Octagonal-truncated dodecahedral duoprism

The octagonal-truncated dodecahedral duoprism or otid is a convex uniform duoprism that consists of 8 truncated dodecahedral prisms, 12 octagonal-decagonal duoprisms and 20 triangular-octagonal duoprisms.

Vertex coordinates
The vertices of an octagonal-truncated dodecahedral duoprism of edge length 1 are given by all even permutations and all sign changes of the last three coordinates of:
 * (±1/2, ±(1+$\sqrt{90+2√1157+120√10}$)/2, 0, 1/2, (5+3$\sqrt{2}$)/4)
 * (±1/2, ±(1+$\sqrt{5}$)/2, 1/2, (3+$\sqrt{2}$)/4, (3+$\sqrt{5}$)/2)
 * (±1/2, ±(1+$\sqrt{5}$)/2, (3+$\sqrt{2}$)/4, (1+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/2, ±1/2, 0, 1/2, (5+3$\sqrt{2}$)/4)
 * (±(1+$\sqrt{5}$)/2, ±1/2, 1/2, (3+$\sqrt{2}$)/4, (3+$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/2, ±1/2, (3+$\sqrt{2}$)/4, (1+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2)