Magic polygon

Not to be confused with Polygon Magic.

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

Perimeter magic polygon

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]

This displays order 3 magic triangles, a type of magic polygon.

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 ${\displaystyle k/2}$ 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]

See also

• Magic square