Now, it turns out the last of the seven crystal systems is triclinic.

In the case of the triclinic lattice system, a, b, and c are not equal.

Nor are the interaxial angles equal to the 90 degrees, or equal to 1 another.

So as a consequence of that we have to specify all those

interaxial angles, along with a, b and c.

So this then describes for us what we mean by the seven crystal systems.

Now, we're going to depart a little bit, and

we're going to talk about the 14 Bravais Lattices.

And what we see here are, again, the representations of the cube,

the tetragonal lattice, the octahedral lattice, and the hexagonal lattice.

And this time, what we see for the cubic lattice,

is we actually have a total of three Bravais Lattices.

One of them, where we have what we refer to as a primitive cell,

that is, that lattice contains one lattice point.

Remember, each one of those corner positions represent one-eighth.

They're eight corners and therefore we have a total of one lattice point.

When we look at the second figure and if you look at that figure carefully,

it's referred to as face center cubic,

that is not only do we have lattice points that sit at the corners at the cube but

we also have lattice points which sit at the face.

So the corner positions now count as, again,

one-eighth times eight of those so that's now one lattice point.

And if you look at the faces, there are total of six faces that are associated

with a cube, and what we'll see then is each of those points are shared

by either the unit cell beside them, above them or in front of them.

So consequently, those six faces then become three lattice points.

So the three lattice points on the faces along with the lattice points

at the corner gives us a total number of four lattice points.

So we refer to this type of cell, since we have more than one lattice point,

a non-primitive cell whereas in the case of the simple cube, it turns out that that

happens to be winding up being a primitive lattice with one lattice point.

We turn our attention now to the third of the cubic structures and

now we have body center cubic.

And again we have a non-primitive unit cell.

We have a total of two lattice points.

The ones that are associated with the corners,

followed by the one that lies holy in the center.

Now, if we go down and we take a look at the tetragonal units, we now

have two of those, a simple tetragonal, and we have a body centered tetragonal.