Triangular cupofastegium

The triangular cupofastegium, or tricuf, also called the triangular orthobicupolic ring, is a CRF segmentochoron (designated K-4.25 on Richard Klitzing's list). It consists of 1+3 triangular prisms, 3 tetrahedra, and 2 triangular cupolas.

The triangular cupofastegium can be thought of as a wedge of the small prismatodecachoron, or as a part of the larger segmentochoron tetrahedron atop cuboctahedron, with the remainder forming the segmentochoron tetrahedron atop triangular cupola.

Vertex coordinates
The vertices of a triangular cupofastegium with edge length 1 are given by:
 * $$\left(±\frac12,\,–-\frac{\sqrt3}{6},\,±\frac12,\,\frac{\sqrt{15}}{6}\right),$$
 * $$\left(0,\,\frac{\sqrt3}{3},\,±\frac12,\,\frac{\sqrt{15}}{6}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt3}{2},\,0,\,0\right),$$
 * $$\left(±1,\,0,\,0,\,0\right).$$

Representations
A triangular cupofastegium has the following Coxeter diagrams:


 * ox xx3xo&#x (full symmetry)
 * xxx3oxo&#x (A2 symmetry only, seen with triangle atop triangular cupola)