A polygon is a collection of coplanar segments that intersect only at their endpoints and where each endpoint is shared by exactly two segments. The segments are called sides; each endpoint is a vertex. A segment that connects to non-adjacent vertices is called a diagonal. Diagonals in most polygons are relatively uninteresting. The diagonals of a quadrilateral, however, can have some interesting properties.
A regular polygon is a polygon where all of the sides are congruent.
A convex polygon is a polygon where any two points inside the polygon can be connected by a segment that never leaves the polygon. A concave polygon is a polygon where there are pairs of points inside the polygon that cannot be connected by a segment that never leaves the polygon.
Polygons are 'named' based on the number of sides they have. An n-sided polygon is called an n-gon. In other words, a 15-sided polygon would be called a 15-gon. Some polygons, ones with a relatively small number of sides, have special names. For reference: all of the examples below are regular, convex polygons.