On the maximum volume solid wrappable by a given sheet of paper
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917382800277504 |
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| author | Nandakumar, R |
| author_facet | Nandakumar, R |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02925 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the maximum volume solid wrappable by a given sheet of paper Nandakumar, R Metric Geometry Combinatorics 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. |
| title | On the maximum volume solid wrappable by a given sheet of paper |
| topic | Metric Geometry Combinatorics |
| url | https://arxiv.org/abs/2604.02925 |