We experimentally investigate the dynamics of quasi-two-dimensional vibrated granular systems composed of geometric solids with identical mass. We analyze both the motion of individual particles and the collective behavior at different packing fractions. For single particles, we find that the number of vertices determines the type of motion. Solids with few vertices exhibit Brownian-like motion, while shapes with many or no vertices display more superdiffusivelike behavior. At the collective level, particle geometry and packing fraction jointly determine whether the system exhibits diffusive, subdiffusive, or superdiffusive dynamics, as revealed by the mean squared displacement, diffusion coefficients, the non-Gaussian parameter, and the probability distribution functions. We conclude that while the packing fraction controls the overall progression across dynamical regimes, the particle geometry dictates the specific pathways and extent of these transitions. These findings establish particle geometry as a design parameter for controlling the dynamics of driven granular media.

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• Brownian motion
• Diffusion
• Granular packing
• Random walks
• Self-organized systems
• Granular materials