Muoctahedron

Muoctahedron
Rank	3
Space	Euclidean
Notation
Schläfli symbol	$\{6,4\mid 4\}$
Elements
Faces	2N hexagons
Edges	6N
Vertices	3N
Related polytopes
Army	Batch
Regiment	Batch
Dual	Mucube
Petrie dual	Petrial muoctahedron
Convex hull	Bitruncated cubic honeycomb
Abstract properties
Schläfli type	{6,4}
Topological properties
Orientable	Yes
Genus	∞
Properties
Symmetry	R4×2
Convex	No

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.

External links

• Wikipedia Contributors. "Regular skew apeirohedron".
• Klitzing, Richard. "shexat".

• Klitzing, Richard. "Skew polytopes".

References

• Conway, John H.; Burgiel, Heidi; Goodman-Strauss, Chaim (2008). The Symmetries of Things. pp. 333–335.
• Coxeter, H.S.M. (1999). The Beauty of Geometry: Twelve essays. Dover Publications, Inc. pp. 157 ff.
• McMullen, Peter; Schulte, Egon (1997). "Regular Polytopes in Ordinary Space". Discrete Computational Geometry. 17: 449–478.
• jan Misali (2020). "there are 48 regular polyhedra".