Ditrigonary dodecadodecahedron

The ditrigonal 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 ditrigonal icosidodecahedron, using its 12 pentagrams along with 12 additional pentagons.