Small icosicosidodecahedron
In geometry, the small icosicosidodecahedron is a nonconvex uniform polyhedron, indexed as U31.
It shares its vertex arrangement with the great stellated truncated dodecahedron. It additionally shares its edges with the small ditrigonal dodecicosidodecahedron (having the triangular and pentagrammic faces in common) and the small dodecicosahedron (having the hexagonal faces in common).
...
Wikipedia