Definition:Polygon/Regular

Definition

A regular polygon is a polygon which is both equilateral and equiangular.

That is, in which all the sides are the same length, and all the vertices have the same angle:

Also known as

In Euclid's The Elements, a regular polygon is referred to as an equilateral and equiangular polygon.

Examples

Specific instances of regular polygons with specific numbers of sides are as follows:

• $3$ sides: Equilateral Triangle
• $4$ sides: Square
• $5$ sides: Regular Pentagon
• $6$ sides: Regular Hexagon
• $7$ sides: Regular Heptagon
• $8$ sides: Regular Octagon
• $9$ sides: Regular Nonagon or Regular Enneagon
• $10$ sides: Regular Decagon
• $11$ sides: Regular Hendecagon or Regular Undecagon
• $12$ sides: Regular Dodecagon

• $17$ sides: Regular Heptadecagon

The term regular $n$-gon is usually used nowadays to specify a regular polygon with a specific number, that is $n$, sides.

The specific name is usually invoked only in order to draw attention to the fact that such a regular polygon has a particularly interesting set of properties.

Also see

• Regular Polygon can be Inscribed in Circle

Sources

• 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{IV}$: The Prince of Amateurs
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.4$: Euclid (flourished ca. $300$ B.C.)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: polygon