Small rhombicosidodecahedron atop truncated dodecahedron

{{Infobox polytope Small rhombicosidodecahedron atop truncated dodecahedron, or sridatid, is a CRF segmentochoron (designated K-4.159 on Richard Klitzing's list). As the name suggests, it consists of a small rhombicosidodecahedron and a truncated dodecahedron as bases, connected by 30 triangular prisms, 20 octahedra, and 12 pentagonal cupolas.
 * img=tid=srid.png
 * off=auto
 * type=Segmentotope
 * dim = 4
 * obsa = Sridatid
 * cells = 30 triangular prisms, 20 octahedra, 12 pentagonal cupolas, 1 small rhombicosidodecahedron, 1 truncated dodecahedron
 * faces = 20+20+60+60 triangles, 30+60 squares, 12 pentagons, 12 decagons
 * edges = 30+60+60+60+120
 * vertices = 60+60
 * verf = 60 square wedges, edge lengths 1 (base square), $\sqrt{2}$ (sides), and (1+$\sqrt{5}$)/2 (top)
 * verf2 = 60 skewed square pyramids, base edge lengths 1, side edge lengths $\sqrt{(5+√5)/2}$ and $\sqrt{2}$
 * coxeter = xx5xo3ox&#x
 * army=Sridatid
 * reg=Sridatid
 * symmetry = H3×I, order 120
 * circum = $$\sqrt{23+10\sqrt5} ≈ 6.73503$$
 * height = $$\frac{\sqrt5-1}{4} ≈ 0.30902$$
 * hypervolume = $$\frac{355+119\sqrt5]{32} ≈ 19.40913$$
 * dich= Oct–3–trip: $$\arccos\left(-\frac{\sqrt6+\sqrt{30}}{8}\right) ≈ 172.23876°$$
 * dich2= Pecu–4–trip: $$\arccos\left(-\frac{\sqrt3+\sqrt{15}}{4}\right) ≈ 159.09484°$$
 * dich3= Srid–4–trip: $$\arccos\left(-\frac{\sqrt3+\sqrt{15}}{4}\right) ≈ 159.09484°$$
 * dich4 = Pecu–3–oct: $$\arccos\left(-\frac{\sqrt{7+3\sqrt5}}{4}\right) ≈ 157.76124°$$
 * dich4 = Srid–3–oct: $$\arccos\left(-\frac{\sqrt{7+3\sqrt5}}{4}\right) ≈ 157.76124°$$
 * dich6 = Srid–5–pecu: 144°
 * dich7= Tid–5–pecu: 36°
 * dich8= Tid–3–oct: $$\arccos\left(\frac{\sqrt{7+3\sqrt5}}{4}\right) ≈ 22.23876°$$
 * dual=Deltoidal hexecontahedral-triakis icosahedral tegmoid
 * conjugate=Quasirhombicosidodecahedron atop quasitruncated great stellated dodecahedron
 * conv = Yes
 * orientable=Yes
 * nat=Tame}}

It can be obtained as a small rhombicosidodecahedron-first cap of the small rhombated hecatonicosachoron.

Vertex coordinates
The vertices of a small rhombicosidodecahedron atop truncated dodecahedron 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:
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac12,\,±\frac12,\,\frac{\sqrt5-1}{4}\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,\frac{\sqrt5-1}{4}\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{3+\sqrt5}{4},\,\frac{\sqrt5-1}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±\frac{5+\sqrt5}{4},\,0\right),$$
 * $$\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,0\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,0\right).$$