1024 minimal stick candidate (12 vertices)

1.142366 -3.888643 1.057117
-0.347514 -3.814136 -1.562196
0.763853 0.476464 3.558440
-2.373890 2.066267 -0.840181
-1.086100 -3.800805 -0.247245
2.979236 -2.461059 0.367122
-2.402422 2.165816 2.984192
2.120917 1.229004 -2.222039
2.435638 3.154211 0.712867
-1.975692 0.879646 -2.811612
-3.027005 -0.092178 0.306321
1.770812 4.085292 -1.302794