rhombicuboctahedron

From Latin rhombicuboctahaedron, referring to the fact that the twelve of the square faces lie in the same planes as the twelve faces of the rhombic dodecahedron, the dual of the cuboctahedron. (See rhombicuboctahedron on Wikipedia.Wikipedia )

rhombicuboctahedron (plural rhombicuboctahedra or rhombicuboctahedrons)

1. (geometry) An Archimedean solid with eight triangular and eighteen square faces; the small rhombicuboctahedron.
   • 1997, Johannes Kepler, trans. by E. J. Aiton, Alistair Matheson Duncan, and Judith Veronica Field, The harmony of the world, American Philosophical Society, page 119

     Therefore eight triangles and eighteen (that is, twelve and six) squares join up to make an icosihexahedron, which I call a truncated cuboctahedral rhombus or a rhombicuboctahedron.

   • 2009, Walter Steurer, Sofia Deloudi, Crystallography of Quasicrystals: Concepts, Methods and Structures, page 55,

     The gaps in a face-centered cubic packing of square sharing rhombicuboctahedra can be filled by cubes and tetrahedra (Fig. 2.4(h)).

   • 2016, John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things, page 273,

     So, for instance, covering up the right-hand side of our example (as in Figure 20.2(a)), we see that the rhombicuboctahedron does indeed have three types of face: two four-sided ones and one three-sided one.

2. (in combination) Either of the small rhombicuboctahedron and great rhombicuboctahedron.

• (polyhedron with 8 triangular and 18 square faces): small rhombicuboctahedron

• great rhombicuboctahedron
• rhombicuboctahedral
• pseudo-rhombicuboctahedron / pseudorhombicuboctahedron
• quasirhombicuboctahedron

• Great Rhombicuboctahedron on Wolfram MathWorld
• Small Rhombicuboctahedron on Wolfram MathWorld