Calculations performed at the ab initio level using the recently reported planar concentric π-aromatic B(18)H(6)(2+)(1) [Chen Q et al. (2011) Phys Chem Chem Phys 13:20620] as a building block suggest the possible existence of a new class of B(3n)H(m) polycyclic aromatic hydroboron (PAHB) clusters-B(30)H(8)(2), B(39)H(9)(2-)(3), B(42)H(10)(4/5), B(48)H(10)(6), and B(72)H(12)(7)-which appear to be the inorganic analogs of the corresponding C(n)H(m) polycyclic aromatic hydrocarbon (PAHC) molecules naphthalene C(10)H(8), phenalenyl anion C(13)H(9)(-), phenanthrene/anthracene C(14)H(10), pyrene C(16)H(10), and coronene C(24)H(12), respectively, in a universal atomic ratio of B:C = 3:1. Detailed canonical molecular orbital (CMO), adaptive natural density partitioning (AdNDP), and electron localization function (ELF) analyses indicate that, as they are hydrogenated fragments of a boron snub sheet [Zope RR, Baruah T (2010) Chem Phys Lett 501:193], these PAHB clusters are aromatic in nature, and exhibit the formation of islands of both σ- and π-aromaticity. The predicted ionization potentials of PAHB neutrals and electron detachment energies of small PAHB monoanions should permit them to be characterized experimentally in the future. The results obtained in this work expand the domain of planar boron-based clusters to a region well beyond B(20), and experimental syntheses of these snub B(3n)H(m) clusters through partial hydrogenation of the corresponding bare B(3n) may open up a new area of boron chemistry parallel to that of PAHCs in carbon chemistry.