For examples, see the 59 stellations of the icosahedron . The term compound refers to an interpenetrating set of identical or related polyhedra arranged in a manner which has some overall polyhedral symmetry . Names for many of the nonconvex uniform polyhedra and their duals have been in flux. The two books by Wenninger which illustrate these polyhedra list names largely due to Norman Johnson. I have incorporated his most recent naming suggestions at the time of this writing.
Crystallographers use a slightly different set of names for certain crystal forms .
For a systematic method of naming a great many interesting symmetric polyhedra, I like John Conway's notation . Name this , this , this , and this . Hecato means 100. Think of the other two ways to assemble those same 100 triangles into a convex polyhedron. This and this .