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We characterize the subRiemannian cut locus of the origin in the free Carnotgroup of step two with three generators. We also calculate explicitly the cuttime of any extremal path and the distance from the origin of all points of thecut locus. Finally, by using the Hamiltonian approach, we show that the cuttime of strictly normal extremal paths is a smooth explicit function of theinitial velocity covector. Finally, using our previous results, we show that atany cut point the distance has a corner-like singularity.

On the subRiemannian cut locus in a model of free two-step Carnot group