Classifications of Polygons

Classifications of Polygons

You might be aware of certain names of special polygons, such as pentagon, hexagon, and octagon.  These terms classify a polygon by the number of sides.  In fact, the common names of polygons with 3 to 10 sides are:

# sides	name	examples
3	triangle
4	quadrilateral
5	pentagon
6	hexagon
7	heptagon
8	octagon
9	nonagon
10	decagon

You may be surprised that an object like this is called a pentagon:
We are accustomed to seeing pentagons that look like this:

Both these figures are polygons with 5 sides according to our definition.  What is peculiar about the first figure is it "caves in" at the top.  Such a polygon is called concave.  In fact, a definition of "concave" is this:
DEFINITION:  A polygon is concave if there are two points somewhere inside it for which a segment with these as its endpoints cuts at least 2 of the sides of the polygon.

For example,

is concave, because the segment with points A and B as its endpoints cuts two sides:

A polygon that is not concave is called convex.
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