compound polyhedra

Interpenetrating two or more polyhedra gives also nice solids. Many combinations and dispositions may be imagined: identical polyhedra, two dual polyhedra, ...
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
(vertices of a regular dodecahedron)

five tetrahedra
(vertices of a regular dodecahedron)

five anticubes
(vertices of a regular dodecahedron)

five regular octahedra
(vertices of an icosidodecahedron)

five regular tetrahedra
("stella icosangula")

ten tetrahedra
(five anticubes)

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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convex polyhedra - non convex polyhedra - interesting polyhedra - related subjects March 1999
updated 10-11-2003