Polyhedrons are solids with faces formed from plane polygons. The intersections of faces are called edges and the points where three or more edges meet are called vertices. If the faces are congruent regular polygons and the polyhedral angles are congruent, the polyhedron is regular. There are only five regular polyhedra, known to mathematicians as the Platonic Solids. Their vital statistics are: tetrahedron, 4 equilateral triangles; hexahedron, aka cube, 6 squares; octahedron, 8 equilateral triangles; dodecahedron, 12 pentagons; and icosahedron, 20 equilateral triangles.

You can find out a whole lot more about the underlying mathematics of our interlocking cube polyhedron by checking out "Symmetry Orbits," by Hugo F. Verheyen, published by Birkhauser Boston, 1996.

Special thanks to Prof. Michael Gass, St. John's University and, of course, Fr. Magnus Wenninger.