Abstract
Pegged tilings localize the defining property of
or Laguerre tilings, and, like them, admit a natural duality (corresponding to the Delaunay tilings of
tilings). It can thus be shown that the projection method, which is generally used to construct quasi-periodic tilings related to
tilings of higher dimensional lattices, applies to this wider class of tilings. Of further importance is that pegged tilings are just those which can be lifted to the graphs of convex functions with a certain strong locally polyhedrality property. The context of convex functions also provides a direct way of viewing the projection method, and leads to alternative pictures of special cases such as various grid methods.
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McMullen, P. Duality, sections and projections of certain Euclidean tilings. Geom Dedicata 49, 183–202 (1994). https://doi.org/10.1007/BF01610620
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DOI: https://doi.org/10.1007/BF01610620