Volume 6, 2000, Number 3

We consider the following enumeration problem: how many are there ’’distinct” k-gons with integer sides and perimeter n. A solution is known for k = 3 when ’’distinct” means ”non-congruent” . This does not hold in the general case since for k > 3 a k-gon is not uniquely determined by its side lengths. We define the concept ’’distinct” in an appropriate way and reduce the problem to an enumeration of all distinct integer labels on the sides of a fixed regular k-gone satisfying a given condition. This enumeration can be done by the well known Polya’s Theory of Counting. The simple structure of the considered objects (a regular k-gon and the dihedral group of order k) allows us to prove our results in an alternative way using only elementary concepts and techniques from Group Theory and Number Theory