Icositetrachoric antiprism

The icositetrachoric antiprism or icoap is a convex scaliform polyteron that consists of 2 icositetrachora, 48 octahedral pyramids and 192 pentachora.

Vertex coordinates
The vertices of an icositetrachoric antiprism of edge length 1 are given by all permutations and sign changes excluding the last coordinate of:
 * (0, 0, 0, 1, –$\sqrt{3+√2}$/2),
 * (1/2, 1/2, 1/2, 1/2, –$\sqrt{{{radic|2}}–1}$/2),
 * (0, 0, $\sqrt{{{radic|2}}–1}$/2, $\sqrt{2}$/2, $\sqrt{2}$/2).