# What is the smallest diameter ring a non-convex polyhedron can pass through in 3-space?

The question is mostly in the title.

Imagine I have some non-convex polyhedron $P$, and I would like to find the smallest diameter ring that it can pass through in 3-space, undergoing any necessary rotations as it does so. Is there an efficient way to calculate $D_{ring}$? Pressing my luck, can I find the set of rotations for $P$ as it passes through the ring?

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