Remember from our discussions in class that a Unit Cell is the smallest bit of a crystal which preserves BOTH its symmetry and its composition. Unit Cells are arranged in crystals in a selection of structures called Lattices, which can essentially be thought of as permssible frameworks for arranging Unit Cells: for any kind of unit cell, there is at least one lattice via which it can be arranged (read: via which a crystal can grow). There may be more than one permissible Lattice for any given Unit Cell - the only constraint here is that the lattice may not have a higher order of symmetry than the unit cells which are being arranged (though the lattice MAY possess lower order symmetry).

But what, in fact, does any of this mean? The best way to find out is to try and distinguish the Unit Cells and lattice structures of a variety of symmetrical objects.

What I have done below is uploaded several Escher pictures, which offer all sorts of symmetrical arrangements. What I want you to do is

The pictures I want you to work with are below. Print them out, and then you can overlay a transparency on them to identify the patterns. Or, you can download them into a drafting program and scribble on them through your computer - either way will work! The goal here is to assess the symmetry of the individual "blocks" and their arrangement as a complete image.