Heptagonal-truncated octahedral duoprism

{{Infobox polytope The heptagonal-truncated octahedral duoprism or hetoe is a convex uniform duoprism that consists of 7 truncated octahedral prisms, 8 hexagonal-heptagonal duoprisms and 6 square-heptagonal duoprisms. Each vertex joins 2 truncated octahedral prisms, 1 square-heptagonal duoprism, and 2 hexagonal-heptagonal duoprisms.
 * type=Uniform
 * dim = 5
 * img=
 * off = auto
 * obsa = Hetoe
 * coxeter = x7o o4x3x
 * army = Hetoe
 * reg = Hetoe
 * terons = 6 square-heptagonal duoprisms, 8 hexagonal-heptagonal duoprisms, 7 truncated octahedral prisms
 * cells = 42 cubes, 56 hexagonal prisms, 12+24 heptagonal prisms, 7 truncated octahedra
 * faces = 42+84+168 squares, 56 hexagons, 42 heptagons
 * edges = 84+168+168
 * vertices = 168
 * circum = $$\frac{\sqrt{10+\frac{1}{\sin^2\frac\pi7}}{2} ≈ 1.95652$$
 * hypervol = $$\frac{14\sqrt2}{\tan\frac\pi7} ≈ 41.11303$$
 * dit = Tope–toe–tope: $$\frac{5\pi}{7} ≈ 128.57143°$$
 * dit2 = Squahedip–hep–haheddip: $$\arccos\left(-\frac{\sqrt3}{3}\right) ≈ 125.26439°$$
 * dit3 = Haheddip–hep–haheddip: $$\arccos\left(-\frac13\right) ≈ 109.47122°$$
 * dit4 = Squahedip–cube–tope: 90°
 * dit5 = Haheddip–hip–tope: 90°
 * verf = Digonal disphenoidal pyramid, edge lengths $\sqrt{2}$, $\sqrt{3}$, $\sqrt{3}$ (base triangle), 2cos(π/7) (top), $\sqrt{2}$ (side edges)
 * symmetry = BC{{sub|3}}×I2(7), order 672
 * pieces = 21
 * loc = 30
 * dual=Heptagonal-tetrakis hexahedral duotegum
 * conjugate = Heptagrammic-truncated octahedral duoprism, Great heptagrammic-truncated octahedral duoprism
 * conv = Yes
 * orientable=Yes
 * nat=Tame}}

Vertex coordinates
The vertices of a heptagonal-truncated octahedral duoprism of edge length 2sin(π/7) are given by all permutations of the last three coordinates of: where j = 2, 4, 6.
 * $$\left(1,\,0,\,0,\,±\sqrt2\sin\frac\pi7,\,±2\sqrt2\sin\frac\pi7\right),$$
 * $$\left(\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right),\,0,\,±\sqrt2\sin\frac\pi7,\,±2\sqrt2\sin\frac\pi7\right),$$