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Graphite has sublattice symmetry (2 C in a
unit cell) which protects the Dirac point in its band structure, and thus is
gapless. On the other hand, in BN the sublattice symmetry is broken (1B and 1N
in a unit cell), which opens the band gap and makes it insulating. In another
word, as free electron tends to be bonded to the nitrogen atom in BN, it has a
quite stable structure and will not move. So BN is an insulator.
In a simplified model, the SP2 orbit of
symmetric C-C bond in graphite gives possibility for free move of electron.
Therefore, graphite is a conductor.