Square-snub cubic duoprism

The square-snub cubic duoprism or squasnic is a convex uniform duoprism that consists of 4 snub cubic prisms, 6 tesseracts and 32 triangular-square duoprisms of two kinds. Each vertex joins 2 snub cubic prisms, 4 triangular-square duoprisms, and 1 tesseract. It is a duoprism based on a square and a snub cube, which makes it a convex segmentoteron.

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