Cyclotruncated tetrahedral-octahedral honeycomb

Cyclotruncated tetrahedral-octahedral honeycomb
Rank	4
Type	uniform
Space	Euclidean
Notation
Bowers style acronym	Cytatoh (old: Batatoh)
Coxeter diagram	x3x3o3o3*a ()
Elements
Cells	N tetrahedra, N truncated tetrahedra
Faces	4N triangles, 2N hexagons
Edges	6N
Vertices	2N
Vertex figure	Triangular antiprism, edge lengths 1 (base) and √3 (sides)
Measures (edge length 1)
Vertex density	$\frac{\sqrt2}2 \approx 0.70710678119$
Related polytopes
Army	Cytatoh
Regiment	Cytatoh
Dual	Triangular antitegmatic honeycomb
Conjugate	None
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	P4×2
Convex	Yes

The cyclotruncated tetrahedral-octahedral honeycomb, also known as the quarter cubic honeycomb, is a convex uniform honeycomb. 2 tetrahedra and 6 truncated tetrahedra join at each vertex of this honeycomb. It can be formed by applying two successive alternated faceting to the cubic honeycomb.

Representations

A cyclotruncated tetrahedral-octahedral honeycomb has the following Coxeter diagrams:

• x3x3o3o3*a () (full symmetry)
• x3o3o *b4s () (as single alternated faceting)
• s4o3o4s' () (as double alternated faceting)

Gallery

• 

  Wireframe

• 

  Slab

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External links

• Klitzing, Richard. "cytatoh".

• Wikipedia Contributors. "Quarter cubic honeycomb".
• Binnendyk, Eric. "Category 7: Triangular Podiumverts" (#140).