An Eberhard-Like Theorem for Pentagons and Heptagons

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F10%3A10051751" target="_blank" >RIV/00216208:11320/10:10051751 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
An Eberhard-Like Theorem for Pentagons and Heptagons
Original language description
Eberhard proved that for every sequence $(p_k), 3le kle r, kne 6$ of non-negative integers satisfying Euler's formula $sum_{kge3} (6-k) p_k = 12$, 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 $kge3$, where $p_k=0$ if $k}r$. In this paper we prove a similar statement when non-negative integers $p_k$ are given for $3le kle r$, 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 $kge3$. 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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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