Truncated cuboctahedron
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Type	Archimedean
Faces	12 squares 8 hexagons 6 octagons
Edges	72
Vertices	48
Vertex configuration	4,6,8
Symmetry group	octahedral (Oh)
Dual polyhedron	disdyakis dodecahedron
Properties	convex, semi-regular (vertex-uniform), zonohedron

The truncated cuboctahedron, or great rhombicuboctahedron, is an Archimedean solid. It has 12 regular square faces, 8 regular hexagonal faces, 6 regular octagonal faces, 48 vertices and 72 edges. Since each of its faces has point symmetry (equivalently, 180° rotational symmetry), the truncated cuboctahedron is a zonohedron.

Note that the name truncated cuboctahedron may be a little misleading. If you truncate a cuboctahedron by cutting the corners off, you do not get an actual regular truncated cuboctahedron: some of the faces will be irregular polygons. However, the resulting figure is topologically equivalent to truncated cuboctahedron and can always be deformed until the faces are regular. The alternative name great rhombicuboctahedron refers to the fact that the 12 square faces lie in the same planes as the 12 faces of the rhombic dodecahedron which is dual to the cuboctahedron. Compare to small rhombicuboctahedron.

Canonical coordinates for the vertices of a truncated cuboctahedron centered at the origin are all permutations of (±1, ±(1+√2), ±(1+√8)).

See also

• cube
• cuboctahedron
• octahedron
• truncated icosidodecahedron

External links

• The Uniform Polyhedra
• Virtual Reality Polyhedra The Encyclopedia of Polyhedra