Dodecagonal-snub cubic duoprism

The dodecagonal-snub cubic duoprism or twasnic is a convex uniform duoprism that consists of 12 snub cubic prisms, 6 square-dodecagonal duoprisms, and 32 triangular-dodecagonal duoprisms of two kinds. Each vertex joins 2 snub cubic prisms, 4 triangular-dodecagonal duoprisms, and 1 square-dodecagonal duoprism.

Vertex coordinates
The vertices of a dodecagonal-snub cubic duoprism of edge length 1 are given by by all even permutations with an even number of sign changes, plus all odd permutations with an odd amount of sign changes, of the last three coordinates of: where
 * $$\left(±\frac{1+\sqrt3}2,\,±\frac{1+\sqrt3}2,\,c_1,\,c_2,\,c_3\right),$$
 * $$\left(±\frac12,\,±\frac{2+\sqrt3}2,\,c_1,\,c_2,\,c_3\right),$$
 * $$\left(±\frac{2+\sqrt3}2,\,±\frac12,\,c_1,\,c_2,\,c_3\right),$$
 * $$c_1=\sqrt{\frac{1}{12}\left(4-\sqrt[3]{17+3\sqrt{33}}-\sqrt[3]{17-3\sqrt{33}}\right)},$$
 * $$c_2=\sqrt{\frac{1}{12}\left(2+\sqrt[3]{17+3\sqrt{33}}+\sqrt[3]{17-3\sqrt{33}}\right)},$$
 * $$c_3=\sqrt{\frac{1}{12}\left(4+\sqrt[3]{199+3\sqrt{33}}+\sqrt[3]{199-3\sqrt{33}}\right)}.$$