The above polyhedron was first described in Professor Bonnie Stewart's "

The minimal non-self-intersecting case can be improved upon if we permit self-intersection. Dr Richard Klitzing has studied the facets of the small ditrigonal icosidodecahedron amongst which was the above 9-faced figure. Dr Klitzing informs me that he has to date only studied facets with a three-fold or five-fold symmetry, so this result may still be improved upon.

The full results of Dr Klitzing's work on faceting a number of the uniform polyhedra are hosted by Ulrich Mikloweit here.