The existence on non-tiles and non-facets in three dimensions
type: Item
instance of: scholarly article
title: The existence on non-tiles and non-facets in three dimensions
zbMATH Open document ID: 0554.52010
DOI: 10.1016/0097-3165(85)90023-8
author: Egon Schulte
published in: Journal of Combinatorial Theory. Series A
publication date: 1985-01-01T00:00:00Z
review text: 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.
reviewed by: Károly Bezdek
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 05B45
Mathematics Subject Classification ID: 52Bxx
zbMATH DE Number: 3883116
zbMATH Keywords: convex polytopes
zbMATH Keywords: non-tiles
zbMATH Keywords: non-facets
MaRDI profile type: Publication
full work available at URL: 0097-3165(85)90023-8
OpenAlex ID: W2011736325
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description: scientific article; zbMATH DE number 3883116