A polygonal diagonal is a line segment connecting two nonadjacent polygon vertices of a polygon. The number of ways a fixed convex n-gon can be divided into triangles by nonintersecting diagonals is C_(n - 2) (with C_(n - 3) diagonals), where C_n is a Catalan number. This is Euler's polygon division problem. Counting the number of regions determined by drawing the diagonals of a regular n-gon is a more difficult problem, as is determining the number of n-tuples of concurrent diagonals.

Catalan number | Euler's polygon division problem | polygon | polygon diagonal intersection graph | polygon diameter | polyhedron diagonal | polyhedron vertex | regular polygon division by diagonals