How can a random assortment of molecules arrange themselves in geometric shapes with such smooth sides and precise angles?

It has to do with how the molecules fit together. Imagine a jigsaw puzzle. You start with a pile of strangely shaped pieces, but when you put them together, you wind up with a rectangular shape, with smooth sides and sharp corners. No matter how many times you take it apart and put it back together, the puzzle will always form the same shape, with the same angles at the corners.

While molecules in a quartz crystal are not shaped like jigsaw pieces, they do fit together in a very specific way to form the crystal. A common example is a quartz crystal. A well formed quartz crystal has six sides, forming a hexagonal crystal that usually comes together at the end to form a point. The angles where those six sides meet will always be exactly 120°. It does not matter if the crystal is large or small, thick or thin, long or short. The flat parts of the crystal, called crystal faces, may be different sizes, producing crystals with different shapes, but the angles between those faces will still be 120°. If you have several quartz crystals, you can explore that for yourself.

You will need:

• several quartz crystals
• The printable Quartz Angle Sheet
• a printer
• a piece of stiff paper
• scissors

If you can't print the Quartz Angle Sheet, you will also need:

• a pen or pencil
• a protractor

Carefully cut out the Quartz Angle Sheet, being especially careful with the notch. If you can't print the sheet, cut a notch with an angle of exactly 120°. When you hold the notch against the crystal, it should fit perfectly with the angle between any of the six sides. This should work with any quartz crystal, no matter how large or how small the crystal is.

Note: It will not fit the angles from the crystal faces at the point. Those faces have different angles, which are also constant from one crystal to another.