The hexagonal crystal system is one of the seven crystal systems in crystallography. It includes all point groups with a six fold rotation and roto inversion axis. This division is based on the symmetry axis of the crystals, whereas the division into lattice systems is based on the metrics of the lattice. In addition, the division into lattice systems in the hexagonal crystal system is based on the space groups, not the point groups. This results in the following image for a hexagonal cell.
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