Difference between revisions of "Spacefiller"
From Encyclopedia of Mathematics
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Latest revision as of 12:16, 12 December 2013
$ \def\T{\mathcal T} % tiling \def\P{\mathcal P} % protoset $
In the theory of tilings a spacefiller is a prototile that admits a monohedral tiling.
In other words, a tile $T$ is a spacefiller iff there is a tiling $ \T = \{ T_i \} $ such that all its tiles $T_i$ are congruent to $T$.
Simple examples of spacefillers are all triangles and all quadrangles for the plane, and all parallelepipeds for the space.
How to Cite This Entry:
Spacefiller. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Spacefiller&oldid=30990
Spacefiller. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Spacefiller&oldid=30990