A region R is convex if, given any two points A and B in R, kA + (1-k)*B is also inside R for all k such that 0 ≤ k ≤ 1. In other words the whole of the line joining AB is inside the region R.
If there is even one pair of points A, B and just one value of k such that the relevant point is not in R, then R is not convex.
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A non convex is a concave and a convex is differently shaped
In a non-convex (or concave) polygon, at least one interior angle is a reflex angle. An alternative definition is that if you take any two points inside a conves polygon, the line joining them is wholly inside the polygon.
Any polygon that has an angle that is > 180º is a concave polygon. A convex polygon does not. e.g. All regular polygons are convex.
Take any two points on or inside a body. If every point on the straight line joining the two points lies within the shape, then it is convex. If not, it is non-convex.
I believe the fewest number of sides in a planar, non-convex polygon is four.