First noble ditrapezoidal 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 icosahedron hull.

The ratio between the shortest and longest edges is 1:$$\frac{\sqrt{5+\sqrt5}}{2}$$ ≈ 1:1.34500.

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, fourth kisombreroidal hexecontahedron, and second kisombreroidal hexecontahedron.
 * $$\left(\pm\left(5-\sqrt5\right),\,\pm\left(3-\sqrt5\right),\,0\right)$$,
 * $$\left(\pm\left(3-\sqrt5\right),\,\pm\left(2\sqrt5-2\right),\,\pm\left(\sqrt5-1\right)\right)$$,
 * $$\left(\pm2,\,\pm2,\,\pm\left(2\sqrt5-4\right)\right)$$.