31 minimal stick candidate (6 vertices)

0.300775 1.301248 -0.702434
-0.976281 -0.910795 0.701983
0.976171 -0.910795 -0.702076
-0.300495 1.300967 0.702620
-1.276451 -0.390204 -0.702474
1.276282 -0.390420 0.702381