text: The following polyhedra are closo polyhedra, and are the basis for the 4n rules; each of these have triangular faces. The number of vertices in the cluster determines what polyhedron the structure is based on.
  Using the electron count, the predicted structure can be found. n is the number of vertices in the cluster. The 4n rules are enumerated in the following table.
  When counting electrons for each cluster, the number of valence electrons is enumerated. For each transition metal present, 10 electrons are subtracted from the total electron count. For example, in Rh(CO) the total number of electrons would be  =  = 26. Therefore, the cluster is a closo polyhedron because , with .
  Other rules may be considered when predicting the structure of clusters:
  # For clusters consisting mostly of transition metals, any main group elements present are often best counted as ligands or interstitial atoms, rather than vertices.
  # Larger and more electropositive atoms tend to occupy vertices of high connectivity and smaller more electronegative atoms tend to occupy vertices of low connectivity.
  # In the special case of boron hydride clusters, each boron atom connected to 3 or more vertices has one terminal hydride, while a boron atom connected to two other vertices has two terminal hydrogen atoms. If more hydrogen atoms are present, they are placed in open face positions to even out the coordination number of the vertices.
  # For the special case of transition metal clusters, ligands are added to the metal centers to give the metals reasonable coordination numbers, and if any hydrogen atoms are present they are placed in bridging positions to even out the coordination numbers of the vertices.
  In general, closo structures with n vertices are n-vertex polyhedra.
  To predict the structure of a nido cluster, the closo cluster with n + 1 vertices is used as a starting point; if the cluster is composed of small atoms a high connectivity vertex is removed, while if the cluster is composed of large atoms a low connectivity vertex is removed.
  To predict the structure of an arachno cluster, the closo polyhedron with n + 2 vertices is used as the starting point, and the n + 1 vertex nido complex is generated by following the rule above; a second vertex adjacent to the first is removed if the cluster is composed of mostly small atoms, a second vertex not adjacent to the first is removed if the cluster is composed mostly of  large atoms.
  Example: 
  :Electron count: 10 × Pb + 2 (for the negative charge) = 10 × 4 + 2 = 42 electrons.
  :Since n = 10, 4n + 2 = 42, so the cluster is a closo bicapped square antiprism.
  Example: 
  :Electron count: 4 × S – 2 (for the positive charge) = 4 × 6 – 2 = 22 electrons.
  :Since n = 4, 4n + 6 = 22, so the cluster is arachno.
  :Starting from an octahedron, a vertex of high connectivity is removed, and then a non-adjacent vertex is removed.
  Example: Os(CO)
  :Electron 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: CBH
  :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