Heptagrammic-hendecagonal duoprism

{{Infobox polytope The heptagrammic-hendecagonal duoprism, also known as the 7/2-11 duoprism, is a uniform duoprism that consists of 11 heptagrammic prisms and 7 hendecagonal prisms, with 2 of each at each vertex.
 * dim=4
 * type=Uniform
 * obsa=
 * img=
 * off=auto
 * coxeter=x7/2o x11o ({{CDD|node_1|7|rat|2x|node|2|node_1|11|node}})
 * symmetry=I{{sub|2}}(7)×I{{sub|2}}(11), order 308
 * army=Semi-uniform hehendip
 * reg=
 * verf=Digonal disphenoid, edge lengths 2cos(2π/7) (base 1), 2cos(π/11) (base 2), $\sqrt{2}$ (sides)
 * cells=11 heptagrammic prisms, 7 hendecagonal prisms
 * faces=77 squares, 11 heptagrams, 7 hendecagons
 * edges=77+77
 * vertices=77
 * rad=$$\sqrt{\frac{1}{4\sin^2\frac{2\pi}{7}}+\frac{1}{4\sin^2\frac{\pi}{11}}}≈1.88644$$
 * dich=Ship–7/2–ship: $$\frac{9\pi}{11} ≈ 147.27273°$$
 * dich2=Ship–4–henp: 90°
 * dich3=Henp–11–henp: $$\frac{3\pi}{7 ≈ 77.14286°$$
 * hypervol=$$\frac{77}{16\tan\frac{2\pi}{7}\tan\frac{\pi}{11}}≈13.07049$$
 * den=2
 * dual=Heptagrammic-hendecagonal duotegum
 * conjugate=Heptagonal-hendecagonal duoprism, Heptagonal-small hendecagrammic duoprism, Heptagonal-hendecagrammic duoprism, Heptagonal-great hendecagrammic duoprism, Heptagonal-grand hendecagrammic duoprism, Heptagrammic-small hendecagrammic duoprism, Heptagrammic-hendecagrammic duoprism, Heptagrammic-great hendecagrammic duoprism, Heptagrammic-grand hendecagrammic duoprism, Great heptagrammic-hendecagonal duoprism, Great heptagrammic-small hendecagrammic duoprism, Great heptagrammic-hendecagrammic duoprism, Great heptagrammic-great hendecagrammic duoprism, Great heptagrammic-grand hendecagrammic duoprism
 * conv=No
 * orientable=Yes
 * nat=Tame
 * pieces=25
 * euler=0
 * loc=12}}

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

Vertex coordinates
The coordinates of a heptagrammic-hendecagonal duoprism, centered at the origin and with edge length 4sin(2π/7)sin(π/11), are given by: where j = 2, 4, 6 and k = 2, 4, 6, 8, 10.
 * $$\left(2\sin\frac{\pi}{11},\,0,\,2\sin\frac{2\pi}{7},\,0\right),$$
 * $$\left(2\sin\frac{\pi}{11},\,0,\,2\sin\frac{2\pi}{7}\cos\left(\frac{k\pi}{11}\right),\,±2\sin\frac{2\pi}{7}\sin\left(\frac{k\pi}{11}\right)\right),$$
 * $$\left(2\sin\frac{\pi}{11}\cos\left(\frac{j\pi}{7}\right),\,±2\sin\frac{\pi}{11}\sin\left(\frac{j\pi}{7}\right),\,2\sin\frac{2\pi}{7},\,0\right),$$
 * $$\left(2\sin\frac{\pi}{11}\cos\left(\frac{j\pi}{7}\right),\,±2\sin\frac{\pi}{11}\sin\left(\frac{j\pi}{7}\right),\,2\sin\frac{2\pi}{7}\cos\left(\frac{k\pi}{11}\right),\,±2\sin\frac{2\pi}{7}\sin\left(\frac{k\pi}{11}\right)\right),$$