A simple concave polygon will always have an interior angle with a measure that is greater than 180 degrees.

It is always possible to partition a concave polygon into a set of convex polygons.

A simple concave polygon has at least one interior angle that is a reflex angle.

Non-convex cells which pack without overlapping, analogous to tilings of concave polygons.

One or more concave polygons may produce more than one intersecting polygon.

For convex polygons one can cut off each vertex in turn, while for concave polygons this requires more care.

In geometry, a star polygon (not to be confused with a star-shaped polygon) is a concave polygon.

Tănase and Veltkamp propose to decompose concave polygons into unions of convex regions using straight skeletons, as a preprocessing step for shape matching in image processing.

Signals are of two types: Input signal (Message receiving activity) shown by a concave polygon and Output signal (Message sending activity) shown by a convex polygon.

Branko Grünbaum identified two primary definitions used by Kepler, one being the regular star polygons with intersecting edges that don't generate new vertices, and a second are simple isotoxal concave polygons.

The faces usually consist of triangles (triangle mesh), quadrilaterals, or other simple convex polygons, since this simplifies rendering, but may also be composed of more general concave polygons, or polygons with holes.

Prismatic dials are a special case of polar dials, in which the sharp edges of a prism of a concave polygon serve as the styles and the sides of the prism receive the shadow.

A polygon that is not a convex polygon is sometimes called a concave polygon, and some sources more generally use the term concave set to mean a non-convex set, but most authorities prohibit this usage.

While Euclid's proof only applied to convex polygons, the theorem also applies to concave polygons and even to similar figures that have curved boundaries (but still with part of a figure's boundary being the side of the original triangle).