Email this article An intermediate value theorem for face polytopes
- Authors: Matveev M.N.1
-
Affiliations:
- Moscow Institute of Physics and Technology
- Issue: Vol 37, No 3 (2016)
- Pages: 307-315
- Section: Article
- URL: https://bakhtiniada.ru/1995-0802/article/view/197751
- DOI: https://doi.org/10.1134/S1995080216030173
- ID: 197751
Cite item
Open Access
Access granted
Subscription Access
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.
Keywords
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
Supplementary files
