Definition:Polygon/Multilateral
Definition
A multilateral 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.
Also known as
The term multilateral polygon can also be seen hyphenated: multi-lateral polygon.
A polygon with $n$ sides is known as an $n$-gon.
Also see
- Results about polygons can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): n-gon
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): n-gon