Dodecateric prism

The dodecateric prism or dotip is a prismatic uniform polypeton that consists of 2 dodecatera and 12 rectified pentachoric prisms as facets. Each vertex joins 1 dodecateron and 6 rectified pentachoric prisms. As the name suggests, it is a prism based on the dodecateron, which also makes it a convex segmentopeton.

The dodecateric prism can be vertex-inscribed into the pentacontatetrapeton.

Vertex coordinates
The vertices of a dodecateric prism of edge length 1 are given by:
 * $$±\left(\frac{\sqrt{15}}{10},\,-\frac{3\sqrt{10}}{20},\,-\frac{\sqrt6}{4},\,0,\,0,\,±\frac12\right),$$
 * $$±\left(\frac{\sqrt{15}}{10},\,-\frac{3\sqrt{10}}{20},\,\frac{\sqrt6}{12},\,-\frac{\sqrt3}{3},\,0,\,±\frac12\right),$$
 * $$±\left(-\frac{\sqrt{15}}{10},\,-\frac{3\sqrt{10}}{20},\,\frac{\sqrt6}{12},\,\frac{\sqrt3}{6},\,±\frac12,\,±\frac12\right),$$
 * $$±\left(\frac{\sqrt{15}}{10},\,\frac{\sqrt{10}}{10},\,\frac{\sqrt6}{6},\,\frac{\sqrt3}{3},\,0,\,±\frac12\right),$$
 * $$±\left(\frac{\sqrt{15}}{10},\,\frac{\sqrt{10}}{10},\,-\frac{\sqrt6}{6},\,-\frac{\sqrt3}{3},\,0,\,±\frac12\right),$$
 * $$±\left(\frac{\sqrt{15}}{10},\,\frac{\sqrt{10}}{10},\,\frac{\sqrt6}{6},\,-\frac{\sqrt3}{6},\,±\frac12,\,±\frac12\right),$$
 * $$\left(\frac{\sqrt{15}}{10},\,\frac{\sqrt{10}}{10},\,-\frac{\sqrt6}{6},\,\frac{\sqrt3}{6},\,±\frac12,\,±\frac12\right).$$

Representations
A dodecateric prism has the following Coxeter diagrams:


 * x o3o3x3o3o (full symmetry)
 * oo3oo3xx3oo3oo&#x (dodecateron atop dodecateron)
 * xx oo3xo3ox3oo&#x (rectified pentachoric prism atop inverted rectified pentachoric prism)