Ditrigonary dodecadodecahedron

The ditrigonary dodecadodecahedron, or ditdid, is a quasiregular uniform polyhedron. It consists of 12 pentagons and 12 pentagrams, with three of each joining at a vertex.

It is a faceting of the small ditrigonary icosidodecahedron, using its 12 pentagrams along with 12 additional pentagons.

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