Truncated cyclotruncated tetrahedral-octahedral honeycomb

Truncated cyclotruncated tetrahedral-octahedral honeycomb
Rank	4
Type	Isogonal
Space	Euclidean
Notation
Bowers style acronym	Tabtatoh
Elements
Cells	2N triangular antiprisms, N truncated tetrahedra, N ditruncated tetrahedra
Faces	4N triangles, 12N isosceles triangles, 4N ditrigons, 2N dihexagons
Edges	6N+12N+12N
Vertices	12N
Vertex figure	Skew rectangular pyramid
Measures (variant with regular hexagons of edge length 1)
Edge lengths	Edges of hexagons (6N+12N): 1
	Lacing edges (12N): ${\sqrt {3}}\approx 1.73205$
Related polytopes
Dual	Hexakis triangular antitegmatic honeycomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	P4×2
Convex	Yes
Nature	Tame

The truncated cyclotruncated tetrahedral-octahedral honeycomb, also called the truncated bitruncated tetrahedral-octahedral honeycomb or tabtatoh is an isogonal honeycomb that consists of ditruncated tetrahedra, truncated tetrahedra, and triangular antiprisms. 3 ditruncated tetrahedra, 1 truncated tetrahedron, and 1 triangular antiprism join at each vertex. It can be formed by truncating the cyclotruncated tetrahedral-octahedral honeycomb.

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform variants of the truncated tetrahedral-octahedral honeycomb with P₄ symmetry, where if the truncated tetrahedral-octahedral honeycombs are of the form a3b3c3o3*a, then c = b+3a.

The ratio between the longest and shortest edges is 1:${\sqrt {3}}$ ≈ 1:1.73205.

External links

• Klitzing, Richard. "tabtatoh".