Augmented rectified pentachoron

The augmented rectified pentachoron, or aurap, is a CRF polychoron (also Blind polytope). It has 1+4+4 regular tetrahedra and 4 regular octahedra as cells. It can be constructed by augmenting an octahedral cell of the rectified pentachoron with an octahedral pyramid.

Vertex coordinates
The vertices of an augmented rectified pentachoron of edge length 1 are given by:
 * $$\left(-\frac{3\sqrt{10}}{20},\,-\frac{\sqrt6}{4},\,0,\,0\right),$$
 * $$\left(-\frac{3\sqrt{10}}{20},\,\frac{\sqrt6}{12},\,-\frac{\sqrt3}{3},\,0\right),$$
 * $$\left(-\frac{3\sqrt{10}}{20},\,\frac{\sqrt6}{12},\,\frac{\sqrt3}{6},\,±\frac12\right),$$
 * $$\left(\frac{\sqrt{10}}{10},\,\frac{\sqrt6}{6},\,\frac{\sqrt3}{3},\,0\right),$$
 * $$\left(\frac{\sqrt{10}}{10},\,-\frac{\sqrt6}{6},\,-\frac{\sqrt3}{3},\,0\right),$$
 * $$\left(\frac{\sqrt{10}}{10},\,\frac{\sqrt6}{6},\,-\frac{\sqrt3}{6},\,±\frac12\right),$$
 * $$\left(\frac{\sqrt{10}}{10},\,-\frac{\sqrt6}{6},\,\frac{\sqrt3}{6},\,±\frac12\right),$$
 * $$\left(\frac{5\sqrt2+\sqrt{10}}{10},\,0,\,0,\,0\right).$$