Cubohemioctahedron

Cubohemioctahedron
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Cho
Coxeter diagram	(o4/3x3x4*a)/2 ()/2
Elements
Faces	6 squares, 4 hexagons
Edges	24
Vertices	12
Vertex figure	Bowtie, edge lengths √2 and √3
Measures (edge length 1)
Circumradius	1
Dihedral angle	$\arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.73561^\circ$
Number of external pieces	30
Level of complexity	4
Related polytopes
Army	Co
Regiment	Co
Dual	Hexahemioctacron
Conjugate	None
Abstract & topological properties
Flag count	96
Euler characteristic	–2
Orientable	No
Genus	5
Properties
Symmetry	B3, order 48
Convex	No
Nature	Tame

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.

External links

• Bowers, Jonathan. "Polyhedron Category 3: Quasiregulars" (#23).

• Bowers, Jonathan. "Batch 1: Oct and Co Facetings" (#3 under co).

• Klitzing, Richard. "cho".

• Wikipedia Contributors. "Cubohemioctahedron".
• McCooey, David. "Cubohemioctahedron"