# Order-6 hexagonal tiling

Order-6 hexagonal tiling
Rank3
TypeRegular
SpaceHyperbolic
Notation
Bowers style acronymHihexat
Coxeter diagramx6o6o ()
Schläfli symbol{6,6}
Elements
FacesN hexagons
Edges3N
VerticesN
Vertex figureHexagon, edge length 3
Measures (edge length 1)
Circumradius${\displaystyle {\frac {i{\sqrt {2}}}{4}}\approx 0.35355i}$
Related polytopes
ArmyHihexat
RegimentHihexat
DualOrder-6 hexagonal tiling
φ 2 Order-3 apeirogonal tiling
Abstract & topological properties
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry[6,6]
ConvexYes

The order-6 hexagonal tiling is a regular tiling of the hyperbolic plane. 6 hexagons join at each vertex. It is self-dual.

It can be formed by alternating the order-6 square tiling.

## Representations

The order-6 hexagonal tiling has the following Coxeter diagrams:

• x6o6o () (main symmetry)
• s4o6o () (as alternated order-6 square tiling)
• o3o4s4*a () (alternating order-6 square tiling with half symmetry)
• o6x6o3*a () (hexagons of two types)