Email this article An intermediate value theorem for face polytopes
- Authors: Matveev M.N.1
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Affiliations:
- Moscow Institute of Physics and Technology
- Issue: Vol 37, No 3 (2016)
- Pages: 307-315
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/197751
- DOI: https://doi.org/10.1134/S1995080216030173
- ID: 197751
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Abstract
The paper proves a theorem on polytopal fans and face polytopes that can be treated as an intermediate value theorem for face polytopes. According to this theorem if all fans FS obtained from a fan F by replacing one of its cones K with a subdivision S of K in some set H are polytopal, then the fan F is polytopal as well. Moreover, if PS, S ∈ H, are arbitrary face polytopes of the fans FS, then some positive combination of PS, S ∈ H, is a face polytope of the fan F. The reverse of the theorem is not true.
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About the authors
M. N. Matveev
Moscow Institute of Physics and Technology
Author for correspondence.
Email: miklem@mail.mipt.ru
Russian Federation, Institutskii per. 9, Dolgoprudny, 141700
