count: 6 × Os + 18 × CO – 60 (for 6 osmium atoms) = 6 × 8 + 18 × 2 – 60 = 24 Since n = 6, 4n = 24, so the cluster is capped closo. Starting from a trigonal bipyramid, a face is capped. The carbonyls have been omitted for clarity. Example: Electron count: 5 × B + 5 × H + 4 (for the negative charge) = 5 × 3 + 5 × 1 + 4 = 24 Since n = 5, 4n + 4 = 24, so the cluster is nido. Starting from an octahedron, one of the vertices is removed. The rules are useful in also predicting the structure of carboranes. Example: C2B7H13 Electron count = 2 × C + 7 × B + 13 × H = 2 × 4 + 7 × 3 + 13 × 1 = 42 Since n in this case is 9, 4n + 6 = 42, the cluster is arachno. The bookkeeping for deltahedral clusters is sometimes carried out by counting skeletal electrons instead of the total number of electrons. The skeletal orbital (electron pair) and skeletal electron counts for the four types of deltahedral clusters are: n-vertex closo: n + 1 skeletal orbitals, 2n + 2 skeletal electrons n-vertex nido: n + 2 skeletal orbitals, 2n + 4 skeletal electrons n-vertex arachno: n + 3 skeletal orbitals, 2n + 6 skeletal electrons n-vertex hypho: n + 4 skeletal orbitals, 2n + 8 skeletal electrons The skeletal electron counts are determined by summing the total of the following number of electrons: 2 from each BH unit 3 from each CH unit 1 from each additional hydrogen atom (over and above the ones on the BH and CH units) the anionic charge electrons 5n rules 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: P4 Electron count: