A magnetic monopole is placed at the center of a ball whose surface S-2 is
tiled by the symmetry group, Gamma, of a regular solid. The quantum mechani
cs on the two-dimensional quotient S-2/Gamma is developed and the monopole
charge is found to be quantized in an expected manner. The heat-kernel and
zeta -functions are evaluated and the Casimir energy is computed. Numerical
approaches to the calculation of the derivative of the Barnes zeta -functi
on are presented. (C) 2001 American Institute of Physics.