  The steady state packing fraction of a tapped granular bed is studied for
different grain shapes via a discrete element method. Grains are monosized
regular polygons, from triangles to icosagons. Comparisons with disk packings
show that the steady state packing fraction as a function of the tapping
intensity presents the same general trends in polygon packings. However, better
packing fractions are obtained, as expected, for shapes that can tessellate the
plane (triangles, squares and hexagons). In addition, we find a sharp
transition for packings of polygons with more than 13 vertices signaled by a
discontinuity in the packing fraction at a particular tapping intensity.
Density fluctuations for most shapes are consistent with recent experimental
findings in disk packing; however, a peculiar behavior is found for triangles
and squares.
