Quaternionic construction of the \(W(F_{4})\) polytopes with their dual polytopes and branching under the subgroups \(W(B_{4})\) and \(W(B_{3})\times W(A_{1})\) (Q2836541)
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scientific article; zbMATH DE number 6183424
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quaternionic construction of the \(W(F_{4})\) polytopes with their dual polytopes and branching under the subgroups \(W(B_{4})\) and \(W(B_{3})\times W(A_{1})\) |
scientific article; zbMATH DE number 6183424 |
Statements
3 July 2013
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regular polytope
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semi-regular polytope
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4D polytope
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maximal subgroup
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branching
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dual polytopes
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quaternions
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Coxeter-Weyl group \(W(F_4)\)
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Quaternionic construction of the \(W(F_{4})\) polytopes with their dual polytopes and branching under the subgroups \(W(B_{4})\) and \(W(B_{3})\times W(A_{1})\) (English)
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Representing the group elements and the vertices of the polytopes by quaternions, the authors construct 4-dimensional \(F_4\) polytopes and their dual polytopes as the orbits of the Coxeter-Weyl group \(W(F_4)\).
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