# Muoctahedron

Muoctahedron
Rank3
SpaceEuclidean
Notation
Schläfli symbol${\displaystyle \{6,4\mid 4\}}$
Elements
Faces2N hexagons
Edges6N
Vertices3N
Related polytopes
ArmyBatch
RegimentBatch
DualMucube
Petrie dualPetrial muoctahedron
Convex hullBitruncated cubic honeycomb
Abstract properties
Schläfli type{6,4}
Topological properties
OrientableYes
Genus
Properties
SymmetryR4×2
ConvexNo

The muoctahedron or muo, short for multiple octahedron, is one of the three regular skew apeirohedra in Euclidean 3-space. It’s an infinite polyhedron that consists solely of hexagons, with 4 meeting at each vertex.

The muoctahedron is based on the bitruncated cubic honeycomb. Its faces are the hexagonal faces of the bitruncated cubic honeycomb.

It can also be formed as a modwrap of the order-4 hexagonal tiling by identifying every 4th vertex on each hole.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the bitruncated cubic honeycomb.