This is a dodecahedron with faces replace by inward-pointing pyramids. I've been calling this transfrom 'anti-stellate' but I've no idea if that's the right term. The OpenSCAD was output from my polyhedra generator and tweaked. The holes are not part of the ideal polyhedron.

I think its same as Hugel's polyhedron which is one of the polyhedron included in David McCooeys collection. http://kitwallace.co.uk/3d/solid-index.xq#Hugel