Truncated cuboctahedron
The
truncated cuboctahedron 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.
Alternate interchangeable names are:
*
Rhombitruncated cuboctahedron*
Great rhombicuboctahedron*
Omnitruncated cuboctahedronThe name
truncated cuboctahedron, given originally by
Johannes Kepler, is a little misleading. If you
truncate a cuboctahedron by cutting the corners off, you do
not get this uniform figure: some of the faces will be
rectangles. However, the resulting figure is
topologically equivalent to a 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.
One unfortunate point of confusion: There is a nonconvex uniform polyhedron by the same name. See
uniform great rhombicuboctahedron.
Cartesian coordinates for the vertices of a truncated cuboctahedron centered at the origin are all permutations of: (±1, ±(1+√2), ±(1+√8)).
*
cube*
cuboctahedron*
octahedron*
truncated icosidodecahedron*
The Uniform Polyhedra*
Virtual Reality Polyhedra The Encyclopedia of Polyhedra
