# Blended hexagonal tiling

Blended hexagonal tiling
Rank3
TypeRegular
SpaceEuclidean
Notation
Schläfli symbol${\displaystyle \{6,3\}\#\{\}}$
Elements
FacesN skew hexagons
Edges3N
Vertices2N
Vertex figureTriangle, 0 < edge length < ${\displaystyle \sqrt{3}}$
Abstract & topological properties
OrientableYes
Genus0
Properties
ConvexNo

The blended hexagonal tiling is a regular skew polyhedron consisting of an infinite amount of skew hexagons, with 3 at a vertex. It can be obtained as the blend of a line segment and a hexagonal tiling, and so it has a Schlafli symbol of ${\displaystyle \{6,3\}\#\{\}}$. It is abstractly identical to the hexagonal tiling. Just like the skew hexagon, the blended hexagonal tiling can vary in height but it is considered one polyhedron.

## Vertex coordinates

The vertex coordinates of a blended hexagonal tiling centered at the origin with edge length 1 and height h are

• ${\displaystyle (3Hi-\frac{1}{2},\sqrt{3}Hj+\frac{\sqrt{3}}{2},\frac{h}{2})}$
• ${\displaystyle (3Hi-1,\sqrt{3}Hj,-\frac{h}{2})}$
• ${\displaystyle (3Hi+\frac{1}{2},\sqrt{3}Hj+\frac{\sqrt{3}}{2},-\frac{h}{2})}$
• ${\displaystyle (3Hi+1,\sqrt{3}Hj,\frac{h}{2})}$

where i and j range over the integers, and ${\displaystyle H = \sqrt{1-h^2}}$.