Mucubic honeycomb
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Mucubic honeycomb | |
---|---|
Rank | 4 |
Type | Regular |
Space | Euclidean |
Notation | |
Schläfli symbol | , |
Elements | |
Cells | 4 mucubes |
Faces | 3N squares |
Edges | 3N |
Vertices | N |
Vertex figure | Petrial octahedron, edge length √2 |
Related polytopes | |
Army | Chon |
Regiment | Chon |
Company | Chon |
Petrie dual | Cubic honeycomb |
Abstract & topological properties | |
Schläfli type | {4,6,4} |
Orientable | No |
Properties | |
Symmetry | R4 |
Convex | No |
Dimension vector | (2,1,2,2) |
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 can be derived as the Petrie dual[1] or the κ 1 of the cubic honeycomb.
Vertex coordinates[edit | edit source]
The vertex coordinates of the mucubic honeycomb are the same as those of the cubic honeycomb, its regiment colonel.
External links[edit | edit source]
- McMullen, Peter; Schulte, Egon (1997). "Regular Polytopes in Ordinary Space" (PDF). Discrete Computational Geometry (47): 449–478. doi:10.1007/PL00009304.
References[edit | edit source]
- ↑ McMullen, Peter (2004). "Regular Polytopes of Full Rank" (PDF). Discrete Computational Geometry: 20.