Definition:Polygonal Number

Definition
Polygonal numbers are those denumerating a collection of objects which can be arranged in the form of an regular polygon.

Definition 2
For a given $k$, polygonal numbers are referred to by the name of the appropriate $k$-sided polygon.

For large $k$, they are therefore called (when used) $k$-gonal numbers.

Also see

 * Equivalence of Definitions of Polygonal Number