Blend of small rhombicosidodecahedron and small rhombidodecahedron

The  is an orbiform polyhedron. It consists of 20 triangles, 48 squares, 12 pentagons, and 12 decagons. As the name suggests, it can be constructed by blending a small rhombicosidodecahedron and a small rhombidodecahedron together by six square faces.

Vertex coordinates
A of edge length 1 has vertex coordinates given by all permutations of
 * $$\left(\pm\frac{2+\sqrt5}{2},\,\pm\frac12,\,\pm\frac12\right),$$
 * $$\left(0,\,\pm\frac{3+\sqrt5}{4},\,\pm\frac{5+\sqrt5}{4}\right),$$
 * $$\left(\pm\frac{1+\sqrt5}{4},\,\pm\frac{1+\sqrt5}{2},\,\pm\frac{3+\sqrt5}{4}\right).$$

Related polytopes
The appears as a cell in several scaliform polychora. These include the:
 * small snub hexacosifusihexacosichoron
 * small dishexacosifusihexacosichoron
 * small hexacosihexacosifusihexacosichoron
 * small fusihexacosidishexacosichoron
 * small disnub dishexacosifusihexacosichoron