Complexity of convex stereohedra (Q1274100)
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scientific article; zbMATH DE number 1238058
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Complexity of convex stereohedra |
scientific article; zbMATH DE number 1238058 |
Statements
Complexity of convex stereohedra (English)
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21 November 1999
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The author proves that any \(d\)-dimensional stereohedron, i.e., a spacefiller which admits an isohedral face-to-face tiling (that is, a tiling for which its symmetry group acts transitively on the tiles), has at most \( f(d) = 2^d ( H(d) - {1\over 2}) - 2 \) \((d-1)\)-dimensional faces where \( H(d) \) is the maximal index of the translation subgroup in an arbitrary crystallographic group (of dimension \(d\)). This improves the known bound by Delaunay (=Delone) (1961) by \( 3 \cdot 2^{d-1} \).
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isohedral tilings (of Euclidean \(d\)-space)
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stereohedra
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spacefiller
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0.7423802614212036
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0.7359281182289124
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0.7243875861167908
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