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What exactly is a frieze pattern?

A frieze pattern, like the one's you saw in the architecture earlier, are patterns that extend to the left and the right. In their simplest form, these patterns can be mapped onto themselves by a horizontal translation. There are also a few other transformations that produce more complicated frieze patterns.

Let's take a look at some examples. Click on the following images to learn more.

This is an example of a frieze pattern. Notice that you have one main pattern that repeats by being translated horizontally to the left and right. This is another example of a frieze pattern. Notice the left foot and right foot are repeated over and over again by a horizontal translation to the left and right.

Question

What other transformations might be used to make a frieze pattern? Are there any transformations that won't work?

We know we can use translation. We can also use reflections and rotations. These transformations preserve the shape and size of the figure. We can't use dilations since they do not preserve the size of the figure.