Truncated cube atop great rhombicuboctahedron

{{Infobox polytope Truncated cube atop great rhombicuboctahedron, or ticagirco, is a CRF segmentochoron (designated K-4.128 on Richard Klitzing's list). As the name suggests, it consists of a truncated cube and a great rhombicuboctahedron as bases, connected by 12 triangular prisms, 8 triangular cupolas, and 6 octagonal prisms.
 * type=Segmentotope
 * dim = 4
 * obsa = Ticagirco
 * cells = 12 triangular prisms, 8 triangular cupolas, 6 octagonal prisms, 1 truncated cube, 1 great rhombicuboctahedron
 * faces = 8+24 triangles, 12+24+24 squares, 8 hexagons, 6+6 octagons
 * edges = 12+24+24+24+24+48
 * vertices = 24+48
 * verf = 24 skewed rectangular pyramids, base edge lengths 1, $\sqrt{2}$, 1, $\sqrt{2}$; lateral edge lengths $\sqrt{2}$, $\sqrt{2}$, $\sqrt{2+√2}$, $\sqrt{2+√2}$
 * verf2 = 48 irregular tetrahedra, edge lengths 1 (2), $\sqrt{2}$ (2), $\sqrt{3}$ (1) and $\sqrt{2+ (1)
 * coxeter = xx4xx3ox&#x
 * army=Ticagirco
 * reg=Ticagirco
 * symmetry = BC3×I, order 48
 * circum = √4+2√2 ≈ 2.61313
 * height = √2/2 ≈ 0.70711
 * hypervolume = (107+84√2)/12 ≈ 18.81616
 * dich= Tricu–3–trip: 150º
 * dich2= Op–4–trip: acos(–√6/3) ≈ 144.73561°
 * dich3= Tic–8–op: 135°
 * dich4= Tricu–4–op: 135°
 * dich5 = Tic–3–tricu: 120º
 * dich6 = Girco–6–tricu: 60º
 * dich7 = Girco–4–trip: acos(√3/3) ≈ 54.73561º
 * dich8 = Girco–8–op: 45º
 * dual=Triakis octahedral-disdyakis dodecahedral tegmoid
 * conjugate=Quasitruncated hexahedron atop quasitruncated cuboctahedron
 * conv = Yes
 * orientable=Yes
 * nat=Tame}$

It can be constructed as a cap of the prismatorhombated hexadecachoron, with a truncated cube at the top.

Vertex coordinates
The vertices of a truncated cube atop great rhombicuboctahedron segmentochoron of edge length 1 are given by:
 * (±(1+$\sqrt{2}$)/2, ±(1+$\sqrt{2}$)/2, ±1/2, $\sqrt{2}$/2) and all permutations of first three coordinates
 * (±(1+2$\sqrt{2}$)/2, ±(1+$\sqrt{2}$)/2, ±1/2, 0) and all permutations of first three coordinates