text: The structure of β-rhombohedral boron is complicated by the presence of partial occupancies and vacancies.   The idealized unit cell,  has been shown to be electron-deficient and hence metallic according to theoretical studies, but β-boron is a semiconductor.  Application of the Jemmis rule shows that the partial occupancies and vacancies are necessary for electron sufficiency.
   can be conceptually divided into a  fragment and a  () fragment. According to Wades rule, the  fragment requires 8 electrons (the icosahedron at the centre (green) requires 2 electrons; each of the six pentagonal pyramids (black and red) completes an icosahedron in the extended structure; as such the electronic requirement for each of them is 1). The  or  is formed by the condensation of 6 icosahedra and two trigonal bipyramids. Here, m + n + o + p − q' = 8 + 57 + 1 + 0 − 0 = 66 pairs required for stability, but  are available. Therefore the  fragment has 3 excess electrons and the idealized  is missing 5 electrons. The 3 excess electrons in the  fragment can be removed by removing one B atom, which leads to  (). The requirement of 8 electrons by the  fragment can be satisfied by  boron atoms and the unit cell contains 48 + 56 +  = , which is very close to the experimental result.