Jump to page: 1 2 3 4 5 6 7 8 9 10 11 12 Hands-On

Connecting the top of each of four adjacent white-colored men produces a parallelogram. If we continue joining the tops of the white-colored men, we find that another parallelogram is made. However, this new parallelogram is not a translated version of the first. (In other words, the first parallelogram cannot be simply moved onto the second.) Notice, however, that the second parallelogram and its design is a reflected version of the first parallelogram and its design. Specifically, the second parallelogram is obtained by reflecting the first over a vertical axis and then translating. The following animation explains the process:

Such a transformation, consisting of a reflection and a translation is called a glide reflection. The first parallelogram and its design produces the second parallelogram and its design by a glide reflection.

Now notice that the two parallelograms, put together, can tessellate the rest of the design through simple translations.