Thus new relations appear between the five regular polyhedra:
• the eight vertices of a cube are the vertices of two regular tetrahedra which build the anticube, also known as the Kepler star or stella octangula.
• the twenty vertices of the regular dodecahedron are the vertices of five regular tetrahedra ("stella icosangula");
more curiously they are also the vertices of five cubes, therefore also the vertices of ten tetrahedra building five anticubes.
five cubes 
five tetrahedra 
five anticubes 
five regular octahedra 
five regular tetrahedra 
ten tetrahedra 
two cubes 
three cubes 
five cubes 
reference:  The 75 uniform compounds of uniform polyhedra site with nice animated pictures and interesting links 
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