Cuboctahedron atop small rhombicuboctahedron

{{Infobox polytope Cuboctahedron atop small rhombicuboctahedron, or coasirco, is a CRF segmentochoron (designated K-4.61 on Richard Klitzing's list). As the name suggests, it consists of a cuboctahedron and a small rhombicuboctahedron as bases, connected by 8 octahedra, 12 square pyramids, and 6 square antiprisms.
 * img=sirco=co.png
 * type=Segmentotope
 * dim = 4
 * obsa = Coasirco
 * cells = 12 square pyramids, 8 octahedra, 6 square antiprisms, 1 cuboctahedron, 1 small rhombicuboctahedron
 * faces = 8+8+24+24+24 triangles, 6+6+12 squares
 * edges = 24+24+24+48
 * vertices = 12+24
 * verf = 12 rectangular-square trapezoprisms, one base a rectangle of edge lengths 1 and $\sqrt{2}$, other base a square of edge length 1, side lengths 1
 * verf2 = 24 skewed wedges, edge lengths 1 (6) and $\sqrt{2}$ (3)
 * coxeter = ox4xo3ox&#x
 * army=Coasirco
 * reg=Coasirco
 * symmetry = BC3×I, order 48
 * circum = ($\sqrt{7}$+2$\sqrt{14}$)/7 ≈ 1.44701
 * height = $\sqrt{2√2–1}$/2 ≈ 0.67610
 * hypervolume = $\sqrt{103+74√2}$/4 ≈ 3.60253
 * dich = Oct–3–squippy: acos((1–3$\sqrt{2}$)/4) ≈ 144.16048°
 * dich2 = Oct–3–squap: acos(–$\sqrt{4+3√2}$/4) ≈ 135.86903°
 * dich3 = Squippy–3–squap: acos(–$\sqrt{4+3√2}$/4) ≈ 135.86903°
 * dich4 = Co–4–squap: acos(–$\sqrt$/2) ≈ 126.48438°
 * dich5 = Co–3–oct: acos((2–3$\sqrt{2}$)/4) ≈ 124.10147°
 * dich6 = Sirco–4–squippy: acos((2–$\sqrt{2}$)/2) ≈ 72.96875°
 * dich7 = Sirco–3–oct: acos((3$\sqrt{2}$–2}/4) ≈ 55.89854°
 * dich8 = Sirco–4–squap: acos($\sqrt$/2) ≈ 53.51562°
 * dual=Rhombic dodecahedral-deltoidal icositetrahedral tegmoid
 * conjugate=Cuboctahedron atop small rhombicuboctahedron
 * conv = Yes
 * orientable=Yes
 * nat=Tame}}

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