Elongated triangular prismatic honeycomb

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Elongated triangular prismatic honeycomb
Rank4
TypeUniform
SpaceEuclidean
Notation
Bowers style acronymEtoph
Elements
Cells2N triangular prisms, N cubes
Faces2N triangles, N+N+2N+2N = 6N squares
EdgesN+2N+2N+2N = 7N
Vertices2N
Vertex figureIrregular pentagonal tegum, edge lengths 1 (two adjacent equatorial edges) and 2 (remaining edges)
Related polytopes
ArmyEtoph
RegimentEtoph
DualPrismatic pentagonal prismatic honeycomb
ConjugateRetroelongated triangular prismatic honeycomb
Abstract & topological properties
OrientableYes
Properties
SymmetryW2❘W2❘W2+
ConvexYes
NatureTame

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[edit | edit source]

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

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

External links[edit | edit source]