Transcript

INSTRUCTOR

We’ll start by building the simplest of the models, which is the hexagonal close-packed array. First, we fill a tray with transparent spheres so that the row of spheres furthest away from you contains five and the row nearest to you contains four. Next, we put on another layer of the clear spheres. You will find that these fit neatly in the hollows created by the bottom layer.

Notice that the hollows have an almost triangular shape. There are two possible positions for the second layer, covering either triangles with tips pointing away from you or over triangles with their tips pointing towards you. We’re putting the second layer of the triangles with the tips pointing away from you, but it’s an arbitrary choice. It doesn’t matter which you choose.

The second layer now has three rows of spheres - four in the first, three in the middle and four in the next. Now, we add the third layer of spheres. For hexagonal close-packing, they have to lie directly above the first layer. Looking down on the model, you will see that we can do this now by covering the triangles with the tips pointing towards you.

Layer three of the model contains five spheres. Now, look again at the hexagonal close-packed model. We have coloured a sphere in the middle of the second layer.

Count up the number that are touching it. There are three in the bottom layer. There are six in the same layer. In the layer above, there are also three that touch it - making 12 in all.