Dodecahedron atop rhombidodecadodecahedron

The  is a segmentochoron. It consists of 1 dodecahedron, 1 rhombidodecadodecahedron, 12 pentagonal antiprisms, 12 pentagrammic cuploids, and 30 triangular prisms.

It appears as a facet of the medial hecatonicosafaceted prismatodishecatonicosachoric alterprism.

Vertex coordinates
The vertices of a of edge length 1 are given by all permutations of the first three coordinates of: along with all even permutations of the first three coordinates of:
 * $$\left(\pm\frac{1+\sqrt{5}}{4},\,\pm\frac{1+\sqrt{5}}{4},\,\pm\frac{1+\sqrt{5}}{4},\,0\right),$$
 * $$\left(\pm\frac{\sqrt5}{2},\,\pm\frac12,\,\pm\frac12,\,\sqrt{\frac{3\sqrt5-1}{8}}\right),$$
 * $$\left(\pm\frac{3+\sqrt{5}}{4},\,\pm\frac{1}{2},\,0,\,0\right),$$
 * $$\left(0,\,\pm\frac{3-\sqrt5}{4},\,\pm\frac{3+\sqrt5}{4},\,\sqrt{\frac{3\sqrt5-1}{8}}\right),$$
 * $$\left(\pm1,\,\pm\frac{1+\sqrt5}{4},\,\pm\frac{\sqrt5-1}{4},\,\sqrt{\frac{3\sqrt5-1}{8}}\right).$$