# Regular polygons

From Encyclopedia of Mathematics

2010 Mathematics Subject Classification: *Primary:* 51M05 [MSN][ZBL]

A regular polygon is a polygon, all angles of which are equal and all sides of which are equal.

In other words, a regular polygon is a polygon whose vertices all lie on one circle while its sides all touch a concentric circle. If the polygon is convex and has $n$ vertices, it is called an $n$-gon, and is denoted by $\{n\}$. If it is non-convex and its $n$ sides surround its centre $d$ times, it is called a star polygon, or a star $n$-gon of density $d$, and is denoted by $\{n/d\}$. For instance, the pentagram is $\{5/2\}$.

#### References

[Co] | H.S.M. Coxeter, "Regular complex polytopes", Cambridge Univ. Press (1990) pp. Chapt. 1 |

**How to Cite This Entry:**

Regular polygons.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Regular_polygons&oldid=27206