In this paper we find a geometric condition for the weaker principle of spatial averaging (PSA) for a class of polyhedral domains. Let ulcorner be a polyhedron in Rulcorner, n$leq$3. If all dihedral angles of ulcorner are submultiples of $pi$, then there exists a parallelopiped ulcorner generated by n linearily independent vectors {ulcorner}ulcorner in Rulcorner containing ulcorner so that solutions of $Delta$u+λu=0 in ulcorner with either the boundary condition u=0 or ∂u/∂n=0 are expressed by linear combinations of those of $Delta$u+λn=0 in ulcorner with periodic boundary condition. Moreover, if {ulcorner}ulcorner satisfies rational condition, we guarantee the weaker PSA for the domain ulcorner.