A polygonal number is a type of figurate number that represents a polygonal shape. These numbers can be arranged in the shape of a polygon, such as triangles, squares, or pentagons. The nth polygonal number can be calculated using a specific formula that depends on the number of sides of the polygon. For example, the triangular numbers are a sequence of polygonal numbers where each number can be represented as a triangle. The first few triangular numbers are 1, 3, 6, and 10. Other types of polygonal numbers include square numbers and pentagonal numbers, each following their own unique formulas.