Mucubic honeycomb

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Mucubic honeycomb
Rank4
TypeRegular
SpaceEuclidean
Notation
Schläfli symbol,
Elements
Cells4 mucubes
Faces3N squares
Edges3N
VerticesN
Vertex figurePetrial octahedron, edge length 2
Related polytopes
ArmyChon
RegimentChon
CompanyChon
Petrie dualCubic honeycomb
Abstract & topological properties
Schläfli type{4,6,4}
OrientableNo
Properties
SymmetryR4
ConvexNo
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]

  1. McMullen, Peter (2004). "Regular Polytopes of Full Rank" (PDF). Discrete Computational Geometry: 20.