Fourth kisombreroidal hexecontahedron

The  is a noble polyhedron. Its 60 congruent faces are irregular pentagons meeting at congruent order-5 vertices. It is a faceting of a semi-uniform truncated icosahedron hull.

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

Vertex coordinates
The coordinates of a are all even permutations of: plus all permutations of These are the same coordinates as the crossed kignathogrammic hexecontahedron, first kipentagrammic hexecontahedron, first noble ditrapezoidal hexecontahedron, and second kisombreroidal hexecontahedron.
 * $$\left(\pm\left(5-\sqrt5\right),\,\pm\left(3-\sqrt5\right),\,0\right)$$,
 * $$\left(\pm\left(3-\sqrt5\right),\,\pm\left(2\sqrt5-2\right),\,\pm\left(\sqrt5-1\right)\right)$$,
 * $$\left(\pm2,\,\pm2,\,\pm\left(2\sqrt5-4\right)\right)$$.