  In this study, we investigate the stability and solid fraction of columns
comprised of highly non-convex particles. These particles are constructed by
extruding arms onto the faces of Platonic solids, a configuration we term
\emph{Platonic polypods}. We explore the emergence and disappearance of
solid-like behavior in the absence of adhesive forces between the particles,
referred to as \emph{geometric cohesion}. This investigation is conducted by
varying the number of arms of the particles and the thickness of these arms. To
accomplish this, columns are assembled by depositing particles within a
cylindrical container, followed by the removal of the container to evaluate the
stability of the resulting structures. Experiments were carried out using three
distinct materials to assess the influence of the friction coefficient between
the grains. Our findings reveal that certain granular systems exhibit geometric
cohesion, depending on their geometrical and contact properties. Furthermore,
we analyze the initial solid fraction of the columns, demonstrating that these
arrangements can achieve stability even at highly loose states, which contrasts
with traditional granular materials.
