We present a computational investigation of free-standing graphene bilayer edge (BLE) structures, aka “fractional nanotubes.” We demonstrate that these curved carbon nanostructures possess a number of interesting properties, electronic in origin. The BLEs, quite atypical of elemental carbon, have large permanent electric dipoles of 0.87 and 1.14 debye/Å for zigzag and armchair inclinations, respectively. An unusual, weak AA interlayer coupling leads to a twinned double-cone dispersion of the electronic states near the Dirac points. This entails a type of quantum Hall behavior markedly different from what has been observed in graphenebased materials, characterized by a magnetic field-dependent resonance in the Hall conductivity.