98)( 68, 97)( 69, 96)( 70, 95)
( 71, 94)( 72, 93)( 73, 92)( 74, 91)( 75, 90)( 76, 89)( 77, 88)( 78, 87)
( 79, 86)( 80, 85)( 81, 84)( 82, 83);;
s2 := (  3, 57)(  4, 56)(  5,108)(  6,107)(  7,106)(  8,105)(  9,104)( 10,103)
( 11,102)( 12,101)( 13,100)( 14, 99)( 15, 98)( 16, 97)( 17, 96)( 18, 95)
( 19, 94)( 20, 93)( 21, 92)( 22, 91)( 23, 90)( 24, 89)( 25, 88)( 26, 87)
( 27, 86)( 28, 85)( 29, 84)( 30, 83)( 31, 82)( 32, 81)( 33, 80)( 34, 79)
( 35, 78)( 36, 77)( 37, 76)( 38, 75)( 39, 74)( 40, 73)( 41, 72)( 42, 71)
( 43, 70)( 44, 69)( 45, 68)( 46, 67)( 47, 66)( 48, 65)( 49, 64)( 50, 63)
( 51, 62)( 52, 61)( 53, 60)( 54, 59)( 55, 58);;
s3 := (109,110);;
s4 := (111,112);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, 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*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*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*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*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(112)!(1,2);
s1 := Sym(112)!(  4, 55)(  5, 54)(  6, 53)(  7, 52)(  8, 51)(  9, 50)( 10, 49)
( 11, 48)( 12, 47)( 13, 46)( 14, 45)( 15, 44)( 16, 43)( 17, 42)( 18, 41)
( 19, 40)( 20, 39)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)
( 27, 32)( 28, 31)( 29, 30)( 57,108)( 58,107)( 59,106)( 60,105)( 61,104)
( 62,103)( 63,102)( 64,101)( 65,100)( 66, 99)( 67, 98)( 68, 97)( 69, 96)
( 70, 95)( 71, 94)( 72, 93)( 73, 92)( 74, 91)( 75, 90)( 76, 89)( 77, 88)
( 78, 87)( 79, 86)( 80, 85)( 81, 84)( 82, 83);
s2 := Sym(112)!(  3, 57)(  4, 56)(  5,108)(  6,107)(  7,106)(  8,105)(  9,104)
( 10,103)( 11,102)( 12,101)( 13,100)( 14, 99)( 15, 98)( 16, 97)( 17, 96)
( 18, 95)( 19, 94)( 20, 93)( 21, 92)( 22, 91)( 23, 90)( 24, 89)( 25, 88)
( 26, 87)( 27, 86)( 28, 85)( 29, 84)( 30, 83)( 31, 82)( 32, 81)( 33, 80)
( 34, 79)( 35, 78)( 36, 77)( 37, 76)( 38, 75)( 39, 74)( 40, 73)( 41, 72)
( 42, 71)( 43, 70)( 44, 69)( 45, 68)( 46, 67)( 47, 66)( 48, 65)( 49, 64)
( 50, 63)( 51, 62)( 52, 61)( 53, 60)( 54, 59)( 55, 58);
s3 := Sym(112)!(109,110);
s4 := Sym(112)!(111,112);
poly := sub<Sym(112)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, 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*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*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*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*s1*s2*s1*s2 >;

to this polytope