Order-4 hexagonal tiling

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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
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[edit | edit source]

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)

External links[edit | edit source]