Third noble stellation of rhombic triacontahedron

The  is a noble polyhedron. Its 30 congruent faces are rectangular-symmetric octagrams meeting at congruent order-4 vertices. It is a faceting of a uniform small rhombicosidodecahedron hull.

The ratio between the shortest and longest edges is 1:$$\sqrt{\frac{5+2\sqrt5}{5}}$$ ≈ 1:1.37638.

Vertex coordinates
A, centered at the origin, has vertex coordinates given by all permutations of along with all even permutations of Other noble polyhedra that can have these coordinates are the Crennell number 4 stellation of the icosahedron and the third noble unihexagrammic hexecontahedron.
 * $$\left(\pm\frac{2+\sqrt5}{2},\,\pm\frac12,\,\pm\frac12\right),$$
 * $$\left(0,\,\pm\frac{3+\sqrt5}{4},\,\pm\frac{5+\sqrt5}{4}\right),$$
 * $$\left(\pm\frac{1+\sqrt5}{4},\,\pm\frac{1+\sqrt5}{2},\,\pm\frac{3+\sqrt5}{4}\right).$$