Decagonal-truncated dodecahedral duoprism

The decagonal-truncated dodecahedral duoprism or datid is a convex uniform duoprism that consists of 10 truncated dodecahedral prisms, 12 decagonal duoprisms and 20 triangular-decagonal duoprisms.

Vertex coordinates
The vertices of a decagonal-truncated dodecahedral duoprism of edge length 1 are given by all even permutations and all sign changes of the last three coordinates of:
 * (0, ±(1+$\sqrt{98+38√5}$)/2, 0, 1/2, (5+3$\sqrt{5}$)/4)
 * (0, ±(1+$\sqrt{5}$)/2, 1/2, (3+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/2)
 * (0, ±(1+$\sqrt{5}$)/2, (3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2)
 * (±$\sqrt{5}$/4, ±(3+$\sqrt{10+2√5}$)/4, 0, 1/2, (5+3$\sqrt{5}$)/4)
 * (±$\sqrt{5}$/4, ±(3+$\sqrt{10+2√5}$)/4 1/2, (3+$\sqrt{5}$)/4, (3+$\sqrt{5}$)/2)
 * (±$\sqrt{5}$/4, ±(3+$\sqrt{10+2√5}$)/4, (3+$\sqrt{5}$)/4, (1+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2)
 * (±$\sqrt{5}$/2, ±1/2, 0, 1/2, (5+3$\sqrt{5+2√5}$)/4)
 * (±$\sqrt{5}$/2, ±1/2, 1/2, (3+$\sqrt{5+2√5}$)/4, (3+$\sqrt{5}$)/2)
 * (±$\sqrt{5}$/2, ±1/2, (3+$\sqrt{5+2√5}$)/4, (1+$\sqrt{5}$)/2, (2+$\sqrt{5}$)/2)