Great quasitruncated icosidodecahedron

The great quasitruncated icosidodecahedron or gaquatid, also called the great truncated icosidodecahedron, is a uniform polyhedron. It consists of 12 decagrams, 20 hexagons, and 30 squares, with one of each type of face meeting per vertex. It can be obtained by quasicantitruncation of the great stellated dodecahedron or great icosahedron, or equivalently by quasitruncating the vertices of a great icosidodecahedron and then adjusting the edge lengths to be all equal.

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

Vertex coordinates
A great quasitruncated icosidodecahedron of edge length 1 has vertex coordinates given by all permutations of along with all even permutations of:
 * $$\left(±\frac12,\,±\frac12,\,±\frac{2\sqrt5-3}{2}\right),$$
 * $$\left(±\frac12,\,±\frac{\sqrt5-2}{2},\,±\frac{4-\sqrt5}{2}\right),$$
 * $$\left(±1,\,±\frac{3-\sqrt5}{4},\,±\frac{7-3\sqrt5}{4}\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±3\frac{\sqrt5-1}{4},\,±\frac{3-\sqrt5}{2}\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{3\sqrt5-5}{4},\,±\frac{5-\sqrt5}{4}\right).$$