  This paper derives the exact cumulative density function of the distance
between a randomly located node and any arbitrary reference point inside a
regular $\el$-sided polygon. Using this result, we obtain the closed-form
probability density function (PDF) of the Euclidean distance between any
arbitrary reference point and its $n$-th neighbour node, when $N$ nodes are
uniformly and independently distributed inside a regular $\ell$-sided polygon.
First, we exploit the rotational symmetry of the regular polygons and quantify
the effect of polygon sides and vertices on the distance distributions. Then we
propose an algorithm to determine the distance distributions given any
arbitrary location of the reference point inside the polygon. For the special
case when the arbitrary reference point is located at the center of the
polygon, our framework reproduces the existing result in the literature.
