The unit cell described in the question where a = b ≠ c, α = β = 90°, and γ = 120° corresponds to the hexagonal crystal system. This is characteristic of graphite, where the carbon atoms are arranged in hexagonal layers.
Graphite has a hexagonal unit cell, with layers of carbon atoms arranged in a 2D honeycomb structure, and the angle between the axes is 120° for γ. This geometry fits the given unit cell characteristics.