Square cupofastegium

The square cupofastegium, or squicuf, also sometimes called the square orthobicupolic ring, is a CRF segmentochoron (designated K-4.73 on Richard Klitzing's list). It consists of 1 cube, 4 tetrahedra, 4 triangular prisms, and 2 square cupolas.

It has two representations as a segmentochoron: square atop square cupola or cube atop octagon.

The square cupofastegium can be obtained as a cap of the small disprismatotesseractihexadecachoron from one of the 24 cubes with square prism symmetry.

Vertex coordinates
The vertices of a square cupofastegium with edge length 1 are given by:
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,\frac12\right),$$
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}{2},\,0,\,0\right),$$
 * $$\left(±\frac{1+\sqrt2}{2},\,±\frac12,\,0,\,0\right).$$

Representations
A square cupofastegium has the following Coxeter diagrams:


 * ox xx4xo&#x (full symmetry)
 * xxx4oxo&#x (BC2 symmetry only, seen with square atop square cupola)