A direct connection is established between tridimensional aromatic closo boron hydride clusters and planar aromatic [n]annulenes for medium and large size boron clusters. In particular, our results prove the existence of a link between the two-dimensional Hückel rule followed by aromatic [n]-annulenes and Wade-Mingos' rule of three-dimensional aromaticity applied to the aromatic [BnHn]2- closo boron hydride clusters. Our results show that closo boron hydride clusters can be categorized into different series according to the n value of the Hückel (4n+2) rule. The distinct categories studied in this work correspond to values of n = 1, 2, and 3. Each category increases in geometrical difficulty but, more importantly, it is possible to associate each category with the number of pentagonal layers in the structure perpendicular to the main axis. Category 1 has one pentagonal layer, category 2 has two, and category 3 has three

This work has been supported by the Ministerio de Economía y Competitividad (MINECO) of Spain (Projects CTQ2014-54306-P and CTQ2013-44670-R) and the Generalitat de Catalunya (projects 2014SGR931 and 2014SGR149, Xarxa de Referència en Química Teòrica i Computacional, and ICREA Academia 2014 prize for M.S.). The EU under the FEDER grant UNGI10-4E-801 (European Fund for Regional Development) has also funded this research