Ditrigonal icosahedron

The ditrigonal icosahedron, or ditti, also called the excavated dodecahedron, is a noble semi-uniform polyhedron. It consists of 20 propeller tripods, with six of each joining at a vertex. It has two lengths of edges, but it has no degrees of variance; the longer edges are (3+$\sqrt{5}$)/2 times the length of the shorter edges. The longer edges are also the edges of a great stellated dodecahedron, while the shorter edges are the edges of a dodecahedron.

All its flags are isomorphic, leading some to consider it regular. In fact, it is a pseudoregular polyhedron.