Nilpotent (3,6) sub-Riemannian problem

In this paper we study the nilpotent (3, 6) sub-Riemannian problem. We describe the envelope of sub-Riemannian geodesics starting from a fixed point. We also describe the wave fronts propagating from the point. For general nilpotent (n, n(n + 1)/2) sub-Riemannian problem we formulate a conjecture about the form of the variety where geodesics starting from a fixed point lose optimality.