# Mucubic honeycomb

Mucubic honeycomb
Rank4
TypeRegular
SpaceEuclidean
Notation
Schläfli symbol${\displaystyle \{4,3,4\}^\pi}$
Elements
Cells4 mucubes
Faces3n squares
Edges3n
Verticesn
Vertex figurePetrial octahedron, edge length 2
Related polytopes
ArmyChon
RegimentChon
Petrie dualCubic honeycomb
Abstract properties
Schläfli type{4,6,4}
Properties
SymmetryR4
ConvexNo

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.[1]

## Vertex coordinates

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