Polytope of Type {16,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,6}*1344a
if this polytope has a name.
Group : SmallGroup(1344,11291)
Rank : 3
Schlafli Type : {16,6}
Number of vertices, edges, etc : 112, 336, 42
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 28
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,6}*672e
   4-fold quotients : {8,6}*336a
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 7)( 3,19)( 4,31)( 5,22)( 6,30)( 8,27)( 9,28)(10,14)(12,13)(15,20)
(16,24)(17,21)(23,25)(26,29);;
s1 := ( 1, 3)( 2, 9)( 4, 5)( 6,31)( 7,21)( 8,19)(10,29)(11,26)(12,30)(13,14)
(15,28)(16,20)(17,27)(18,24)(22,25)(23,32);;
s2 := ( 1,11)( 2,30)( 3,15)( 4, 5)( 6, 7)( 8,16)( 9,26)(10,12)(13,14)(17,25)
(18,32)(19,20)(21,23)(22,31)(24,27)(28,29);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(32)!( 2, 7)( 3,19)( 4,31)( 5,22)( 6,30)( 8,27)( 9,28)(10,14)(12,13)
(15,20)(16,24)(17,21)(23,25)(26,29);
s1 := Sym(32)!( 1, 3)( 2, 9)( 4, 5)( 6,31)( 7,21)( 8,19)(10,29)(11,26)(12,30)
(13,14)(15,28)(16,20)(17,27)(18,24)(22,25)(23,32);
s2 := Sym(32)!( 1,11)( 2,30)( 3,15)( 4, 5)( 6, 7)( 8,16)( 9,26)(10,12)(13,14)
(17,25)(18,32)(19,20)(21,23)(22,31)(24,27)(28,29);
poly := sub<Sym(32)|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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2 >;

References : None.
to this polytope