Mucubic honeycomb

Mucubic honeycomb
Rank	4
Type	Regular
Space	Euclidean
Notation
Schläfli symbol	$\{4,3,4\}^\pi$
Elements
Cells	4 mucubes
Faces	3n squares
Edges	3n
Vertices	n
Vertex figure	Petrial octahedron, edge length √2
Related polytopes
Army	Chon
Regiment	Chon
Petrie dual	Cubic honeycomb
Abstract properties
Schläfli type	{4,6,4}
Properties
Symmetry	R4
Convex	No

The mucubic honeycomb or petrial cubic honeycomb is a regular skew polychoron consisting of 4 mucubes. It shares its faces, edges, and vertices with the cubic honeycomb, and it has a petrial octahedron vertex figure. It is also the Petrie dual of the cubic honeycomb.

Vertex coordinates

The vertex coordinates of the mucubic honeycomb are the same as that of its regiment colonel, the cubic honeycomb.

External links

• McMullen, Peter; Schulte, Egon (1997). "Regular Polytopes in Ordinary Space" (PDF). Discrete Computational Geometry (47): 449–478. doi:10.1007/PL00009304.