Square-dodecahedral duoprism

The square-dodecahedral duoprism or squadoe is a convex uniform duoprism that consists of 4 dodecahedral prisms and 12 square-pentagonal duoprisms. Each vertex joins 2 dodecahedral prisms and 3 square-pentagonal duoprisms. It is a duoprism based on a square and a dodecahedron, which makes it a convex segmentoteron.

Vertex coordinates
The vertices of a square-dodecahedral duoprism of edge length 1 are given by: as well as all even permutations of the last three coordinates of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac12,\,0\right).$$

Representations
A square-dodecahedral duoprism has the following Coxeter diagrams:
 * x4o x5o3o (full symmetry)
 * x x x5o3o (dodecagonal prismatic prism)