Introduction to Polygons

You may want to review:

DEFINITION polygon

A polygon is a closed figure in a plane made by joining line segments, where each line segment intersects exactly two others.

Note: Strictly speaking, a polygon does not include its interior (the space inside the polygon).

A polygon

Not closed;
not a polygon

Not made of line segments;
not a polygon

Line segment intersects more than two others;
not a polygon

Polygons are usually classified according to how many sides they have:

DEFINITIONS names of polygons with various numbers of sides

A triangle is a polygon with $\,3\,$ sides.

A quadrilateral is a polygon with $\,4\,$ sides.

A pentagon is a polygon with $\,5\,$ sides.

A hexagon is a polygon with $\,6\,$ sides.

A heptagon is a polygon with $\,7\,$ sides.

An octagon is a polygon with $\,8\,$ sides.

A nonagon is a polygon with $\,9\,$ sides.

A decagon is a polygon with $\,10\,$ sides.

More generally, a polygon with $\,n\,$ sides can be called an $\,n\,$-gon.

For example, a polygon with $\,27\,$ sides can be called a $\,27$-gon.

DEFINITION vertex of a polygon; vertices

The vertices of a polygon are the points where its sides intersect. The singular form of vertices is vertex.

Naming Polygons

When naming polygons, the vertices must be listed in consecutive order. For example, the polygon above could be named:

polygon $\,ABCD\,$ (start with $\,A\,,$ move clockwise)
polygon $\,ADCB\,$ (start with $\,A\,,$ move counter-clockwise)
polygon $\,BCDA\,$ (start with $\,B\,,$ move clockwise)
polygon $\,BADC\,$ (start with $\,B\,,$ move counter-clockwise)
polygon $\,CDAB\,$ (start with $\,C\,,$ move clockwise)
polygon $\,CBAD\,$ (start with $\,C\,,$ move counter-clockwise)
polygon $\,DABC\,$ (start with $\,D\,,$ move clockwise)
polygon $\,DCBA\,$ (start with $\,D\,,$ move counter-clockwise)

More generally, when naming an $\,n$-gon, there are $\,n\,$ choices for listing the first vertex. Then, there are $\,2\,$ choices for the next vertex (moving clockwise or counterclockwise). The remaining vertices are then completely determined. Thus, there are $\,2n\,$ choices for the polygon name.