Trihexagonal prismatic honeycomb

Trihexagonal prismatic honeycomb
Rank	4
Type	uniform
Space	Euclidean
Notation
Bowers style acronym	Thiph
Coxeter diagram	x∞o o6x3o
Elements
Cells	2N triangular prisms, N hexagonal prisms
Faces	2N triangles, 6N squares, N hexagons
Edges	3N+6N
Vertices	3N
Vertex figure	Rectangular tegum, edge lengths 1 and √3 (equatorial) and √2 (sides)
Related polytopes
Army	Thiph
Regiment	Thiph
Dual	Rhombic prismatic honeycomb
Conjugate	None
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	V3❘W2
Convex	Yes

The trihexagonal prismatic honeycomb, or thiph, is a convex uniform honeycomb. 4 triangular prisms and 4 hexagonal prisms join at each vertex of this honeycomb. As the name suggests, it is the honeycomb product of the trihexagonal tiling and the apeirogon.

Vertex coordinates

The vertices of a trihexagonal prismatic honeycomb of edge length 1 are given by:

• $\left(\sqrt3i,\,i+2j+1,\,k\right),$
• $\left(\sqrt3i+\frac{\sqrt3}{2},\,j+\frac12,\,k\right).$

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

Representations

A trihexagonal prismatic honeycomb has the following Coxeter diagrams:

• x∞o o6x3o
• x∞x o6x3o
• x∞o x3x3o3*a
• x∞x x3x3o3*a

External links

• Klitzing, Richard. "thiph".

• Wikipedia Contributors. "Trihexagonal prismatic honeycomb".