The density of points in balls and regular shapes within a metric space offers insights into optimal packing, geometric patterns, and constraint-based optimization. It enhances computational efficiency, models natural systems, and enables metric comparisons, revealing how geometry and distribution vary with different distance measures. Building on previous investigations into density extrema for various \(\ell _p\) -balls, this paper presents novel results essential to understanding the density extrema (i.e., minima and maxima) of integer points in standard hexagons. A key observation from our findings, along with earlier results, is that for real radii, the density extrema consistently occur at small radii, regardless of shape. However, with integer radii, the behavior changes drastically, posing a fascinating and unresolved research challenge.