Triangular cupofastegium

The triangular cupofastegium, or tricuf, also sometimes called the triangular orthobicupolic ring, is a CRF segmentochoron (designated K-4.25 on Richard Klitzing's list). It consists of 1+3 triangular prism, 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:
 * (±1/2, –$\sqrt{2}$/6, ±1/2, $\sqrt{2}$/6)
 * (0, $\sqrt{2}$/3, ±1/2, $\sqrt{2}$)/6)
 * (±1/2, ±$\sqrt{2}$/2, 0, 0)
 * (±1, 0, 0, 0)

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)