Small rhombicosidodecahedron atop truncated icosahedron

{{Infobox polytope Small rhombicosidodecahedron atop truncated icosahedron , or sridati, is a CRF segmentochoron (designated K-4.126 on Richard Klitzing's list). As the name suggests, it consists of a small rhombicosidodecahedron and a truncated icosahedron as bases, connected by 30 triangular prisms, 12 pentagonal antiprisms, and 20 triangular cupolas.
 * img=srid=ti.png
 * off=auto
 * type=Segmentotope
 * dim = 4
 * obsa = Sridati
 * cells = 30 triangular prisms, 12 pentagonal antiprisms, 20 triangular cupolas, 1 small rhombicosidodecahedron, 1 truncated icosahedron
 * faces = 20+60+60 triangles, 30+60 squares, 12+12 pentagons, 20 hexagons
 * edges = 30+60+60+60+120
 * vertices = 60+60
 * verf = 60 skewed wedges, edge lengths 1 (4), $\sqrt{2}$ (4), and (1+$\sqrt{5}$)/2 (1)
 * verf2 = 60 isosceles trapezoidal pyramids, base edge lengths 1, 1, 1, (1+$\sqrt{5}$)/2, side edge lengths $\sqrt{2}$, $\sqrt{2}$, $\sqrt{3}$, $\sqrt{3}$
 * coxeter = ox5xo3xx&#x
 * army=Sridati
 * reg=Sridati
 * symmetry = H3×I, order 120
 * circum = $$\sqrt{\frac{106+41\sqrt5}{32}} ≈ 2.48545$$
 * height = $$\frac{1+\sqrt5}{4] ≈ 0.80902$$
 * hypervolume = ≈ 40.66582
 * dich= Tricu–4–trip: $$\arccos\left(-\frac{\sqrt{30}}{6}\right) ≈ 155.90516°$$
 * dich2= Pap–3–trip: 150°
 * dich3 = Pap–3–tricu: $$\arccos\left(-\frac{\sqrt{10}}{4}\right) ≈ 142.23876°$$
 * dich4 = Srid–4–trip: $$\arccos\left(\frac{\sqrt3-\sqrt{15}}{6}\right) ≈ 110.90516°$$
 * dich5 = Srid–5–pap: 108°
 * dich6= Srid–3–tricu: $$\arccos\left(\frac{\sqrt{10}-3\sqrt2}{4}\right) ≈ 97.76124°$$
 * dich7= Ti–6–tricu: $$\arccos\left(\frac{3\sqrt2-\sqrt{10}}{4}\right) ≈ 82.23876°$$
 * dich8 = Ti–5–pap: 72°
 * dual=Deltoidal hexecontahedral-pentakis dodecahedral tegmoid
 * conjugate=Quasirhombicosidodecahedron atop truncated great icosahedron
 * conv = Yes
 * orientable=Yes
 * nat=Tame}}

Vertex coordinates
The vertices of a small rhombicosidodecahedron atop truncated icosahedron segmentochoron 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:
 * $$\left(±\frac{2+\sqrt5}{2},\,±\frac12,\,±\frac12,\,\frac{1+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac{1+s\qrt5}{4}, ±\frac{1+\sqrt5}{2},\,±\frac{3+\sqrt5}{4},\,\frac{1+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac12,\,±3\frac{1+\sqrt5}{4},\,0\right),$$
 * $$\left(±\frac12,\,±\frac{5+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,0\right),$$
 * $$\left(±\frac{1+\sqrt5}{4},\,±1,\,±\frac{2+\sqrt5}{2},\,0\right).$$