  We use a simple tight-binding (TB) model to study electronic properties of
free graphene flakes. Valence electrons of triangular graphene flakes show a
shell and supershell structure which follows an analytical expression derived
from the solution of the wave equation for triangular cavity. However, the
solution has different selection rules for triangles with armchair and zigzag
edges, and roughly 40000 atoms are needed to see clearly the first supershell
oscillation. In the case of spherical flakes, the edge states of the zigzag
regions dominate the shell structure which is thus sensitive to the flake
diameter and center. A potential well that is made with external gates cannot
have true bound states in graphene due to the zero energy band gap. However, it
can cause strong resonances in the conduction band.
