Triangular-dodecagonal duoprism

The triangular-dodecagonal duoprism or titwadip, also known as the 3-12 duoprism, is a uniform duoprism that consists of 3 dodecagonal prisms and 12 triangular prisms, with two of each joining at each vertex. It can also be seen as a convex segmentochoron, being a dodecagon atop a dodecagonal prism.

This polychoron can be subsymmetrically faceted into a 12-4 step prism, although it cannot be made uniform.

Vertex coordinates
The vertices of a triangular-dodecagonal duoprism of edge length 1, centered at the origin, are given by:
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac{1+\sqrt3}{2},\,±\frac{1+\sqrt3}{2}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,±\frac{2+\sqrt3}{2}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac{2+\sqrt3}{2},\,±\frac12\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac{2+\sqrt3}{2},\,±\frac12\right).$$