First noble stellation of rhombic triacontahedron

The  is a noble polyhedron. Its 30 congruent faces are rectangular-symmetric octagons meeting at congruent order-4 vertices. It is a faceting of a semi-uniform truncated icosahedron hull.

The ratio between the shortest and longest edges is 1:$$\sqrt{5+2\sqrt5}$$ ≈ 1:3.07768.

Vertex coordinates
A, centered at the origin, has vertex coordinates given by all permutations of: plus all even permutations of: These are the same coordinates as the truncated great dodecahedron.
 * $$\left(\pm\frac{\sqrt5-1}{4},\,\pm\frac{3+\sqrt5}{4},\,\pm\frac{3+\sqrt5}{4}\right),$$
 * $$\left(0,\,\pm\frac12,\,\pm\frac{5+\sqrt5}{4}\right),$$
 * $$\left(\pm\frac12,\,\pm\frac{1+\sqrt5}{4},\,\pm\frac{1+\sqrt5}{2}\right).$$