Decagonal trioprism

The decagonal trioprism or dettip is a convex uniform trioprism that consists of 30 decagonal duoprismatic prisms as facets. 6 facets join at each vertex.

This polypeton can be alternated into a pentagonal trioantiprism, although it cannot be made uniform.

Vertex coordinates
The vertices of a decagonal trioprism of edge length 1 are given by:
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,0,\,±\frac{1+\sqrt5}{2},\,0,\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,0,\,±\frac{1+\sqrt5}{2},\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,0,\,±\frac{1+\sqrt5}{2},\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,0,\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,0,\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(0,\,±\frac{1+\sqrt5}{2},\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,0,\,±\frac{1+\sqrt5}{2},\,0,\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,0,\,±\frac{1+\sqrt5}{2},\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,0,\,±\frac{1+\sqrt5}{2},\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,0,\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,0,\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,0,\,±\frac{1+\sqrt5}{2},\,0,\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,0,\,±\frac{1+\sqrt5}{2},\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,0,\,±\frac{1+\sqrt5}{2},\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,0,\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4},\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,0,\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,±\sqrt{\frac{5+\sqrt5}{8}},\,±\frac{3+\sqrt5}{4}\right),$$
 * $$\left(±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12,\,±\frac{\sqrt{5+2\sqrt5}}{2},\,±\frac12\right).$$