Year: 2026
Type: preprint
Abstract: We consider the problem of wrapping three-dimensional solid bodies with a given planar sheet of paper, where the paper may be folded or wrinkled but not stretched or torn. We propose a conjecture characterising the maximumvolume solid wrappable by any given sheet: the maximum is always achieved (or approached) by a non-convex body. In other words, for any convex solid wrappable by a given sheet, there exists a non-convex solid of strictly greater volume that the same sheet can wrap. We discuss related work, a key subquestion involving the sphere, and several further directions.
Source: arXiv (Cornell University)
Author: Nandakumar, R
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7151074405
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