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arXiv · 2604.02925

On the maximum volume solid wrappable by a given sheet of paper

R Nandakumar
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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.

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R Nandakumar. 2026-04-03. On the maximum volume solid wrappable by a given sheet of paper. https://arxiv.org/abs/2604.02925

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