# Definition:Polygon/Multi-lateral

< Definition:Polygon(Redirected from Definition:Multi-lateral Polygon)

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## Definition

A **multi-lateral polygon** is a term to define a polygon with more than four sides.

In the words of Euclid:

**Rectilineal figures**are those which are contained by straight lines,**trilateral**figures being those contained by three,**quadrilateral**those contained by four, and**multi-lateral**those contained by more than four straight lines.

(*The Elements*: Book $\text{I}$: Definition $19$)

This definition is somewhat arbitrary and is rarely used, as its applications are limited.

## Examples

There are specific names for polygons with specific numbers of sides, as follows:

- $5$ sides: Pentagon
- $6$ sides: Hexagon
- $7$ sides: Heptagon
- $8$ sides: Octagon
- $9$ sides: Nonagon or Enneagon
- $10$ sides: Decagon
- $11$ sides: Hendecagon or Undecagon
- $12$ sides: Dodecagon
- $13$ sides: Triskaidecagon

- $17$ sides: Heptadecagon

The list goes on, but learning the names of them all is something which, mercifully, is rarely inflicted upon children nowadays.

Instead, the term $n$-gon is usually used nowadays to specify a 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 polygon has a particularly interesting set of properties.