In general, building granular columns is only possible when the grains are cemented together (as a sandcastle). In this case, adhesive forces transform the forces network into a self- stressed network of tensile and compressive forces assuring the stability of the column. But, as soon as the cohesive forces disappear, the columns collapse into a pile of grains, whose angle of repose depends mainly on the shape of the grains. Nevertheless, self-supported granular structures can also emerge without the need of any binder when considering non- convex grains. The non-convex grains can entangle inducing a cohesion of geometric origin. We designed 2D simulations in order to systematically explore the occurrence and magnitude (defined from the maximum height of a stable column) of geometric cohesion with star-shaped grains. Numerically, the arms of the stars are made of rectangles with rounded caps. The number of arms increases from 3 to 14. We performed a series of collapse tests on columns of increasing size. We find that the geometric cohesion increases with the number of arms up to a maximum value for 9 arms, and then declines until the behavior of the assembly remains only frictional. By studying the microstructure of the initial states, we show that the generated columns are hyperstatic (quantified via the coordination number), and that the degree of hyperstaticity is maximum for precisely 9 arms. This is explained by the entanglement of the grains and the increase in the number of multiple contacts between them as a function of the number of arms, revealing “frozen” local structures. Finally, 3D experiments are developed in parallel to the numerical tests by printing a large quantity of grains composed of [XX, YY] arms. Our preliminary experimental results confirm the existence of a maximum for the geometric cohesion with the number of arms.