Elongated triangular prismatic honeycomb

Elongated triangular prismatic honeycomb
Rank	4
Type	Uniform
Space	Euclidean
Notation
Bowers style acronym	Etoph
Elements
Cells	2N triangular prisms, N cubes
Faces	2N triangles, N+N+2N+2N = 6N squares
Edges	N+2N+2N+2N = 7N
Vertices	2N
Vertex figure	Irregular pentagonal tegum, edge lengths 1 (two adjacent equatorial edges) and √2 (remaining edges)
Related polytopes
Army	Etoph
Regiment	Etoph
Dual	Prismatic pentagonal prismatic honeycomb
Conjugate	Retroelongated triangular prismatic honeycomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	W2❘W2❘W2+
Convex	Yes

The elongated triangular prismatic honeycomb, or etoph, is a convex uniform honeycomb. 4 cubes and 6 triangular prisms join at each vertex of this honeycomb. As the name suggests, it is the honeycomb product of the elongated triangular tiling and the apeirogon. It can also be thought of as a triangular prismatic honeycomb with layers of cubes inserted between adjacent layers of triangular prisms.

Vertex coordinates

The vertices of an elongated triangular prismatic honeycomb of edge length 1 are given by

• $\left(i\frac{2+\sqrt3}{2}\pm\frac12,\,j+\frac{i}{2},\,k\right),$

where i, j, and k range over the integers.

External links

• Klitzing, Richard. "etoph".

• Wikipedia Contributors. "Elongated triangular prismatic honeycomb".