# Magic Polygons and Degenerated Magic Polygons: Characterization and Properties

## TL;DR

This paper introduces and characterizes Magic Polygons P(n, k) and Degenerated Magic Polygons D(n, k), analyzing their properties, existence conditions, and key parameters such as magic sum and root vertex value.

## Contribution

It provides a formal definition, main properties, and existence conditions for both Magic Polygons and Degenerated Magic Polygons, expanding the understanding of these geometric structures.

## Key findings

- Defined Magic Polygons P(n, k) and D(n, k)
- Derived properties like magic sum and root vertex value
- Discussed existence conditions for various n and k

## Abstract

In this work we define Magic Polygons P (n, k) and Degenerated Magic Polygons D(n, k) and we obtain their main properties, such as the magic sum and the value corresponding to the root vertex. The existence of magic polygons P (n, k) and degenerated magic polygons D(n, k) are discussed for certain values of n and k.