Great birhombitetrahedral honeycomb

Great birhombitetrahedral honeycomb
Rank	4
Type	Isogonal
Space	Euclidean
Notation
Bowers style acronym	Gabreth
Coxeter diagram	s4x3x4s ()
Elements
Cells	3N rectangular trapezoprisms, 2N ditrigonal trapezoprisms, N great rhombitetratetrahedra
Faces	6N rectangles, 12N isosceles trapezoids, 2N hexagons, 4N ditrigons
Edges	6N+12N+12N
Vertices	12N
Vertex figure	Chiral notch
Measures (based on great prismated cubic honeycomb of edge length 1)
Edge lengths	Edges of hexagons (12N): 1
	Edges from diagonals of original squarees (6N): ${\sqrt {2}}$ $\approx 1.41421$
	Long edges of rectangles (12N): $1+{\sqrt {2}}$ $\approx 2.41421$
Related polytopes
Army	Gabreth
Regiment	Gabreth
Dual	Chirowedge honeycomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	P4×2
Convex	Yes
Nature	Tame

The great birhombitetrahedral honeycomb or gabreth is an isogonal honeycomb that consists of great rhombitetratetrahedra, ditrigonal trapezoprisms, and rectangular trapezoprisms. 2 of each type of cell join at each vertex. It can be obtained as a subsymmetrical faceting of the great prismated cubic honeycomb, by alternating its hexagons. However, it cannot be made uniform.

This honeycomb can be alternated into a snub bitetrahedral honeycomb, which is also nonuniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:2.

External links

• Klitzing, Richard. "Gabreth".