Arbitrarily large neighborly families of symmetric convex polytopes (Q1074868)
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scientific article; zbMATH DE number 3949174
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Arbitrarily large neighborly families of symmetric convex polytopes |
scientific article; zbMATH DE number 3949174 |
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Arbitrarily large neighborly families of symmetric convex polytopes (English)
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1986
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A family of convex d-polytopes in \(E^ d\) is called neighborly if every two of them have a (d-l)-dimensional intersection. The purpose of this paper is to solve a problem of Grünbaum, showing that for every d, \(d\geq 3\), there exist arbitrarily large neighborly families of centrally symmetric convex d-polytopes in \(E^ d\), moreover, each member in such a family can be chosen to have a k-flat center of symmetry, for any k, \(0\leq k\leq d-1.\) In addition the author proves that for every \(d\geq 4\), m and t, \(0\leq t\leq d-1,\) there exists in \(E^ d\) a neighborly family of m congruent d-polytopes having a t-flat center of symmetry.
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neighborly families of centrally symmetric convex d-polytopes in
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\(E^ d\)
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neighborly families of centrally symmetric convex d-polytopes in \(E^ d\)
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