The existence on non-tiles and non-facets in three dimensions (Q760012)
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scientific article; zbMATH DE number 3883116
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The existence on non-tiles and non-facets in three dimensions |
scientific article; zbMATH DE number 3883116 |
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The existence on non-tiles and non-facets in three dimensions (English)
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1985
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Non-tiles are convex polytopes, of which isomorphic copies will not tile the space locally finite and face-to-face (that is, neighbouring tiles meet in a face of each). Non-facets are convex polytopes, of which isomorphic copies will not fit together as the facets of a higher dimensional convex polytope. It is proved that there are infinitely many 3-dimensional convex polytopes which are non-tiles as well as non-facets, thereby answering a question of Danzer.
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convex polytopes
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non-tiles
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non-facets
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