Great complex icosidodecahedral alterprism

The great complex icosidodecahedral alterprism is an exotic-combo-celled uniform polychoron that consists of 2 great icosahedra, 2 small stellated dodecahedra, 12 pentagrammic antiprisms, and 20 octahedra. The great icosahedra and small stellated dodecahedra lie in the same hyperplanes, forming great complex icosidodecahedron combo-cells. The octahedra go through the centre of the polychoron.

Vertex coordinates
The vertices of a great complex icosidodecahedral alterprism of edge length 1 are given by all even permutations of the first three coordinates of:
 * $$\Biggl(0, \pm\frac{1}{2}, \pm\frac{\sqrt{5}-1}{4}, \pm\frac{\sqrt{2\sqrt{5}-2}}{4}\Biggr)$$