Structure and electronic properties of two unusual boron clusters obtained by fusion of borozene rings have been studied by means of first principles calculations based on the generalized-gradient approximation of the density functional theory. Moreover, a semiempirical tight-binding model has been appropriately calibrated for transport calculations on these clusters. Results show that the pure boron clusters are topologically planar and characterized by (3c–2e) bonds, which can explain, together with the aromaticity (estimated by means of NICS), the remarkable cohesive energy values obtained. Such feature makes these systems competitive with the most stable boron clusters to date. The energy gap values indicate that these clusters possess a semiconducting character, while when the larger system is considered, zero-values of the density of states are found exclusively within the HOMO–LUMO gap. Electron transport calculations within the Landauer formalism confirm these indications, showing semiconductor-like low bias differential conductance for these structures. Differences and similarities with carbon clusters are highlighted in the discussion.