Unfoldings and nets of regular polytopes
| Autor: | Satyan L. Devadoss, Matthew Harvey |
|---|---|
| Rok vydání: | 2023 |
| Předmět: |
Computational Geometry (cs.CG)
FOS: Computer and information sciences Computational Mathematics Control and Optimization Computational Theory and Mathematics FOS: Mathematics Computer Science - Computational Geometry Mathematics - Combinatorics Mathematics::Metric Geometry Combinatorics (math.CO) Geometry and Topology Computer Science Applications |
| Zdroj: | Computational Geometry. 111:101977 |
| ISSN: | 0925-7721 |
| DOI: | 10.1016/j.comgeo.2022.101977 |
| Popis: | Over a decade ago, it was shown that every edge unfolding of the Platonic solids was without self-overlap, yielding a valid net. We consider this property for regular polytopes in arbitrary dimensions, notably the simplex, cube, and orthoplex. It was recently proven that all unfoldings of the $n$-cube yield nets. We show this is also true for the $n$-simplex and the $4$-orthoplex but demonstrate its surprising failure for any orthoplex of higher dimension. Comment: 12 pages, 6 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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