Four icosahedra can meet at a point.
01 January 1988
What is the maximal number of nonoverlapping copies of a regular polyhedron II that can share a common vertex? The answer is shown to be 4 if II is an icosahedron or dodecahedron, and is conjectured to be 7 for an octahedron and 20 for a tetrahedron. (For a cube the answer is trivially 8.).