Editing Octahedral number (section)

===Tetrahedra===
If <math>O_n</math> is the {{nowrap|<math>n</math>th}} octahedral number and <math>T_n</math> is the {{nowrap|<math>n</math>th}} [[tetrahedral number]] then
:<math>O_n+4T_{n-1}=T_{2n-1}.</math>
This represents the geometric fact that gluing a tetrahedron onto each of four non-adjacent faces of an octahedron produces a tetrahedron of twice the size.

Another relation between octahedral numbers and tetrahedral numbers is also possible, based on the fact that an octahedron may be divided into four tetrahedra each having two adjacent original faces (or alternatively, based on the fact that each square pyramidal number is the sum of two tetrahedral numbers):
:<math>O_n = T_n + 2T_{n-1} + T_{n-2}.</math>