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In this paper, we derive formulas for the analytical calculation of themoments of the distance between two uniformly and independently distributedrandom points in an $n$-sided regular polygon. A number of closed formexpressions 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'sknowledge. Applying results of Voss, remarkably short formulas for the secondand the fourth moments are derived.

The moments of the distance between two random points in a regular polygon