These twenty great icosahedra were excavated from the faces of a central icosahedron, which is concealed in the figure’s center. These excavations exceed the limits of the central icosahedron, resulting in each great icosahedron protruding in a direction opposite that of the face from which it is excavated. In a certain sense, then, the figure above has negative volume.

To make this, I used software called Stella 4d: Polyhedron Navigator. It can be researched, bought, or tried for free here.

Also, here is the dual of the polyhedral cluster above, made with the same program.