Fourth noble pterogrammic hexecontahedron

The  is a noble polyhedron. Its 60 congruent faces are mirror-symmetric hexagons meeting at congruent order-6 vertices. It is a faceting of a semi-uniform truncated dodecahedron hull.

The ratio between the shortest and longest edges is 1:$$\sqrt{\frac{1+\sqrt5+\sqrt{2\left(1+\sqrt5\right)}}{2}}$$ ≈ 1:1.70002.

Vertex coordinates
The vertex coordinates of a are given by all even permutations of:
 * $$\left(0,\,\pm\left(\sqrt{4+2\sqrt5}-\sqrt{3+\sqrt5}\right),\,\pm\left(\sqrt2+\sqrt{1+\sqrt5}\right)\right),$$
 * $$\left(\pm\left(\sqrt{3+\sqrt5}-\sqrt{1+\sqrt5}\right),\,±\sqrt2,\,\pm\sqrt{4+2\sqrt5}\right),$$
 * $$\left(\pm\left(\sqrt{4+2\sqrt5}-\sqrt2\right),\,\pm\sqrt{1+\sqrt5},\,\pm\sqrt{3+\sqrt5}\right).$$

Related polyhedra
It shares its vertex coordinates with the fourth noble unihexagrammic hexecontahedron.