  In this paper outer, or dual, billiards outside regular polygons are studied;
in particular, periodic points for cases of strictly convex "tables" and for
regular n-gons with n = 3,4,6,8,12 are discussed. The main results of the paper
are:
  1) proof of an existence of aperiodic points for outer billiards outside
regular octagon and dodecagon; 2) proof of the fact that for regular octagon,
set of periodic points is of full measure; 3) list of all possible periods for
case of regular octagon.
