# Order-4 hexagonal tiling

Order-4 hexagonal tiling
Rank3
TypeRegular
SpaceHyperbolic
Notation
Bowers style acronymShexat
Coxeter diagramx6o4o ()
Schläfli symbol{6,4}
Elements
Faces2N hexagons
Edges6N
Vertices3N
Vertex figureSquare, edge length 3
Measures (edge length 1)
Circumradius${\displaystyle {\frac {i{\sqrt {2}}}{2}}\approx 0.70711i}$
Related polytopes
ArmyShexat
RegimentShexat
DualOrder-6 square tiling
Abstract & topological properties
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry[6,4]
ConvexYes

The order-4 hexagonal tiling is a regular tiling of the hyperbolic plane. 4 hexagons join at each vertex.

As with other regular polyhedra with Schläfli symbols of the form {p,4}, it can also be constructed as the rectification of {p,p}, in this case the order-6 hexagonal tiling.

## Representations

The order-4 hexagonal tiling has the following Coxeter diagrams:

• x6o4o () (full symmetry)
• o6x6o () (as rectified order-6 hexagonal tiling)
• o6x3x6*a () (hexagons of 3 types, trapezivert)