On two-dimensional geometric objects with straight edges: polygons
Polygon means a multiple-sided or multiple-edged figure. These are two-dimensional, closed shapes composed of straight, connected line segments. These segments are known as edges. A vertex with an associated angle lies between any two adjacent edges. Polygons are often named according to the number of their vertices, for example, the triangle. Sometimes, other defining characteristics are included in the name, such as in the case of the right triangle. Polygons are convex if all vertices point outward, concave vertices point inward. Non-convex polygons, that is, those with concave vertices, are sometimes colloquially referred to as concave polygons, a term sometimes used here as well.
There are simple regular polygons, those have a category of their own. All other polygons on these pages are grouped under this category. While mostly less regular, they may still possess a degree of regularity. Regular non-convex polygons, such as the pentagram and hexagram, are also included in this section. Both are regular star polygons. An example of a non-convex polygon that is not a star is the L-shape. This is not a standard geometric name, as no such name exists for many shapes. Consequently, descriptive names that are as clear as possible have been chosen for them.
The polygons are generally arranged by an increasing number of vertices and level of complexity, though this does not imply a strict sequence, unlike the arrangement of simple regular polygons. The final polygon in the list, bearing the unassuming name simple polygon, is the general case. While most of the other polygons listed here could theoretically be calculated using it, doing so would require an enormous amount of input. Therefore, it does not replace the other calculators. In the context of polygons, simple means the shape does not self-intersect. Conversely, self-intersecting shapes, such as the antiparallelogram, cross over themselves.