A magic polygon, also called a perimeter magic polygon,^{[1]}^{[2]} is a polygon with an integers on its sides that all add up to a magic constant.^{[3]}^{[4]} It is where positive integers (from 1 to N) on a k-sided polygon add up to a constant.^{[1]} Magic polygons are a generalization of other magic shapes^{[5]} such as magic triangles.^{[6]}

Magic polygon with a center point

Victoria Jakicic and Rachelle Bouchat defined magic polygons as n-sided regular polygons with 2n+1 nodes such that the sum of the three nodes are equal. In their definition, a 3 × 3 magic square can be viewed as a magic 4-gon. There are no magic odd-gons with this definition.^{[7]}

Magic polygons and degenerated magic polygons

Danniel Dias Augusto and Josimar da Silva defined the magic polygon P(n,k) as a set of vertices of $k/2$ concentric n-gon and a center point. In this definition, magic polygons of Victoria Jakicic and Rachelle Bouchat can be viewed as P(n,2) magic polygons. They also defined degenerated magic polygons.^{[8]}

^Jakicic, Victoria; Bouchat, Rachelle (2018). "Magic Polygons and Their Properties". arXiv:1801.02262 [math.CO].

^Danniel Dias Augusto; Josimar da Silva Rocha (2019). "Magic Polygons and Degenerated Magic Polygons: Characterization and Properties". arXiv:1906.11342 [math.CO].