Magic polygon

A magic polygon is a polygonal magic graph with integers on its vertices.

A magic polygon, also called a perimeter magic polygon,¹² is a polygon with an integers on its sides that all add up to a magic constant.³⁴ 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 shapes⁵ such as magic triangles.⁶

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

Danniel Dias Augusto and Josimar da Silva defined the magic polygon P(n,k) as a set of vertices of ${\displaystyle k/2}$ 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