compound polyhedra

Interpenetrating two or more polyhedra with same center gives also nice solids. Many combinations and dispositions may be imagined with identical polyhedra, two dual polyhedra, ...
The dual of a compound is the compound of the duals of the components.

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

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