Polytope Contractions within Weyl Group Symmetries
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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.
KeywordsCoxeter group Reflection group 3D polytopes Contractions of polytopes Branching rules
Mathematics Subject Classfication (2010)20F55 51F15 52B10 65N45
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