As was his style, Kepler could not resist sharing his unique inter-
pretation of this mathematical observation. He assigned genders to the
solids and used duality to indicate sexual compatibility. The cube and
the dodecahedron (both dominant primaries) were male and contained the
female octahedron and icosahedron (secondaries). The tetrahedron was a
hermaphrodite because it contained itself. The faces and vertices were the
sexual characteristics because that was where the solids met.