rhombicuboctahedron

{{Infobox polyhedron | name = Rhombicuboctahedron | image = Rhombicuboctahedron (green).png | type = ArchimedeanUniform polyhedron | faces = 8 equilateral triangles18 squares | edges = 48 | vertices = 24 | symmetry = Octahedral symmetry \mathrm{O}_\mathrm{h} Pyritohedral symmetry \mathrm{T}_\mathrm{h} | schläfli = r \begin{Bmatrix} 3 \\ 4 \end{Bmatrix} | angle = square-to-square: 135° square-to-triangle: 144.7° | vertex_figure = Polyhedron small rhombi 6-8 vertfig.svg | vertex_config = 24 (3 \cdot 4^3) | dual = Deltoidal icositetrahedron | net = Polyhedron small rhombi 6-8 net.svg }} The rhombicuboctahedron or small rhombicuboctahedron is a polyhedron with 26 faces, consisting of 8 equilateral triangles and 18 squares. It was named by Johannes Kepler in his 1618 Harmonices Mundi, being short for truncated cuboctahedral rhombus, with cuboctahedral rhombus being his name for a rhombic dodecahedron.

The rhombicuboctahedron is an Archimedean solid, and its dual is a Catalan solid, the deltoidal icositetrahedron. The elongated square gyrobicupola, the 37th Johnson solid, is a polyhedron that is similar to a rhombicuboctahedron, but it is not an Archimedean solid because it is not vertex-transitive. The rhombicuboctahedron is found in diverse cultures in architecture, toys, the arts, and elsewhere.