Enneagonal-truncated cubic duoprism

{{Infobox polytope The enneagonal-truncated cubic duoprism or etic is a convex uniform duoprism that consists of 9 truncated cubic prisms, 6 octagonal-enneagonal duoprisms and 8 triangular-enneagonal duoprisms. Each vertex joins 2 truncated cubic prisms, 1 triangular-enneagonal duoprism, and 2 octagonal-enneagonal duoprisms.
 * type=Uniform
 * dim = 5
 * img=
 * off = auto
 * obsa = Etic
 * coxeter = x9o x4x3o
 * army = Etic
 * reg = Etic
 * terons = 8 triangular-enneagonal duoprisms, 9 truncated cubic prisms, 6 octagonal-enneagonal duoprisms
 * cells = 72 triangular prisms, 54 octagonal prisms, 12+24 enneagonal prisms, 9 truncated cubes
 * faces = 72 triangles, 108+216 squares, 54 octagons, 24 enneagons
 * edges = 108+216+216
 * vertices = 216
 * circum = $$\frac{\sqrt{7+4\sqrt2+\frac{1}{\sin^2\frac\pi9}}2 ≈ 2.30247$$
 * hypervol = $$\frac{21(3+2\sqrt2)}{4\tan\frac\pi9} ≈ 84.07073$$
 * dit = Ticcup–tic–ticcup: 140°
 * dit2 = Tedip–ep–oedip: $$\arccos\left(-\frac{\sqrt3}{3}\right) ≈ 125.26439°$$
 * dit3 = Tedip–trip–ticcup: 90°
 * dit4 = Oedip–op–ticcup: 90°
 * dit5 = Oedip–ep–oedip: 90°
 * verf = Digonal disphenoidal pyramid, edge lengths 1, $\sqrt{2+√2}$, $\sqrt{2+√2}$ (base triangle), cos(π/9) (top), $\sqrt{2}$ (side edges)
 * symmetry = BC{{sub|3}}×I2(9), order 864
 * pieces = 23
 * loc = 30
 * dual=Enneagonal-triakis octahedral duotegum
 * conjugate = Enneagrammic-truncated cubic duoprism, Great enneagrammic-truncated cubic duoprism, Enneagonal-quasitruncated hexahedral duoprism, Enneagrammic-quasitruncated hexahedral duoprism, Great enneagrammic-quasitruncated hexahedral duoprism
 * conv = Yes
 * orientable=Yes
 * nat=Tame}}

Vertex coordinates
The vertices of an enneagonal-truncated cubic duoprism of edge length 2sin(π/9) are given by all permutations of the last three coordinates of: where j = 2, 4, 8.
 * $$\left(1,\,0,\,±(1+\sqrt2)\sin\frac\pi9,\,±(1+\sqrt2)\sin\frac\pi9,\,±\sin\frac\pi9\right),$$
 * $$\left(\cos\left(\frac{j\pi}9\right),\,±\sin\left(\frac{j\pi}9\right),\,±(1+\sqrt2)\sin\frac\pi9,\,±(1+\sqrt2)\sin\frac\pi9,\,±\sin\frac\pi9\right),$$
 * $$\left(-\frac12,\,±\frac{\sqrt3}2,\,±(1+\sqrt2)\sin\frac\pi9,\,±(1+\sqrt2)\sin\frac\pi9,\,±\sin\frac\pi9\right),$$