n=12: 21 directions of short trajectories of length <= 6.0; 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, 1.732051, 2.0) | ((1,), (1,), (1,)) | 2 | ((2, 1, 0, 0), ((1,), (1,), (1,)))
   0 | (1.0, 1.732051, 2.0) | ((3,), (3,), (1,)) | 10 | ((1, 0, 0, 0), ((3,), (3,), (1,)))
   1 | (1.0, 2.732051, 3.732051) | ((1,), (1,), (1,)) | 4 | ((3, 3, 0, -1), ((2,), (2,), (2,)))
   1 | (1.0, 2.732051, 3.732051) | ((3,), (1,), (3,)) | 5 | ((-1, -1, 1, 1), ((6,), (2,), (6,)))
patterns with a reduced factor equal to n: 0
