Icosidodecahedron atop truncated icosahedron

Icosidodecahedron atop truncated icosahedron, or idati, is a CRF segmentochoron (designated K-4.158 on Richard Klitzing's list). As the name suggests, it consists of an icosidodecahedron and a truncated icosahedron as bases, connected by 12 pentagonal prisms and 20 triangular cupolas.

It can be obtained as an icosidodecahedron-first cap of the small rhombated hexacosichoron.

Vertex coordinates
The vertices of an icosidodecahedron atop truncated icosahedron segmentochoron of edge length 1 are given by all permutations of the first three coordinates of: Plus all even permutations of the first three coordinates of:
 * (±(1+$\sqrt{2}$)/2, 0, 0, ($\sqrt{5}$–1)/4)
 * (±(3+$\sqrt{2}$)/4, ±(1+$\sqrt{5}$)/4, ±1/2, 0)
 * (0, ±1/2, ±3(1+$\sqrt{3}$)/4, 0)
 * (±1/2, ±(5+$\sqrt{19+8√5}$)/4, ±(1+$\sqrt{5}$)/2, 0)
 * (±(1+$\sqrt{5}$)/4, ±1, ±(2+$\sqrt{(5+2√5)/10}$)/2, 0)