An accurate variational computation is carried out for a particle in a regular-tetrahedral box, a problem for which the Schrodinger equation cannot be solved in closed form. The ground-state energy is approximated by E-0 = 18.15h(2/)mV(2/3), where V is the volume of the tetrahedron. A conjecture on the energies of particles in other regular polyhedra is proposed. (C) 2010 Elsevier B.V. All rights reserved.