Polygons A simple curve does not cross itself, except that if you draw it with a pencil, the starting and stopping points may be the same. A closed curve can be traced using the same starting and stopping points, without retracing any part of the curve. A polygon is a 2-dimensional simple closed figure with sides that are line segments. A point where two sides of a polygon meet is a vertex of the polygon. (The plural of vertex is vertices.) Convex curves are simple, closed, and have no indentations. More precisely, the segment connecting any two points in the interior of the curve is wholly contained in the interior of the curve. Concave curves are simple, closed, and not convex; that is, they have an indentation. Polygons are classified according to the number of sides they have. Polygon Number Examples of Sides Triangle 3 Quadrilateral 4 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 Nonagon 9 Decagon 10 Dodecagon 12 Polygons with more than 10 sides are not usually given special names. A polygon with 11 sides is described as an 11-gon, a polygon with 14 sides as a 14-gon, and so on. Each of the polygons below is a 17-gon. When people talk about a general polygon -- one where you don't know the exact number of sides -- they often refer to it as an n-gon. The diagonal of a polygon is a line segment connecting non-consecutive vertices of the polygon.