Special Tiles

2. Planet of the Shapes

Special Tiles

The design on Penrose Plaza, composed of fat and skinny diamonds, is an example of a Penrose tiling (see "Planet of the Shapes"). It is named after mathematical physicist Roger Penrose, who, in the 1970s, found a way to assemble two related shapes, which he called "kites" and "darts," into patterns that cover a flat surface without leaving any gaps.

What makes both the kite-and-dart pattern and the diamond pattern special is that the tilings are not periodic. They do not repeat themselves at regular intervals, so the patterns are irregular.

Penrose tilings made up of fat and skinny diamond tiles (above) and kite-and-dart tiles (below).

Interestingly, the tiles in both types of patterns have proportions that are related to the golden ratio (see "The Golden Ratio"). For example, the distance from the sharp tip to the blunt end of a kite tile equals the distance from the notch to the sharp tip of a dart times the golden ratio.

Penrose was just playing around when he first put together his non-periodic tiling. Several years later, scientists discovered a group of strange materials, called "quasicrystals," made up of metal atoms arranged in an unexpected pattern. Penrose's tiling patterns gave scientists hints on how it might be possible to position atoms to create an orderly but non-repeating structure.

NEXT: Tilings That Come to Life