Engineered granular materials have gained considerable interest in recent years. For this substance, the primary design variable is grain shape. Optimizing grain form to achieve a macroscopic property is difficult due to the infinite-dimensional function space particle shape inhabits. Nonetheless, by parameterizing morphology the dimension of the problem can be reduced. In this work, we study the effects of both intuitive and machine-picked shape descriptors on granular material properties. First, we investigate the effect of classical shape descriptors (roundness, convexity, and aspect ratio) on packing fraction ϕ and coordination number Z. We use a genetic algorithm to generate a uniform sampling of shapes across these three shape parameters. The shapes are then simulated in the level set discrete element method. We discover that both ϕ and Z decrease with decreasing convexity, and Z increases with decreasing aspect ratio across the large sampling of morphologies—including among highly non-convex grains not commonly found in nature. Further, we find that subtle changes in mesoscopic properties can be attributed to a continuum of geometric phenomena, including tessellation, hexagonal packing, nematic order and arching. Nonetheless, such descriptors alone can not entirely describe a shape. Thus, we find a set of 20 descriptors which uniquely define a morphology via deep generative models. We show how two of these machine-derived parameters affect ϕ and Z. This methodology can be leveraged for topology optimization of granular materials, with applications ranging from robotic grippers to materials with tunable mechanical properties. Graphical Abstract: [Figure not available: see fulltext.].