 I'm going to show you now how to figure out the number of lattice points of a simple cubic cell, a body centered cubic cell, and a face centered cubic cell. What number of lattice points is like? How many total atoms are within the actual unit cell itself? When we look at this, we'll draw some cubes. Simple cubic, what do we say? One, two, body centered cubic, body centered as the same as the simple cubic center of the body. There's a full lattice as a face centered cubic with the same height as the simple with spaces. Any questions about any of this stuff as to why there are all of these things? Now let's think about the lattice points. Like I said, we're trying to determine how many actual atoms are within that unit cell. There's eight atoms associated with the simple cubic. Everybody's okay with that. We call the number of lattice points Z. Z is going to be, well, eight. We get that from the counting, one, two, three, four, five, six, seven, eight. Then we have to ask ourselves, how much of that actual atom is within that unit cell? Well, if you look at it and think about it, you'll find that it's only one eighth of that atom. What we do to find the number of lattice points is say one eighth times eight or eight times one eighth like that. Number of lattice points for this one, what are we going to do if you think at least the first part is going to be the same as this, right? That makes sense because there's eight on the outside and how many of each of those atoms is within the unit cell? One eighth of them. So it's eight times one, one eighth like that, but is there anything else inside of that cell? What? A whole atom, right? So it's eight times one eighth, is there going to be something similar on this one? What is it going to be? Eight. Times one eighth. Now we're going to add something to this one. Six. Right? Six. And can anybody figure out how much is inside by the sides of those poles? Oh. Okay. So what is this? That's one plus six times a half, three. So z equals four. So number of lattice points for FCCs that are always four, number of lattice points for VCCs are always two, number of lattice points for simple qubits are always one or primitive qubits. You might see these called something. Okay. Question? I'm not sure if it's like, say it's like the top, you know, there would be another one on top there. Yeah, exactly. Uh-huh. Yeah. So remember that diagram that we showed earlier where there's going to be another cube. So this one is going to be half inside this one and half inside the bottom one down there. One eighth inside the top one, one eighth inside the bottom. Is everybody okay with that? That's a good question.