We examine basis functions on momentum space for the three-dimensional Euclidean Snyder algebra. We argue that the momentum space is isomorphic to the SO(3) group manifold, and that the basis functions span either one of two Hilbert spaces. This implies the existence of two distinct lattice structures of space. Continuous rotations and translations are unitarily implementable on these lattices. (C) 2011 Elsevier B.V. All rights reserved.