The inertia tensor of a magic cube

Abstract

Magic cubes are shown to have maximally symmetric inertia tensors if they are interpreted as rigid body mass distributions. This symmetry is due to their semi-magic property where each row, column, and pillar has the same mass sum. The moment of inertia depends only on this property and the number of point masses in each row, column, and pillar. Because magic cubes do not possess detailed cubic symmetry, other scenarios that result in maximally symmetric inertia tensors are discussed.