Great icosidodecahedron

The great icosidodecahedron or gid is a quasiregular uniform polyhedron. It consists of 20 equilateral triangles and 12 pentagrams, with two of each joining at a vertex. It can be derived as a rectified great stellated dodecahedron or great icosahedron.

Vertex coordinates
A great icosidodecahedron of side length 1 has vertex coordinates given by all permutations of and even permutations of
 * $$\left(±\frac{\sqrt5-1}{2},\,0,\,0\right),$$
 * $$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac12\right).$$

The first set of vertices corresponds to a scaled octahedron which can be inscribed into the icosidodecahedron.

Related polyhedra
The great icosidodecahedron is the colonel of a three-member regiment that also includes the great icosihemidodecahedron and great dodecahemidodecahedron.