Rhombicuboctahedron
From The Art and Popular Culture Encyclopedia
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In geometry, the rhombicuboctahedron[1], or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces. There are 24 identical vertices, with one triangle and three squares meeting at each. Note that six of the squares only share vertices with the triangles while the other twelve share an edge. The polyhedron has octahedral symmetry, like the cube and octahedron. Its dual is called the deltoidal icositetrahedron or trapezoidal icositetrahedron, although its faces are not really true trapezoids.
The name rhombicuboctahedron refers to the fact that 12 of the square faces lie in the same planes as the 12 faces of the rhombic dodecahedron which is dual to the cuboctahedron. Great rhombicuboctahedron is an alternative name for a truncated cuboctahedron, whose faces are parallel to those of the (small) rhombicuboctahedron.
It can also be called an expanded cube or cantellated cube or a cantellated octahedron from truncation operations of the uniform polyhedron.
The shape is found in Jacopo de' Barbari's painting Portrait of Luca Pacioli.
See also
![[1]](http://commons.wikimedia.org/wiki/File:Leonardo_polyhedra.png){kind=link}