Decagonal-dodecagonal duoprismatic prism

The decagonal-dodecagonal duoprismatic prism or datwip, also known as the decagonal-dodecagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 decagonal-dodecagonal duoprisms, 10 square-dodecagonal duoprisms and 12 square-decagonal duoprisms. Each vertex joins 2 square-decagonal duoprisms, 2 square-dodecagonal duoprisms, and 1 decagonal-dodecagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

This polyteron can be alternated into a pentagonal-hexagonal duoantiprismatic antiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a pentagonal-hexagonal prismatic prismantiprismoid, which is also nonuniform.

Vertex coordinates
The vertices of a decagonal-dodecagonal duoprismatic prism of edge length 1 are given by all permutations of the third and fourth coordinates of:
 * $$\left(0,\,±\frac{1+\sqrt5}2,\,±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,±\frac12\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,±\frac12\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}2,\,±\frac12,\,±\frac{2+\sqrt3}2,\,±\frac12\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}8},\,±\frac{3+\sqrt5}4,\,±\frac12,\,±\frac{2+\sqrt3}2,\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}2,\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt3}2,\,±\frac12\right).$$

Representations
A decagonal-dodecagonal duoprismatic prism has the following Coxeter diagrams:
 * x x10o x12o (full symmetry)
 * x x5x x12o (decagons as dipentagons)
 * x x10o x6x (dodecagons as dihexagons)
 * x x5x x6x
 * xx10oo xx12oo&#x (decagonal-hendecagonal duoprism atop decagonal-hendecagonal duoprism)
 * xx5xx xx12oo&#x
 * xx10oo xx6xx&#x
 * xx5xx xx6xx&#x