In number theory, an octahedral number is a figurate number that represents the number of spheres in an octahedron formed from close-packed spheres. The th octahedral number can be obtained by the formula:

In geometry, an octahedron is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex.