Multidimensional geometric shaping has been shown to outperform uniform quadrature amplitude modulation (QAM) in optical communication systems but the complexity of symbol decision and bit mapping can often be significant as dimensionality increases. In this paper, a low-complexity geometric shaping method based on multidimensional lattices is investigated both in experiments and simulations. The modulation formats designed based on this method are called Voronoi constellations (VCs) and we study them in 8, 16, and 32 dimensions.