In geometry a polygon (IPAEng: ˈpɒlɨɡɒn, ˈpɒliɡɒn) is traditionally a plane figure that is bounded by a closed path or circuit, composed of a finite sequence of straight line segments (i.e., by a closed polygonal chain). These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices or corners. The interior of the polygon is sometimes called its body. A polygon is a 2-dimensional example of the more general polytope in any number of dimensions.

Usually two edges meeting at a corner are required to form an angle that is not straight (180°); otherwise, the line segments will be considered parts of a single edge.

The basic geometrical notion has been adapted in various ways to suit particular purposes. For example in the computer graphics (image generation) field, the term polygon has taken on a slightly altered meaning, more related to the way the shape is stored and manipulated within the computer.

Number of sides

Polygons are primarily classified by the number of sides, see naming polygons below.

Convexity

Polygons may be characterised by their degree of convexity:

• Convex: any line drawn through the polygon (and not tangent to an edge or corner) meets its boundary exactly twice.
• Non-convex: a line may be found which meets its boundary more than twice.
• Simple: the boundary of the polygon does not cross itself. All convex polygons are simple.
• Concave: Non-convex and simple.
• Star-shaped: the whole interior is visible from a single point, without crossing any edge. The polygon must be simple, and may be convex or concave.
• Self-intersecting: the boundary of the polygon crosses itself. Branko Grünbaum calls these coptic, though this term does not seem to be widely used. The term complex is sometimes used in contrast to simple, but this risks confusion with the idea of a complex polygon as one which exists in the complex Hilbert plane consisting of two complex dimensions.
• Star polygon: a polygon which self-intersects in a regular way.

Symmetry

• Equiangular: all its corner angles are equal.
• Cyclic: all corners lie on a single circle.
• Isogonal or vertex-transitive: all corners lie within the same symmetry orbit. The polygon is also cyclic and equiangular.
• Equilateral: all edges are of the same length. (A polygon with 5 or more sides can be equilateral without being convex.) (Williams 1979, pp. 31-32)
• Isotoxal or edge-transitive: all sides lie within the same symmetry orbit. The polygon is also equilateral.
• Regular. A polygon is regular if it is both cyclic and equilateral. A non-convex regular polygon is called a regular star polygon.