A polygon is defined as a concave polygon, when one or more interior angles are greater than 180°.  In simple words, a polygon which is not convex is a concave polygon.

In convex polygon we will find the vertex pointing outside the polygon, whereas in concave polygon the vertex has been 'pushed in', that is vertex point towards the interior of the polygon.

Concave Polygon
Here are few properties of a Concave Polygon:

1. If a line is drawn through a concave polygon, it can intersect the polygon into more than two parts as shown in figure below,

Concave Polygon Line Intersection
2. Few diagonals of a concave polygon lie outside the polygon. In figure below, you see the diagonal at the top is outside the polygon's interior space.

Concave Polygons

Regular concave polygon are the ones which has equal sides and equal interior angles. But a concave polygon has one or more interior angles which is greater than 180°. So, we can say that a concave polygon can never be regular polygon.