Quasitruncated dodecadodecahedron

The quasitruncated dodecadodecahedron or quitdid, also called the truncated dodecadodecahedron, is a uniform polyhedron. It consists of 12 decagrams, 12 decagons, and 30 squares, with one of each type of face meeting per vertex. It can be obtained by quasicantitruncation of the small stellated dodecahedron or great dodecahedron, or equivalently by quasitruncating the vertices of a dodecadodecahedron and then adjusting the edge lengths to be all equal.

It can be alternated into the inverted snub dodecadodecahedron after equalizing edge lengths.

Vertex coordinates
A quasitruncated dodecadodecahedron of edge length 1 has vertex coordinates given by all permutations of along with all even permutations of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac32\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5}{2},\,±\frac{\sqrt5}{2}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt5}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5-1}{2}\right),$$
 * $$\left(±\frac{3+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±1\right).$$