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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.


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

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.

Also see