text: Electron-counting rules are used to predict the preferred electron count for molecules. The octet rule, the 18-electron rule, and Hückels 4n + 2 pi-electron rule are proven to be useful in predicting the molecular stability. Wades rules were formulated to explain the electronic requirement of monopolyhedral borane clusters. The Jemmis mno rules are an extension of Wade's rules, generalized to include condensed polyhedral boranes as well.
  The first condensed polyhedral borane, , is formed by sharing four vertices between two icosahedra. According to Wades n + 1 rule for n-vertex closo structures,  should have a charge of +2 (n + 1 = 20 + 1 = 21 pairs required; 16 BH units provide 16 pairs; four shared boron atoms provide 6 pairs; thus 22 pairs are available). To account for the existence of  as a neutral species, and to understand the electronic requirement of condensed polyhedral clusters, a new variable, m, was introduced and corresponds to the number of polyhedra (sub-clusters). In Wades n + 1 rule, the 1 corresponds to the core bonding molecular orbital (BMO) and the n corresponds to the number of vertices, which in turn is equal to the number of tangential surface BMOs. If m polyhedra condense to form a macropolyhedron, m core BMOs will be formed. Thus the skeletal electron pair (SEP) requirement of closo-condensed polyhedral clusters is m + n.
  Single-vertex sharing is a special case where each subcluster needs to satisfy Wades rule separately. Let a and b be the number of vertices in the subclusters including the shared atom. The first cage requires a + 1 and the second cage requires b + 1 SEPs. Therefore, a total of a + b + 2 or a + b + m SEPs are required; but a + b = n + 1, as the shared atom is counted twice. The rule can be modified to m + n + 1, or generally m + n + o, where o corresponds to the number of single-vertex sharing condensations. The rule can be made more general by introducing a variable, p, corresponding to the number of missing vertices, and q', the number of caps. As such, the generalized Jemmis rule can be stated as follows:
  :The SEP requirement of condensed polyhedral clusters is m + n + o + p − q, where m is the number of subclusters, n is the number of vertices, o is the number of single-vertex shared condensations, p is the number of missing vertices and q is the number of caps.