Heptagrammic-enneagonal duoprism

{{Infobox polytope The heptagrammic-enneagonal duoprism, also known as sheedip or the 7/2-9 duoprism, is a uniform duoprism that consists of 9 heptagrammic prisms and 7 enneagonal prisms, with 2 of each at each vertex.
 * dim=4
 * type=Uniform
 * obsa=Sheedip
 * img=
 * off=auto
 * coxeter=x7/2o x9o ({{CDD|node_1|7|rat|2x|node|2|node_1|9|node}})
 * symmetry=I{{sub|2}}(7)×I{{sub|2}}(9), order 252
 * army=Semi-uniform heendip
 * reg=Sheedip
 * verf=Digonal disphenoid, edge lengths 2cos(2π/7) (base 1), 2cos(π/9) (base 2), $\sqrt{2}$ (sides)
 * cells=9 heptagrammic prisms, 7 enneagonal prisms
 * faces=63 squares, 9 heptagrams, 7 enneagons
 * edges=63+63
 * vertices=63
 * circum=$$\sqrt{\frac1{4\sin^2\frac{2\pi}7}+\frac1{4\sin^2\frac{\pi}9}}≈1.59567$$
 * dich=Ship–7/2–ship: 140°
 * dich2=Ship–4–ep: 90°
 * dich3=Ep–9–ep: $$\frac{3\pi}{7 ≈ 77.14286°$$
 * hypervolume=$$\frac{63}{16\tan\frac{2\pi}7\tan\frac{\pi}9}≈8.62722$$
 * den=2
 * dual=Heptagrammic-enneagonal duotegum
 * conjugate=Heptagonal-enneagonal duoprism, Heptagonal-enneagrammic duoprism, Heptagonal-great enneagrammic duoprism, Heptagrammic-enneagrammic duoprism, Heptagrammic-great enneagrammic duoprism, Great heptagrammic-enneagonal duoprism, Great heptagrammic-enneagrammic duoprism, Great heptagrammic-great enneagrammic duoprism
 * conv=No
 * orientable=Yes
 * nat=Tame
 * pieces=23
 * euler=0
 * loc=12}}

The name can also refer to the great heptagrammic-enneagonal duoprism.

Vertex coordinates
The coordinates of a heptagrammic-enneagonal duoprism, centered at the origin and with edge length 4sin(2π/7)sin(π/9), are given by: where j = 2, 4, 6 and k = 2, 4, 8.
 * $$\left(2\sin\frac{\pi}9,\,0,\,2\sin\frac{2\pi}7,\,0\right),$$
 * $$\left(2\sin\frac{\pi}9,\,0,\,2\sin\frac{2\pi}7\cos\left(\frac{k\pi}9\right),\,±2\sin\frac{2\pi}7\sin\left(\frac{k\pi}9\right)\right),$$
 * $$\left(2\sin\frac{\pi}9,\,0,\,-\sin\frac{2\pi}7,\,±\sqrt3\sin\frac{2\pi}7\right),$$
 * $$\left(2\sin\frac{\pi}9\cos\left(\frac{j\pi}7\right),\,±2\sin\frac{\pi}9\sin\left(\frac{j\pi}7\right),\,2\sin\frac{2\pi}7,\,0\right),$$
 * $$\left(2\sin\frac{\pi}9\cos\left(\frac{j\pi}7\right),\,±2\sin\frac{\pi}9\sin\left(\frac{j\pi}7\right),\,2\sin\frac{2\pi}7\cos\left(\frac{k\pi}9\right),\,±2\sin\frac{2\pi}7\sin\left(\frac{k\pi}9\right)\right),$$
 * $$\left(2\sin\frac{\pi}9\cos\left(\frac{j\pi}7\right),\,±2\sin\frac{\pi}9\sin\left(\frac{j\pi}7\right),\,-\sin\frac{2\pi}7,\,±\sqrt3\sin\frac{2\pi}7\right),$$