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- W2023680143 abstract "Eberhard proved that for every sequence (p k ), 3≤k≤r, k≠6, of nonnegative integers satisfying Euler’s formula ∑k≥3(6−k)p k =12, there are infinitely many values p 6 such that there exists a simple convex polyhedron having precisely p k faces of size k for every k≥3, where p k =0 if k>r. In this paper we prove a similar statement when nonnegative integers p k are given for 3≤k≤r, except for k=5 and k=7 (but including p 6). We prove that there are infinitely many values p 5,p 7 such that there exists a simple convex polyhedron having precisely p k faces of size k for every k≥3. We derive an extension to arbitrary closed surfaces, yielding maps of arbitrarily high face-width. Our proof suggests a general method for obtaining results of this kind." @default.
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- W2023680143 date "2010-05-27" @default.
- W2023680143 modified "2023-09-23" @default.
- W2023680143 title "An Eberhard-Like Theorem for Pentagons and Heptagons" @default.
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- W2023680143 doi "https://doi.org/10.1007/s00454-010-9264-1" @default.
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