Tessellation Symmetry, Page 5 of 6:
Rotation (Turning)

This is the basic "tile" shape of the tessellation on this page: it's a goldfish. We make the tessellation is by repeating the tile and fitting all the tile's copies together.

There are three ways that a tile can repeat: Translation, Reflection, and Rotation (Sliding, Flipping, and Turning).

At right we see the third way: Rotation (Turning). The shape of the fish repeats by rotating...turning...spinning.

In the first example at right, the golfish turns 120 degrees, two times. In other rotational tessellations, like the second example at left, a tile might only rotate 180 degrees once. In still other rotational tessellations the tile might rotate 90 degrees four times, and so on. Can you guess how many times a tile would rotate, if each rotation were 60 degrees? 45 degrees? 30 degrees? 20 degrees? 15 degrees? Hint: 360 is an important number in geometry.