Heptagonal-dodecagonal duoprismatic prism

The heptagonal-dodecagonal duoprismatic prism or hetwip, also known as the heptagonal-dodecagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 heptagonal-dodecagonal duoprisms, 7 square-dodecagonal duoprisms, and 12 square-heptagonal duoprisms. Each vertex joins 2 square-heptagonal duoprisms, 2 square-dodecagonal duoprisms, and 1 heptagonal-dodecagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

Vertex coordinates
The vertices of a heptagonal-dodecagonal duoprismatic prism of edge length 2sin(π/7) are given by all permutations of the third and fourth coordinates of: where j = 2, 4, 6.
 * $$\left(1,\,0,\,±(1+\sqrt3)\sin\frac\pi7,\,±(1+\sqrt3)\sin\frac\pi7,\,±\sin\frac\pi7\right),$$
 * $$\left(\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right),\,±(1+\sqrt3)\sin\frac\pi7,\,±(1+\sqrt3)\sin\frac\pi7,\,±\sin\frac\pi7\right),$$
 * $$\left(1,\,0,\,±\sin\frac\pi7,\,±(2+\sqrt3)\sin\frac\pi7,\,±\sin\frac\pi7\right),$$
 * $$\left(\cos\left(\frac{j\pi}7\right),\,±\sin\left(\frac{j\pi}7\right),\,±\sin\frac\pi7,\,±(2+\sqrt3)\sin\frac\pi7,\,±\sin\frac\pi7\right),$$

Representations
A heptagonal-dodecagonal duoprismatic prism has the following Coxeter diagrams:
 * x x7o x12o (full symmetry)
 * x x7o x6x (dodecagons as dihexagons)
 * xx7oo xx12oo&#x (heptagonal-dodecagonal duoprism atop heptagonal-dodecagonal duoprism)
 * xx7oo xx6xx&#x