Bicubic honeycomb

Bicubic honeycomb
Rank	4
Type	Noble
Space	Euclidean
Notation
Bowers style acronym	Bichon
Coxeter diagram	o4m3m4o ()
Elements
Cells	6N tetragonal disphenoids
Faces	24N isosceles triangles
Edges	3N+4N
Vertices	N
Vertex figure	Tetrakis hexahedron
Measures (based on two cubic honeycombs of edge length 1)
Edge lengths	Lacing edges (4N): ${\frac {\sqrt {3}}{2}}\approx 0.86603$
	Edges of cubic honeycombs (3N): 1
Related polytopes
Army	Bichon
Regiment	Bichon
Dual	Bitruncated cubic honeycomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	R4×2
Convex	Yes
Nature	Tame

The bicubic honeycomb or bichon, also known as the tetragonal disphenoidal honeycomb is a noble honeycomb that consists of tetragonal disphenoid cells. 24 cells join at each vetex, with the vertex figure being a tetrakis hexahedron. It can be constructed as the union of two dual cubic honeycombs.

The ratio between the longest and shortest edges is 1:${\frac {2{\sqrt {3}}}{3}}$ ≈ 1:1.15470.

Vertex coordinates

The vertices of a bicubic honeycomb based on two cubic honeycombs of edge length 1 are given by:

• $\left(i,\,j,\,k\right)$,
• $\left(i+{\frac {1}{2}},\,j+{\frac {1}{2}},\,k+{\frac {1}{2}}\right)$.

where i , j , and k  are integers.

External links

• Klitzing, Richard. "bichon".