Truncated square prismatic honeycomb

Truncated square prismatic honeycomb
Rank	4
Type	uniform
Space	Euclidean
Notation
Bowers style acronym	Tassiph
Coxeter diagram
Elements
Cells	N cubes, N octagonal prisms
Faces	N+2N+4N squares, N octagons
Edges	2N+4N+4N
Vertices	4N
Vertex figure	Notch, edge lengths √2+√2 (two equatorial edges) and √2 (remaining edges)
Related polytopes
Army	Tassiph
Regiment	Tassiph
Dual	Tetrakis square prismatic honeycomb
Conjugate	Quasitruncated square prismatic honeycomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	R3❘W2
Convex	Yes

The truncated square prismatic honeycomb, or tassiph, is a convex uniform honeycomb. 2 cubes and 4 octagonal prisms join at each vertex of this honeycomb. As the name suggests, it is the honeycomb product of the truncated square tiling and the apeirogon.

This honeycomb can be alternated into a snub square antiprismatic honeycomb, although it cannot be made uniform. If all octagons are alternated into long rectangles, the result is a cantic bisnub square prismatic honeycomb, and if only half of the octagons are alternated into long rectangles, the result is a edge-snub square prismatic honeycomb, which are nonuniform. Finally, if the octagonal prisms are reduced to long square prisms and the remaining cells are dissected, the result is a distorted cubic honeycomb.

Vertex coordinates

Coordinates for the vertices of a truncated square prismatic honeycomb of edge length 1 are given by all permutations of

• $\left(±\frac12+(1+\sqrt2)i,\,±\frac{1+\sqrt2}{2}+j(1+\sqrt2),\,k\right),$

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

Representations

A truncated square prismatic honeycomb has the following Coxeter diagrams:

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• 
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External links

• Klitzing, Richard. "tassiph".

• Wikipedia Contributors. "Truncated square prismatic honeycomb".