  In this paper, we derive formulas for the analytical calculation of the
moments of the distance between two uniformly and independently distributed
random points in an $n$-sided regular polygon. A number of closed form
expressions is provided, e.g. the expected distances for $n = 3,4,5,6,8,10,12$,
where the results for $n = 5,8,10,12$ are new to the best of the author's
knowledge. Applying results of Voss, remarkably short formulas for the second
and the fourth moments are derived.
