This is a meta-question, rather than a specific mathematical question. I am seeking a mathematical definition that captures the following physical idea.
Suppose you have a convex polyhedron $P \subset \mathbb{R}^3$. I would like to "wrap" $P$ with string so that (a) the entire surface area is covered with string, and (b) the string does not tend to slip off, even with minimal friction. The closest related literature I've found is this very current paper:
"Wrapping the cube and other polyhedra," T. Tarnai1, F. Kovács, P. W. Fowler and S. D. Guest, Proceedings of the Royal Society, 2012.
I am seeking a mathematical definition of what it might mean to "wrap without slippage." Then the natural follow-on question is to minimize the total string length, for a given $P$, and given string thickness $\delta$. But first I need a clear defintion! Any help would be appreciated—Thanks!
PS. Yes, I am familiar with the closely related work by Demaine, Demaine, and Mitchell.
