Octagonal-truncated icosahedral duoprism

The octagonal-truncated icosahedral duoprism or oti is a convex uniform duoprism that consists of 8 truncated icosahedral prisms, 20 hexagonal-octagonal duoprisms and 12 pentagonal-octagonal duoprisms.

Vertex coordinates
The vertices of an octagonal-truncated icosahedral duoprism of edge length 1 are given by all even permutations and all sign changes of the last three coordinates of:
 * (±1/2, ±(1+$\sqrt{74+2√437+72√10}$)/2, 0, 1/2, (3+3$\sqrt{2}$)/4)
 * (±1/2, ±(1+$\sqrt{5}$)/2, 1/2, (5+$\sqrt{2}$)/4, (1+$\sqrt{5}$)/2)
 * (±1/2, ±(1+$\sqrt{5}$)/2, (1+$\sqrt{2}$)/4, 1, (2+$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/2, ±1/2, 0, 1/2, (3+3$\sqrt{2}$)/4)
 * (±(1+$\sqrt{5}$)/2, ±1/2, 1/2, (5+$\sqrt{2}$)/4, (1+$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/2, ±1/2, (1+$\sqrt{2}$)/4, 1, (2+$\sqrt{5}$)/2)