Which convex bodies can be captured in a knot?
This question is based on the discussion in "Is it possible to capture a sphere in a knot?". We assume that the knot is made from unstretchable, infinitely thin rope.
Comments:
- By the construction Anton Geraschenko, the question is equivalent to existence of a graph embedded in the surface of the convex body that locally minimize the total length. Such embedding exists on some convex bodies, for example on an equilateral triangle shown on the diagram (and on anything sufficiently close).
- According to the original question a ball cannot be captured (in fact it cannot be captured in a link with 3 components). Moreover a circular disk cannot be captured see my answer (thanks to Wlodek Kuperberg for asking). Likely the same idea works for all convex bodies of revolution. Maybe all convex bodies of general position can be captured.