Bidiminished rectified pentachoron

The bidiminished rectified pentachoron, antiduowedge, square-tetrahedral wedge, or bidrap, is a CRF segmentochoron (designated K-4.8 on Richard Klitzing's list). It consists of 1 tetrahedron, 2 triangular prisms, and 4 square pyramids.

It can be viewed as a segmentochoron between a square and a tetrahedron, between a triangle and a square pyramid, or between a triangular prism and a perpendicular line.

It can also be viewed as a wedge of the rectified pentachoron, formed by removing two non-adjacent vertices by cutting off triangular prismatic pyramids. As a result one octahedron cell gets cut down to an equatorial square only, while the other 4 get diminished down to square pyramids.

Vertex coordinates
The vertices of a bidiminished rectified pentachoron of edge length 1 are given by:


 * $$\left(±\frac12,\,0,\,-\frac{\sqrt2}{4},\,0\right),$$
 * $$\left(0,\,±\frac12,\,\frac{\sqrt2}{4},\,0\right),$$
 * $$\left(±\frac12,\,±\frac12,\,0,\,\frac{\sqrt{10}}{4}\right).$$