
Mathematicians ask: What shapes a tile? In what ways do
they tile? In how many ways do they tile? J. Kepler, P.J. MacMahon, and M.C. Escher are
some of the early pioneeers who explored these questions. Many mathematicians (notably, B.
Grünbaum and G.C. Shephard) have contributed to the current state of knowledge in this
active field. But many others are also contributors since tilings provide models for
natural phenomena such as crystal structure and cellular structure of plants, they are
encountered in coding theory and nearest neighbor problems, and they provide wonderful
recreational problems. see "Visions of Symmetry" (Schattschneider), and Computer Software for
Tiling at http://www.geom.umn.edu/software/tilings/TilingSoftware.html
