The paper reports on three direct numerical simulations of sediment transport with different prototypical non-spherical particle shapes, ranging from prolate to oblate to a triaxial ellipsoidal shape, and a fourth simulation with spherical particles. All physical and numerical parameters of these simulations are identical, including bulk Reynolds number, equivalent particle diameter and sphericity of the non-spherical particles, so that the shape is the only difference. Numerous statistical quantities assessing the computed solutions are presented, such as mean particle velocity, sediment-bed porosity, equivalent roughness height, mean fluid velocity and Reynolds stresses. These allow a detailed analysis and reveal the considerable influence of the particle shape on the entire flow: fluid as well as particles. It is found that oblate spheroids yield the highest porosity among the four cases and spherical particles the lowest mean porosity. Prolate particles exhibit the strongest tendency to form spanwise clusters and generate the highest total bed friction. Triaxial ellipsoids representing natural medium-size sand particles yield results in between these cases, still exhibiting substantial differences with respect to spherical particles. The mean sediment transport rate is determined in all four cases showing that this quantity cannot be correlated to the mean shear stress of the fluid alone. This emphasises the importance of the particle shape in modelling the transport of natural sediment, and the results provide well-controlled data points for this task.