Pentagonal-great heptagrammic duoprism

{{Infobox polytope The pentagonal-great heptagrammic duoprism, also known as pagishdip or the 5-7/3 duoprism, is a uniform duoprism that consists of 7 pentagonal prisms and 5 great heptagrammic prisms, with two of each at each vertex.
 * type=Uniform
 * img=
 * off=auto
 * obsa=Pagishdip
 * coxeter=x5o x7/3o ({{CDD|node_1|5|node|2|node_1|7|rat|3x|node}})
 * symmetry=H{{sub|2}}×I{{sub|2}}(7), order 140
 * dimension=4
 * army=Semi-uniform pheddip
 * reg=Pagishdip
 * verf=Digonal disphenoid, edge lengths (1+$\sqrt{5}$)/2 (base 1), 2cos(3π/7) (base 2), $\sqrt{2}$ (sides)
 * cells=7 pentagonal prisms, 5 great heptagrammic prisms
 * faces=35 squares, 7 pentagons, 5 great heptagrams
 * edges=35+35
 * vertices=35
 * circum=$$\sqrt{\frac{5+\sqrt5}{10}+\frac1{4\sin^2\frac{3\pi}7}}≈0.99329$$
 * dich=Giship–7/3–giship: 108°
 * dich2=Pip–4–giship: 90°
 * dich3=Pip–5–pip: $$\frac{\pi}{7{ ≈ 25.71429°$$
 * hypervolume=$$\frac{7\sqrt{25+10\sqrt5}}{16\tan\frac{3\pi}7}≈0.68720$$
 * den=3
 * dual=Pentagonal-great heptagrammic duotegum
 * conjugate=Pentagonal-heptagonal duoprism, Pentagonal-heptagrammic duoprism, Pentagrammic-heptagonal duoprism, Pentagrammic-heptagrammic duoprism, Pentagrammic-great heptagrammic duoprism
 * convex=No
 * orientable=Yes
 * nat=Tame
 * pieces=19
 * euler=0
 * loc=12}}

Vertex coordinates
The coordinates of a pentagonal-great heptagrammic duoprism, centered at the origin and with edge length 2sin(3π/7), are given by: where j = 2, 4, 6.
 * $$\left(±\sin\frac{3\pi}7,\,-\sqrt{\frac{5+2\sqrt5}5}\sin\frac{3\pi}7,\,1,\,0\right),$$
 * $$\left(±\sin\frac{3\pi}7,\,-\sqrt{\frac{5+2\sqrt5}5}\sin\frac{3\pi}7,\,\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right)\right),$$
 * $$\left(±\frac{1+\sqrt5}2\sin\frac{3\pi}7,\,\sqrt{\frac{5-\sqrt5}{10}}\sin\frac{3\pi}7,\,1,\,0\right),$$
 * $$\left(±\frac{1+\sqrt5}2\sin\frac{3\pi}7,\,\sqrt{\frac{5-\sqrt5}{10}}\sin\frac{3\pi}7,\,\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right)\right),$$
 * $$\left(0,\,2\sqrt{\frac{5+\sqrt5}{10}}\sin\frac{3\pi}7,\,1,\,0\right),$$
 * $$\left(0,\,2\sqrt{\frac{5+\sqrt5}{10}}\sin\frac{3\pi}7,\,\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right)\right),$$