# Difference between revisions of "Regular polygons"

From Encyclopedia of Mathematics

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− | + | A regular polygon is a [[Polygon|polygon]], all angles of which are equal and all sides of which are equal. | |

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− | ====References==== | + | 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 $\{5/2\}$. |

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+ | ====References==== | ||

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+ | |valign="top"|{{Ref|Co}}||valign="top"| H.S.M. Coxeter, "Regular complex polytopes", Cambridge Univ. Press (1990) pp. Chapt. 1 | ||

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+ | |} |

## Latest revision as of 17:23, 26 July 2012

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://www.encyclopediaofmath.org/index.php?title=Regular_polygons&oldid=27206