Rhomboctahedron

The rhomboctahedron, ro, or compound of four triangular prisms is a uniform polyhedron compound. It consists of 12 squares and 8 triangles, with one triangle and two squares joining at a vertex.

Its quotient prismatic equivalent is the triangular prismatic tetrahedroorthowedge, which is six-dimensional.

Vertex coordinates
The vertices of a rhomboctahedron of edge length 1 are given by all even sign changes and even permutations, plus all odd sign changes and odd permutatoins, of:
 * $$\left(\frac{\sqrt3+\sqrt6}{6},\,\frac{\sqrt6-\sqrt3}{6},\,\frac{\sqrt3}{6}\right).$$

Related polyhedra
This compound is chiral. The compound of the two enantiomorphs is the disrhomboctahedron.