Dodecagonal-cuboctahedral duoprism

The dodecagonal-cuboctahedral duoprism or twaco is a convex uniform duoprism that consists of 12 cuboctahedral prisms, 6 square-dodecagonal duoprisms and 8 triangular-dodecagonal duoprisms.

Vertex coordinates
The vertices of a dodecagonal-cuboctahedral duoprism of edge length 1 are given by all permutations and sign changes of the last three coordinates of:
 * (±(1+$\sqrt{3+√3}$)/2, ±(1+$\sqrt{3}$)/2, 0, $\sqrt{3}$/2, $\sqrt{2}$/2)
 * (±1/2, ±(2+$\sqrt{2}$)/2, 0, $\sqrt{3}$/2, $\sqrt{2}$/2)
 * (±(2+$\sqrt{2}$)/2, ±1/2, 0, $\sqrt{3}$/2, $\sqrt{2}$/2)