Chamfered dodecahedron

The chamfered dodecahedron is a modification of the dodecahedron that can have one edge length but has irregular faces. It has 12 pentagons and 30 hexagons as faces, and 20 order-3 vertices that can be thought of as coming from the dodecahedron as well as 60 new order-3 vertices.

The hexagonal faces have angles of $$\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505^\circ$$ on a pair of opposite vertices, and angles of $$\arccos\left(-\sqrt{\frac{5-\sqrt5}{10}}\right) ≈ 121.71747^\circ$$ on the four remaining vertices.

It can be modified such that it has a single inradius, or such that it has a single midradius or "edge radius." The latter version is called the "canonical" version.

It can also be viewed as an order-5-truncated rhombic triacontahedron, or as an icosahedrally-symmetric Goldberg polyhedron.