To match the boundary conditions of numerical models and to examine the effect of particle dimensionality on granular friction, we conducted laboratory experiments on rods sheared in 1-D and 2-D configurations, glass beads (3-D), and angular quartz sand (rough 3-D). The average coefficient of friction during stable sliding for 1-D, 2-D, smooth 3-D, and rough 3-D particles is 0.15, 0.3, 0.45, and 0.6, respectively. Frictional strength of 2-D layers exceeds 1-D friction by an amount associated with dilatancy and the additional contact plane in 2-D. We show that 3-D granular friction exceeds 2-D friction by the amount of interparticle friction on the out-of-plane particle contacts that do not exist in 2-D. Data from our 2-D experiments are remarkably similar to numerical results based on 2-D particle dynamic simulations. Our data indicate that application of numerical models of granular friction to tectonic faults will require computations involving rough, 3-D particles.