Small rhombicuboctahedron

The small rhombicuboctahedron, also commonly known as simply the rhombicuboctahedron, or sirco is one of the 13 Archimedean solids. It consists of 8 triangles and 6+12 squares, with one triangle and three squares meeting at each vertex. It can be obtained by cantellation of the cube or octahedron, or equivalently by pushing either polyhedron's faces outward and filling the gaps with the corresponding polygons.

6 of the squares in this figure have full BC2 symmetry, while 12 of them have only A1×A1 symmetry with respect to the whole polyhedron.

It is possible to diminish the small rhombicuboctahedron by removing square cupolas. In fact, it is the result of attaching two square cupolas to an octagonal prism, and can be called an elongated square orthobicupola. If one is removed the result is the elongated square cupola. If one cupola is rotated by 45º, the result is the elongated square gyrobicupola, or pseudo-rhombicuboctahedron.

Vertex coordinates
A small rhombicuboctahedron of edge length 1 has vertex coordinates given by all permutations of:
 * (±(1+$\sqrt{5+2√2}$)/2, ±1/2, ±1/2).