Ede (1958) enumerates 13 basic series of stellations of the rhombic triacontahedron, the total number of which is extremely large. Pawley (1973) gave a set of restrictions upon which a complete enumeration of stellations can be achieved (Wenninger 1983, p. 36). Messer (1995) describes 227 stellations (including the original solid in the count as usual), some of which are illustrated above.
The beautiful figures above show the results of starting with the interior of the cube 5-compound and including successively larger
portions of the space enclosed by its stellations (M. Trott, pers. comm., Feb. 10,
Ede, J. D. "Rhombic Triacontahedra." Math. Gaz.42, 98-100, 1958.Kabai, S. Mathematical Graphics
I: Lessons in Computer Graphics Using Mathematica. Püspökladány,
Hungary: Uniconstant, p. 185, 2002.Messer, P. W. "Stellations
of the Rhombic Triacontahedron and Beyond." Structural Topology21,
25-46, 1995.Pawley, G. S. "The 227 Triacontahedra." Geom.
Dedicata4, 221-232, 1975.Webb, R. "Enumeration of Stellations."
R. "Stellation of Rhombic Triacontahedron." http://www.software3d.com/RTC_Hollow.html.Wenninger,
M. J. Dual
Models. Cambridge, England: Cambridge University Press, p. 36, 1983.