Noble pentagrammic icositetrahedron

The noble faceting of the truncated cube, or the noble pentagrammic icositetrahedron, is a noble polyhedron. Its 24 congruent faces are mirror-symmetric pentagrams meeting at congruent order-5 vertices.

The ratio between the longest and shortest edges is 1:$$\sqrt{\frac{2+\sqrt2}{2}}$$ ≈ 1:1.30656.