Indecomposable Coverings with Concave Polygons

Authors:
Dömötör Pálvölgyi
Affiliations:
Ecole Polytechnique Fédérale de Lausanne, EPFL-SB-IMB-DCG, Station 8, 1015, Lausanne, Switzerland
Venue:
Discrete & Computational Geometry
Year:
2010

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Abstract

We show that for any concave polygon that has no parallel sides and for any k, there is a k-fold covering of some point set by the translates of this polygon that cannot be decomposed into two coverings. Moreover, we give a complete classification of open polygons with this property. We also construct for any polytope (having dimension at least three) and for any k, a k-fold covering of the space by its translates that cannot be decomposed into two coverings.