Octagonal-icosidodecahedral duoprism

The octagonal-icosidodecahedral duoprism or oid is a convex uniform duoprism that consists of 8 icosidodecahedral prisms, 12 pentagonal-octagonal duoprisms and 20 triangular-octagonal duoprisms.

Vertex coordinates
The vertices of an octagonal-icosidodecahedral duoprism of edge length 1 are given by all permutations and sign changes of the last three coordinates of: as well as all even permutations and all sign changes of the last three coordinates of:
 * (±1/2, ±(1+$\sqrt{10+2√7+2√10}$)/2, 0, 0, (1+$\sqrt{2}$)/2)
 * (±(1+$\sqrt{5}$)/2, ±1/2, 0, 0, (1+$\sqrt{2}$)/2)
 * (±1/2, ±(1+$\sqrt{5}$)/2, ±1/2, ±(1+$\sqrt{2}$)/4, ±(3+$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/2, ±1/2, ±1/2, ±(1+$\sqrt{2}$)/4, ±(3+$\sqrt{5}$)/4)