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Typical granular materials are far from optimal in terms of mechanical performance: Random packing leads to poor load transfer in the form of thin and dispersed force lines within the material, to inhomogeneous jamming, and to strain localization. In addition, localized contacts between individual grains result in low stiffness, strength and brittleness. Here we propose a granular material that simultaneously embodies three approaches to increase strength: geometrical design of individual grains, crystallization, and infiltration by an adhesive. Using mechanical vibrations, we assembled millimeter-scale 3D printed grains with rhombic dodecahedral shapes into fully dense FCC granular crystals. We then infiltrated the granular structure with a tacky, polyacrylic adhesive that is orders of magnitude weaker than the grains, but which provides sustained adhesion over large interfacial displacements. The resulting material is a fully dense, free-standing space filling granular crystal. Compressive tests show that these granular crystals are up to 60 times stronger than randomly packed cohesive spheres and they display a rich set of mechanisms: Nonlinear deformations, crystal plasticity reminiscent of atomistic mechanisms, cross-slip, shear-induced dilatancy, micro-buckling, and tensile strength. To capture some of these mechanisms we developed a multiscale model that incorporates local cohesion between grains, resolved shear and normal stresses on available slip planes, and prediction of compressive strength as function of loading orientation. The predicted strength is highly anisotropic and agrees well with the compression experiments. Once fully understood and harnessed, we envision that these mechanisms will lead to granular engineering materials with unusual combinations of mechanical performances attractive for many applications.