Tetrahedron atop triangular cupola

Tetrahedron atop triangular cupola, or tetatricu, is a CRF segmentochoron (designated K-4.24 on Richard Klitzing's list). As the name suggests, it consists of a tetrahedron and a triangular cupola as bases, connected by 1 additional tetrahedron, 1 additional triangular cupola, and 6 triangular prisms.

It can be formed by diminishing a tetrahedron atop cuboctahedron segmentochoron by a triangular cupofastegium, leaving a further triangular cupola behind while removing several tetahedral and triangular prism cells. Therefore, its vertices are a subset of those of the uniform small prismatodecachoron.

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