ISSN:
1572-9168
Keywords:
Primary 52.A45
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Let I be a tiling of the plane such that for every tile T of I there correspond a tile T′ of I (not necessarily unique) and an integer k(T, T′) (depending on T and T′), k(T, T′)〉2, such that T meets T′ in k(T, T′) connected components. Tiles T and T′ satisfying this condition are called associated tiles in I. Various properties concerning I and its singular points are obtained. First, it is not possible that every tile in I have a unique associated tile. In fact, there exist infinite families of tiles {F′} ∪ {F n:n≥1} such that F′ is the unique associated tile for every F n. Next, if x is a singular point of I, then every neighborhood of x contains uncountably many singular points of I. Finally, the set of singular points of I is unbounded.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00151501
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