A polyhedral number is the 3-D extension of the concept of the polygonal number. A point is chosen to be a common vertex of polyhedra of sizes 1, 2, … N, the corresponding faces of the polyhedra are parallel, dots are drawn on the corners and at unit intervals along the edges, and the total number of dots is counted.
Among polyhedral numbers are tetrahedral numbers, cubic numbers, octahedral numbers, square pyramidal numbers, truncated tetrahedral numbers, and many many more.