A hold with 0.04 of clearance, and the poses it leaves

The same four contacts with every obstacle backed off by 0.04, and the part drawn at the extremes of what it may then do. The permitted poses are { p : A p ≥ −c }, a polyhedron, and it is bounded exactly when the arrangement is a hold — an unbounded direction of it would be a ray of the escape cone, and a hold has none. So the two questions this field keeps apart turn out to be the same question at two scales: whether a part is held is whether its pose set is finite, and the clearance is what gives that set a size. The size here is 0.3422 by 0.1646 by 0.1646 in rotation and the two translations, which for 0.04 of clearance is a ratio of 8.56, 4.11, 4.11 — not one, and not equal. positioned by solving, not by drawing.