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Room acoustic simulation using digital waveguide modeling requires three-dimensional waveguide meshes in order to represent fully the acoustic properties of the space. This paper presents a systematic analysis of four mesh topologies suggested in the literature: rectilinear, tetrahedral, cubic close-packed and octahedral. These mesh structures are compared from the standpoint of computational efficiency, bearing in mind specific issues that are important for room acoustic simulation. Each mesh topology offers a different compromise between spatial resolution, bandwidth, dispersion characteristics (including suitability for the application of dispersion-compensation techniques), computation time, memory requirements and implementation complexity.