Truncated square prismatic honeycomb

Truncated square prismatic honeycomb
Rank4
Typeuniform
SpaceEuclidean
Notation
Bowers style acronymTassiph
Coxeter diagram
Elements
CellsN cubes, N octagonal prisms
FacesN+2N+4N squares, N octagons
Edges2N+4N+4N
Vertices4N
Vertex figureNotch, edge lengths 2+2 (two equatorial edges) and 2 (remaining edges)
Related polytopes
ArmyTassiph
RegimentTassiph
DualTetrakis square prismatic honeycomb
ConjugateQuasitruncated square prismatic honeycomb
Abstract & topological properties
OrientableYes
Properties
SymmetryR3❘W2
ConvexYes

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

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

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

Representations

A truncated square prismatic honeycomb has the following Coxeter diagrams: