Using Ag(111) substrates and molecular beam epitaxy, a pio-neering work demonstrated the successful synthesis of atomically thin 2D boron layers organized in islands tens of nanometres in size10,11. Indications of persisting Dirac fermions are present in the photoemission data12,15 of these boron sheets, and their existence is supported by theoretical calculations in several polymorphs14. To the extent that simple tight-binding approximations provide a good parametrization for ab initio band structure calculations in borophene, it is notable that within nearest-neighbour interaction the degeneracy at graphene K points and the presence of associated Dirac cones are preserved for an arbitrary distribution of ‘impurity’ toms that fill the hexagonal centres of any type of supercell of a honeycomb lattice. This remains true in higher-order hopping for several of the theoretically stable sheets of borophene with the con-comitant appearance of flat or weakly dispersive bands that arise from localized orbitals of the centre atoms. This peculiarity of the honeycomb lattice is interesting because flat bands can engender strange, non-Fermi-liquid metals, and perhaps open a path to room-temperature superconductivity16. To realize this potential, it is pressing to explore the synthesis of borophene on other substrates and study the ensuing crystal structures.