Zero-sum cycles in flexible polyhedra

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F22%3A00356902" target="_blank" >RIV/68407700:21240/22:00356902 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1112/blms.12562" target="_blank" >https://doi.org/10.1112/blms.12562</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/blms.12562" target="_blank" >10.1112/blms.12562</a>

Result language
angličtina
Original language name
Zero-sum cycles in flexible polyhedra
Original language description
We show that if a polyhedron in the three-dimensional affine space with triangular faces is flexible, that is, can be continuously deformed preserving the shape of its faces, then there is a cycle of edges whose lengths sum up to zero once suitably weighted by 1 and -1 . We do this via elementary combinatorial considerations, made possible by a well-known compactification of the three-dimensional affine space as a quadric in the four-dimensional projective space. The compactification is related to the Euclidean metric, and allows us to use a simple degeneration technique that reduces the problem to its one-dimensional analog, which is trivial to solve.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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