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We investigate the electronic properties of sculpturenes , formed by sculpting selected shapes from bilayer graphene, boron nitride or graphene–boron nitride hetero-bilayers and allowing the shapes to spontaneously reconstruct. The simplest sculpturenes are periodic nanotubes, containing lines of non-hexagonal rings. More complex sculpturenes formed from shapes with non-trivial topologies, connectivities and materials combinations may also be constructed. Results are presented for the reconstructed geometries, electronic densities of states and current–voltage relations of these new structures.