n=9: 25 directions of short trajectories of length <= 7.0; 9 sample points on a side per direction
parity of the type (n even) | ratios of the preclosed lengths | reduced factors per length | number of directions | example (reachable point, unreduced factors)
   0 | (1.0, 1.879385, 2.532089, 2.879385) | ((1,), (1,), (1,), (1,)) | 1 | ((0, 0, 1, 2, 2, 1), ((1,), (1,), (1,), (1,)))
   0 | (1.0, 1.879385, 2.532089, 2.879385) | ((3,), (3,), (1,), (3,)) | 24 | ((1, 0, 0, 0, 0, 0), ((9,), (9,), (3,), (9,)))
patterns with a reduced factor equal to n: 0
