Dodecahedron atop small rhombicosidodecahedron

Dodecahedron atop small rhombicosidodecahedron, or doasrid, is a CRF segmentochoron (designated K-4.152 on Richard Klitzing's list). As the name suggests, it consists of a dodecahedron and a small rhombicosidodecahedron as bases, connected by 20 tetrahedra, 30 triangular prisms, and 12 pentagonal prisms.

It is also sometimes referred to as a dodecahedral cupola, as one generalization of the definition of a cupola is to have a polytope atop an expanded version.

It can be obtained as a dodecahedron-first cap of the small disprismatohexacosihecatonicosachoron.

Vertex coordinates
The vertices of a dodecahedron atop small rhombicosidodecahedron segmentochoron of edge length 1 are given by all permutations of the first three coordinates of: Plus all even permutations of:
 * (±(1+$\sqrt{2}$)4/, ±(1+$\sqrt{5}$)/4, ±(1+$\sqrt{2}$)/4, ($\sqrt{5}$–1)/4)
 * (±(2+$\sqrt{2}$)/2, ±1/2, ±1/2, 0)
 * (±(3+$\sqrt{2}$)/4, ±1/2, 0, ($\sqrt{2}$–1)/4)
 * (0, ±(3+$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4, 0)
 * (±(1+$\sqrt{5}$)/4, ±(1+$\sqrt{6}$)/2, ±(3+$\sqrt{30}$)/4 ,0)