Regular polygons

2020 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