A concave polygon is a polygon in which at least one line containing a side of the polygon also contains points in the interior of the polygon. Alternatively, a polygon is concave if one or more interior angles have a measure greater than $180^{\circ }.$ Note that only polygons with four or more sides can be concave. Some features can be listed about concave polygons.

• At least one vertex of the polygon points inwards.
• Some of the diagonals may lie partly or entirely outside the polygon.
• There are points inside the polygon for which the segment joining them is not fully contained in the polygon.
• Concave polygons are always irregular.

When a polygon is not concave, it is said to be convex.