Truncated octahedron atop truncated cube

}} Truncated octahedron atop truncated cube, or toatic, is a CRF segmentochoron (designated K-4.98 on Richard Klitzing's list). As the name suggests, it consists of a truncated octahedron and a truncated cube as bases, connected by 12 tetrahedra, 8 triangular cupolas, and 6 square cupolas.
 * verf2 = 24 isosceles trapezoidal pyramids, base edge lengths 1, $\sqrt{2}$, $\sqrt{2+√2}$, $\sqrt{2+}$, side edge lengths 1, 1, $\sqrt{2}$, $\sqrt{2}$
 * coxeter = ox4xx3xo&#x
 * army=Toatic
 * reg=Toatic
 * symmetry = BC3×I, order 48
 * circum = $\sqrt{2}$ ≈ 1.78541
 * height = $\sqrt{3}$/2 ≈ 0.67610
 * hypervolume = ≈ 9.07989
 * dich= Tet–3–tricu: acos(–(3$\sqrt{3}$–1)/4) ≈ 144.16048°
 * dich2= Tet–3–squacu: acos(–(3$\sqrt{(11+8√2)/7}$–2)/4) ≈ 124.10147°
 * dich3= Toe–6–tricu: acos(–(3$\sqrt{2√2–1}$–2)/4) ≈ 124.10147°
 * dich4 = Tic–8–squacu: acos(($\sqrt{2}$–2)/2) ≈ 107.0325º
 * dich5 = Squacu–4–tricu: acos(($\sqrt{2}$–2)/2) ≈ 107.0325º
 * dich6= Toe–4–squacu: acos((2–$\sqrt{2}$)/2) ≈ 72.96875º
 * dich7= Tic–3–tricu: acos((3$\sqrt{2}$–2)/4) ≈ 55.89854º
 * dual=Tetrakis hexahedral-triakis octahedral tegmoid
 * conjugate=Truncated octahedron atop quasitruncated hexahedron
 * conv = Yes
 * orientable=Yes
 * nat=Tame}}

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