Small disnub dodecahedron

The small disnub dodecahedron, sadsid, or compound of twelve pentagrammic antiprisms is a uniform polyhedron compound. It consists of 120 triangles and 24 pentagrams (which fall in pairs into the same planes combining into 12 stellated decagrams), with one pentagram and three triangles joining at a vertex.

It can be formed by combining the two chiral forms of the small snub dodecahedron.

Its quotient prismatic equivalent is the pentagrammic antiprismatic dodecadakoorthowedge, which is fourteen-dimensional.

Vertex coordinates
The vertices of a small disnub dodecahedron of edge length 1 are given by all even permutations of:
 * $$\left(\pm\sqrt{\frac{\sqrt5+\sqrt{5(\sqrt5-2)}}{20}},\,\pm\sqrt{\frac{5-2\sqrt5}{20}},\,\pm\sqrt{\frac{5+\sqrt5-2\sqrt{10(\sqrt5-1)}}{40}}\right),$$
 * $$\left(\pm\sqrt{\frac{3\sqrt5-5}{40}},\,\pm\sqrt{\frac{5-\sqrt5}{10}},\,\pm\frac{\sqrt{5\sqrt5}}{10}\right),$$
 * $$\left(\pm\sqrt{\frac{2\sqrt5+\sqrt{10(\sqrt5-1)}}{20}},\,\pm\sqrt{\frac{5-2\sqrt5}{20}},\,\pm\sqrt{\frac{5+\sqrt5+2\sqrt{10(\sqrt5-1)}}{40}}\right),$$
 * $$\left(\pm\sqrt{\frac{\sqrt5-\sqrt{5(\sqrt5-2)}}{20}},\,\pm\sqrt{\frac{5+\sqrt5}{40}},\,\pm\sqrt{\frac{5-\sqrt5+2\sqrt{15(\sqrt5-2)}}{20}}\right),$$
 * $$\left(\sqrt{\frac{\sqrt5+2\sqrt{5(\sqrt5-2)}}{20}},\,\pm\sqrt{\frac{5+\sqrt5}{40}},\,\pm\sqrt{\frac{5-\sqrt5-2\sqrt{5(\sqrt5-2)}}{20}}\right).$$