The band structure of diamond has been determined using Slater's cellular method. Calculations were carried out with the unit cell partitioned into two and then four space-filling polyhedra. The dependence of the energy-level structure on the choice of matching points and cellular basis functions is carefully examined. Once a sufficient number of cellular basis functions (tetrahedral harmonics) is introduced, the precise arrangement of the matching points is no longer critical, and substantially the same energy-level structure is obtained for a wide variety of matching-point configurations. Tetrahedral harmonic expansions including lmax=12 are sufficient to ensure reasonable convergence at the zone points, X, and L. Some energy levels converge with lmax8. Most early attempts to calculate the band structure of diamond-type crystals using the cellular method were quantitatively unsatisfactory because too few basis functions were used. The present cellular results based on fourfold partitioning compare favorably with orthogonalized-plane-wave (OPW) results and with experiment. The lowest conduction-band level at the zone center is found to be 15 in agreement with OPW calculations but in disagreement with recent nonlocal-empirical-pseudopotential calculations. © 1975 The American Physical Society.