Decachoric prism

The decachoric prism or decap is a prismatic uniform polyteron that consists of 2 decachora and 10 truncated tetrahedral prisms. 1 decachoron and 4 truncated tetrahedral prisms join at each vertex. As the name suggests, it can be obtained as a prism based on the decachoron, which also makes it a convex segmentoteron.

Vertex coordinates
The vertices of a decachoric prism of edge length 1 are given by:
 * $$±\left(0,\,\frac{\sqrt6}{3},\,\frac{2\sqrt3}{3},\,0,\,±\frac12\right),$$
 * $$±\left(0,\,\frac{\sqrt6}{3},\,-\frac{\sqrt3}{3},\,±1,\,±\frac12\right),$$
 * $$±\left(\frac{\sqrt{10}}{4},\,\frac{\sqrt6}{12},\,\frac{2\sqrt3}{3},\,0,\,±\frac12\right),$$
 * $$±\left(\frac{\sqrt{10}}{4},\,\frac{\sqrt6}{12},\,-\frac{\sqrt3}{3},\,±1,\,±\frac12\right),$$
 * $$±\left(\frac{\sqrt{10}}{4},\,\frac{5\sqrt6}{12},\,\frac{\sqrt3}{3},\,0,\,±\frac12\right),$$
 * $$±\left(\frac{\sqrt{10}}{4},\,\frac{5\sqrt6}{12},\,-\frac{\sqrt3}{6},\,±\frac12,\,±\frac12\right),$$
 * $$±\left(\frac{\sqrt{10}}{4},\,-\frac{\sqrt6}{4},\,0,\,±1,\,±\frac12\right),$$
 * $$±\left(\frac{\sqrt{10}}{4},\,-\frac{\sqrt6}{4},\,±\frac{\sqrt3}{2},\,±\frac12,\,±\frac12\right).$$