Enneagonal-cuboctahedral duoprism

{{Infobox polytope The enneagonal-cuboctahedral duoprism or eco is a convex uniform duoprism that consists of 9 cuboctahedral prisms, 6 square-enneagonal duoprisms, and 8 triangular-enneagonal duoprisms. Each vertex joins 2 cuboctahedral prisms, 2 triangular-enneagonal duoprisms, and 2 square-enneagonal duoprisms.
 * type=Uniform
 * dim = 5
 * img=
 * off = auto
 * obsa = Eco
 * coxeter = x9o o4x3o
 * army = Eco
 * reg = Eco
 * terons = 9 cuboctahedral prisms, 8 triangular-enneagonal duoprisms, 6 square-enneagonal duoprisms
 * cells = 72 triangular prisms, 54 cubes, 9 cuboctahedra, 24 enneagonal prisms
 * faces = 72 triangles, 54+216 squares, 12 enneagons
 * edges = 108+216
 * vertices = 108
 * circum = $$\frac{\sqrt{4+\frac{1}{\sin^2\frac\pi9}}{2} ≈ 1.77120$$
 * hypervol = $$\frac{15\sqrt2}{4\tan\frac\pi9} ≈ 14.57070$$
 * dit = Cope–co–cope: 140°
 * dit2 = Tedip–ep–sendip: $$\arccos\left(-\frac{\sqrt3}{3}\right) ≈ 125.26439°$$
 * dit3 = Tedip–trip–cope: 90°
 * dit4 = Sendip–cube–cope: 90°
 * verf = Rectangular scalene, edge lengths 1, $\sqrt{2}$, 1, $\sqrt{2}$ (base rectangle), 2cos(π/9) (top), $\sqrt{2}$ (side edges)
 * symmetry = BC{{sub|3}}×I2(9), order 864
 * pieces = 23
 * loc = 20
 * dual=Enneagonal-rhombic dodecahedral duotegum
 * conjugate = Enneagrammic-cuboctahedral duoprism, Great enneagrammic-cuboctahedral duoprism
 * conv = Yes
 * orientable=Yes
 * nat=Tame}}

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

Representations
An enneagonal-cuboctahedral duoprism has the following Coxeter diagrams:
 * x9o o4x3o (full symmetry)
 * x9o x3o3x