Octagonal-snub cubic duoprism

The octagonal-snub cubic duoprism or osnic is a convex uniform duoprism that consists of 8 snub cubic prisms, 6 square-octagonal duoprisms, and 32 triangular-octagonal duoprisms of two kinds. Each vertex joins 2 snub cubic prisms, 4 triangular-octagonal duoprisms, and 1 square-octagonal duoprism.

Vertex coordinates
The vertices of a octagonal-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
 * $$\left(±\frac12,\,±\frac{1+\sqrt2}2,\,c_1,\,c_2,\,c_3\right),$$
 * $$\left(±\frac{1+\sqrt2}2,\,±\frac12,\,c_1,\,c_2,\,c_3\right),$$
 * $$c_1=\sqrt{\frac{1}{12}\left(4-\sqrt[3]{17+3\sqrt{33}}-\sqrt[3]{17-3\sqrt{33}}\right)},$$
 * $$c_2=\sqrt{\frac{1}{12}\left(2+\sqrt[3]{17+3\sqrt{33}}+\sqrt[3]{17-3\sqrt{33}}\right)},$$
 * $$c_3=\sqrt{\frac{1}{12}\left(4+\sqrt[3]{199+3\sqrt{33}}+\sqrt[3]{199-3\sqrt{33}}\right)}.$$