Some polygons of different kinds
In geometry a polygon /ˈpɒlɪɡɒn/ is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain or circuit. These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices (singular: vertex) or corners. The interior of the polygon is sometimes called its body. An n-gon is a polygon with n sides. A polygon is a 2-dimensional example of the more general polytope in any number of dimensions.
Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up).
If all angles are equal and all sides are equal, then it is regular, otherwise it is irregular.
A convex polygon has no angles pointing inwards. More precisely, no internal angle can be more than 180°.
If any internal angle is greater than 180° then the polygon is concave. (Think: concave has a "cave" in it.
A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself! Many rules about polygons don't work when it is complex.
The basic geometrical notion has been adapted in various ways to suit particular purposes. Mathematicians are often concerned only with the bounding closed polygonal chain and with simple polygons which do not self-intersect, and they often define a polygon accordingly. A polygonal boundary may be allowed to intersect itself, creating star polygons. Geometrically two edges meeting at a corner are required to form an angle that is not straight (180°); otherwise, the line segments may be considered parts of a single edge; however mathematically, such corners may sometimes be allowed. These and other generalizations of polygons are described below.
Convex: any line drawn through the polygon (and not tangent to an edge or corner) meets its boundary exactly twice. As a consequence, all its interior angles are less than 180°. Equivalently,...