Cubohemioctahedron

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Cubohemioctahedron
Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymCho
Coxeter diagram(o4/3x3x4*a)/2
()/2
Elements
Faces6 squares, 4 hexagons
Edges24
Vertices12
Vertex figureBowtie, edge lengths 2 and 3
Measures (edge length 1)
Circumradius1
Dihedral angle${\displaystyle \arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.73561^\circ}$
Number of external pieces30
Level of complexity4
Related polytopes
ArmyCo
RegimentCo
DualHexahemioctacron
ConjugateNone
Abstract & topological properties
Flag count96
Euler characteristic–2
OrientableNo
Genus5
Properties
SymmetryB3, order 48
ConvexNo
NatureTame

The cubohemioctahedron, or cho, is a quasiregular polyhedron and one of 10 uniform hemipolyhedra. It consists of 6 squares and 4 "hemi" hexagons, passing through its center, with two of each joining at a vertex. It also has 8 triangular pseudofaces. Its square faces are parallel to those of a cube, and its hemi hexagonal faces are parallel to those of an octahedron: hence the name. It can be derived as a rectified petrial octahedron.

The visible portion of this solid resembles a cuboctahedron with eight tetrahedra carved out. In fact the square faces are the same ones as those of the cuboctahedron, while the hexagons are its equatorial planes.

It is uniform under both cubic and tetrahedral symmetry. In fact it occurs far more often with tetrahedral symmetry in higher uniform polytopes.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the cuboctahedron.

Related polyhedra

The great antirhombicosahedron is a uniform polyhedron compound composed of 5 cubohemioctahedra.