Disnub icosidodecahedron (near-miss)

This non-convex isogonal polyhedron is a faceting of a slightly deformed great snub icosidodecahedron.

The name disnub icosidodecahedron means that this polyhedron has two types of snub triangles.

It has 5 different edge lengths: 1, ~1.00549, ~1.0358, ~1.04804, ~1.04932.

Faces:

Its dual is an isohedral octagrammic hexecontahedron