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Polytope Contractions within Weyl Group Symmetries

  • Marzena SzajewskaEmail author
Open Access
Article

Abstract

A general scheme for constructing polytopes is implemented here specifically for the classes of the most important 3D polytopes, namely those whose vertices are labeled by integers relative to a particular basis, here called the ω-basis. The actual number of non-isomorphic polytopes of the same group has no limit. To put practical bounds on the number of polytopes to consider for each group we limit our consideration to polytopes with dominant point (vertex) that contains only nonnegative integers in ω-basis. A natural place to start the consideration of polytopes from is the generic dominant weight which were all three coordinates are the lowest positive integer numbers. Contraction is a continuous change of one or several coordinates to zero.

Keywords

Coxeter group Reflection group 3D polytopes Contractions of polytopes Branching rules 

Mathematics Subject Classfication (2010)

20F55 51F15 52B10 65N45 

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Copyright information

© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of BialystokBialystokPoland
  2. 2.Centre de recherches mathématiquesUniversité de MontréalQuébecCanada

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