The Great Rhombicuboctahedron


The great rhombicuboctahedron is a 3D uniform polyhedron bounded by 8 hexagons, 12 squares, and 6 octagons. It may be constructed by radially expanding the octagonal faces of the truncated cube outwards, or equivalently, radially expanding the hexagonal faces of the truncated octahedron, or the non-axial square faces of the rhombicuboctahedron.

The great
rhombicuboctahedron

The great rhombicuboctahedron is also known as the truncated cuboctahedron; however, this is a misnomer. Truncating the cuboctahedron does not yield a uniform polyhedron, only a non-uniform topological equivalent of the great rhombicuboctahedron. The correct derivation is as described above.

Projections

In order to be able to identify the great rhombicuboctahedron in various projections of 4D objects, it is useful to know how it appears from various viewpoints. The following are some of the commonly-encountered views:

Projection Envelope Description
Octagon

Parallel projection centered on an octagonal face.

Dodecagon

Parallel projection centered on a hexagonal face.

Octagon

Parallel projection centered on a square face.

Coordinates

The Cartesian coordinates of the great rhombicuboctahedron, centered on the origin and having edge length 2, are all permutations of coordinates and changes of sign of:

Occurrences

The great rhombicuboctahedron appears as cells in the following 4D uniform polytopes:


Last updated 28 Feb 2013.

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