As discussed previously, the 4n rule mainly deals with clusters with electron counts of , in which approximately 4 electrons are on each vertex. As more electrons are added per vertex, the number of the electrons per vertex approaches 5. Rather than adopting structures based on deltahedra, the 5n-type clusters have structures based on a different series of polyhedra known as the 3-connected polyhedra, in which each vertex is connected to 3 other vertices. The 3-connected polyhedra are the duals of the deltahedra. The common types of 3-connected polyhedra are listed below.
The 5n rules are as follows.
Example: P
:Electron count: 4 × P = 4 × 5 = 20
:It is a 5n structure with n = 4, so it is tetrahedral
Example: PS
:Electron count 4 × P + 3 × S = 4 × 5 + 3 × 6 = 38
:It is a 5n + 3 structure with n = 7. Three vertices are inserted into edges
Example: PO
:Electron count 4 × P + 6 × O = 4 × 5 + 6 × 6 = 56
:It is a 5n + 6 structure with n = 10. Six vertices are inserted into edges