Gyroelongated triangular prismatic honeycomb

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

The gyroelongated triangular prismatic honeycomb, or gyetaph, is a convex uniform honeycomb. 4 cubes and 6 triangular prisms join at each vertex of this honeycomb.

It can be thought of as a gyrated triangular prismatic honeycomb with layers of cubes inserted between adjacent layers of triangular prisms, an elongated gyrobifastigial honeycomb with the elongated gyrobifastigia dissected into a cube and two triangular prisms, or an elongated triangular prismatic honeycomb where layers of triangular prisms are rotated by 90º. It shares its vertex figure with the latter.

External links

• Klitzing, Richard. "gyetaph".

• Wikipedia Contributors. "Gyroelongated triangular prismatic honeycomb".