In this article, you can read about many different kinds of tiling, the math behind them, how to make them, and classify them! You can also experiment interactively with tilings using .

Contents

The Tilings Around Us What is a tiling? We are surrounded by familiar tilings every day, like brick walls and tile floors.

Tiling Terminology To mathematicians and scientists, there are an infinite number of different kinds of tilings -- symmetric ones, ones made with one shape of tile, even completely random ones. Learn some of the mathematical terms and definitions about tilings

Periodic Tilings Tilings naturally fall into two classes. Some have repeating patterns, and some don't. This page takes a closer look at repeating, or periodic tilings.

Symmetric Tilings A floor covered with square tiles and a floor covered with hexagonal tiles both have regular, symmetric, repeating patterns, but they are clearly different. What is symmetry, and how do you measure it?

Wallpaper Groups Wallpaper groups are sets of rules for building highly symmteric tilings froma single piece. Surprisingly, there are exactly 17 of them! See animations of these beautiful and intriguing tilings here.

Non-Periodic Tilings Some tilings don't repeat. However, that doesn't mean that they a totally random. Some of the most fascinating tilings have an element of randomness mixed in with a basically regular pattern.

Penrose Tilings Penrose tilings are aparticularly famous family of nonperiodic tilings. Using two kinds of tiles and a simple set of rules, amazing nonperiodic tilings develop.

Learning More Links to other tiling pages on the Web and a bibligraphy of tiling books point the way to further study on your own.