What Is a Regular Polygon?

The answer to this question must seem so obvious that regular readers of this periodical will assume there has to be more to it than meets the eye. There is. As with most good geometric discussions this one hinges on definitions. In particular, what do we mean by the word polygon and under what conditions is a polygon regular?

I believe that everyone has a sense of what a polygon is and what a polygon is not, and if it is, whether it is regular or not. For example, everyone agrees that to be regular a polygon must be both equilateral and equiangular.

All the objects in this article have equal sides and, in a sense, equal angles, but you may object that some of them are not even polygons, let alone regular polygons. I shall offer definitions of polygon and regular polygon later in the article.

As you read on, you may find it helpful to make models of some of the more recondite polygons (if you believe they are polygons) you will meet later in the article. I have had great success using Zometool components to make such models.