In this lesson I'm going to introduce a little device that we can use to help understand some of the things that we just been describing with respect to face center cubic structures. It's called the Thompson Tetrahedron. What we have is the very 4 of the surfaces of the tetrahedron, we determined those two lessons back and we're able then to identify the vectors that describe the directions of closest approach and corresponding we can talk about the planes. And since we have 4 of those surfaces, we have a tetrahedron that we can take a look at. So, if I fold all of those out, and I look at them in this image that I have up here. What I've done is to take each one of those faces, paste them together, and I paste them together in a particular way. So if you look at the D's, those are all going to match when I do my folding. And then I have fold lines along AB, BC, and CA. So the first thing you want to do is to cut out the tetrahedron, or I'm sorry, print the triangle out and then cut along the lines D to D, D to D, and D to D on all 3 sides of the triangle. Now what can be done, is to take this image and print it out on paper, and then what you can do is take that paper and do a couple of simple things. That is, you cut along these lines on the outer edges of the triangle. And what you can then do is fold along these lines. And then what you'll do is you'll wind up producing your tetrahedron. So here it's printed out on the paper and now i'll cut and fold and when I do that, I get this image that I have over here. This is my tetrahedron and I can begin to see how by orienting this tetrahedron in different directions, I'm going to see different planes and directions that are going to be susceptible to the process of deformation. So for example, let's take a look at the way I have the tetrahedron oriented now. If I were to say that along this axis is the axis of my stress. Then, what I would know is, that the axis of my stress acting along here with my crystal oriented the way I have it oriented. I would immediately know that this plane down here at the bottom is a one one one type plane. And I would also know that the normal to that plane would be the one one one direction. So if my stress axis were acting along this direction here, what I would immediately see, is that any slip on this plane would not occur. In other words, I have no deformation that can occur on this particular slip plane and in these directions associated with applying a tensile stress along this direction perpendicular to that one one one face. However, each one of these faces and each one of those slip systems would wind up being able to deform as a result of the deformation axes. So you begin to see how you that you can put some of these notions together and come up with a visualization of the process of deformation in these FCC crystals. Thank you.