Conductive rings of nonpolytopal fans
- Authors: Matveev M.N.1
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Affiliations:
- Department of Mathematics
- Issue: Vol 38, No 1 (2017)
- Pages: 82-93
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/198669
- DOI: https://doi.org/10.1134/S1995080217010139
- ID: 198669
Cite item
Abstract
Although there is a lot of polytopality criteria for fans, it is generally not clear how to visualize the reason why a fan is (non)polytopal. The paper describes a geometric structure called a conductive ring that is easy to find visually in fans. Found in a fan, a conductive ring means that the fan is nonpolytopal. The paper shows that conductive rings provide a very simple and useful tool for analysing, modifying, and creating fans. In particular, constructing a nonpolytopal fan with a conductive ring, the paper discovers a paradox concerning intermediate value properties of face polytopes: in a bundle of very similar conditions the properties either reveal themselves or not depending on small details.
Keywords
About the authors
M. N. Matveev
Department of Mathematics
Author for correspondence.
Email: miklem@mail.mipt.ru
Russian Federation, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700