First noble kisombreroidal icositetrahedron

The first noble kisombreroidal icositetrahedron is a self-dual noble polyhedron. Its 24 congruent faces are irregular pentagons meeting at congruent order-5 vertices. It is a faceting of an non-uniform snub cubic hull, the alternation of cotco's hull.

The ratio between the longest and shortest edges is $$1:1+\sqrt2$$ ≈ 1:2.41421.