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Modular structures of space-filling building blocks having dimension orders of magnitude larger (≈1000 μm) than the particle size (0.1–10 μm) may offer a high potential for near net shape manufacturing as well as toughening of brittle ceramic materials. We demonstrate vibration assisted periodic pattern formation of alumina cubes with an edge lengths of 1.3 mm. Two-dimensional and three-dimensional modular assembly structures of different unit cell symmetry were prepared. Unlike colloidal crystallization which suffers from a high degree of packing defects, vibration assisted gravitational assembly of space-filling building blocks offers a high potential for achieving periodic assembly structures with quasi-crystalline order, high packing densities and low defect content.