Aste T., Weaire D. Pursuit of perfect packing (IOP 2000)(147s).pdf
Aste T., Weaire D. Pursuit of perfect packing (IOP 2000)(147s).pdf
Aste T., Weaire D. Pursuit of perfect packing (IOP 2000)(147s).pdf
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12 Loose change and tight <strong>packing</strong><br />
Figure 2.7. Spontaneous clustering into the triangular lattice for bearings on a plane shaken<br />
vertically from high (top) to low accelerations (bottom). Single images (right column) and<br />
second averaged images (left column). (Courtesy <strong>of</strong> J S Olafsen and J S Urbach.)<br />
the plane made with equal, regular triangular tiles. This tessellation has three<br />
properties:<br />
(1) all the vertices are identical, that is, lines come together in the same way at<br />
each <strong>of</strong> them;<br />
(2) all tiles are regular (that is, completely symmetrical) polygons;<br />
(3) all polygons are identical.<br />
This is called a regular tessellation. How many tessellations with such regularity<br />
exist The answer is three: they correspond to the triangular, square and hexagonal<br />
cases, which are shown in figure 2.9. In these three <strong>packing</strong>s the discs are<br />
locally disposed in highly symmetrical arrangements and the whole <strong>packing</strong> can<br />
be generated by translating on the plane a unique local configuration, as in the<br />
simplest kinds <strong>of</strong> wallpaper.