Dodecahedron atop icosidodecahedron

Dodecahedron atop icosidodecahedron, or doaid, is a CRF segmentochoron (designated K-4.77 on Richard Klitzing's list). As the name suggests, it consists of a dodecahedron and an icosidodecahedron as bases, connected by 20 tetrahedra and 12 pentagonal antiprisms.

It is a segment of the hexacosichoron, with the icosidodecahedral base lying on the hexacosichoron's equator.

Vertex coordinates
The vertices of a dodecahedron atop icosidodecahedron segmentochoron of edge length 1 are given by:
 * (±(3+$\sqrt{5}$)/4, ±1/2, 0, (1+$\sqrt{5}$)/4) and all permutations of first three coordinates
 * (±(1+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4, ±(1+$\sqrt{5}$)/4, (1+$\sqrt{10}$)/4)
 * (±(1+$\sqrt{2}$)/2, 0, 0, 0) and all permutations of first three coordinates
 * (±(3+$\sqrt{10}$)/4, ±·1+$\sqrt{5}$)/4, 0, 0) and all permutations of first three coordinates