Next picture. Now we are looking at the three on the top which you do rotate.

Next picture. I want to show you how to go from the polarized to the vector equilibrium, just rotate them.

Next picture. Now they're beginning to look at a little larger vector equilibrium of a there are four balls to the edge so it is a three frequency vector equilibrium. And notice, then, there is a triangular face towards us, and there is a red ball at the center, there is a new nucleus beginning to show in the eight faces, but it will not be a nucleus until it has it's two layers around it. But this is the one that has 92 balls in the outer layer that I gave you yesterday, 42 in the inner and l2 in the innermost.

Next picture please. Now I've opened that up so you could see all the different layers as they come together and these balls have different colors when the amount of light that they get from the nucleus differ. Because I talked to you about trying to find a nuclear set of events that would repeat itself, and so I get absolute uniqueness with those first three, four, up to the four, and then the fifth we get suddenly repeating. But these colors, relate then to the amount of light or radiation available or the attraction from the central nucleus to any given layer of ball.

Next picture. You can see on the top one, the twelve corners are always in direct contact, so the light goes right through them.

Next picture. This is a picture taken through one of my models. I have used the beads which Meddy found over there the other day. They are lovely beads that were developed during W.W.I, very uniform radius, and they are glued together. And they are all transparent, but some of them are colored. You are looking at the vector equilibrium. Would you remove me now so that I am not in the way of the picture. And, I want you to see, what really kind of extraordinary thing, the bright white lights of the twelve corners, you can see how they go, is simply giving, there is a red at the center, but it gives you a little sense of what I mean by the relative amount of light that can come through the different balls in a different position. And this particular model, we get where you'll find enormous agreement with much of the light emission microscope kind of things of atoms.

Next picture. Now, I spoke about spaces between spheres. And here is a tetrahedron. Wait a second, will you have the picture still. I'm doing this so you can really look at the picture on the wall because it is well done. There is a space, then, inside here. And what do we know about it? Well, it's got four balls around it. If I made this out of pingpong balls and glued them together. Then I took a safety razor and cut away everything except between, we'd find then there is a little triangular concave triangle up at the top here nesting down, touching three others making would you remove my picture from here over in the left hand side there you will see them coming together. There are four triangles, and I have four spaces, therefore it is the octahedron. But it is a concave octahedron. So at the center of the tetrahedra there are concave octahedra.

And now I'm going to make an octahedron, here are three and three, our friend "precess" and it becomes the octahedron. If I would have done that before you did the cube one, you might have thought of it. But there is your octahedron. Now the octahedron, then, has six balls. And you see a square section. And you remember then, how when we made it a three ball it had a square section, so you really feel those things. And, so there are six balls, and they make a square section so six balls touch each other, each ball touches each other with a square section. See this top one here if we glued in the ping pong ball and cut away everything, it would leave me with a concave square. So there are six concave squares where the six balls are. But that also then, there are eight triangular windows, because it is the octahedron. So what you have then,

Next picture, will be the vector equilibrium. The concave vector equilibrium with eight with the six concave squares and the eight triangular windows. These are all the spaces there are. There are only two kinds of spaces between closest packed spheres. Concave octahedra, and concave vector equilibrium. And they are pretty interesting because you start with the vector equilibrium and it goes down to that octahedron where the things double up, so it looks like it could be that the openness doubles up to itself to it's octahedron in its own space in here, something to do with that.

Next picture please. Now I am going to take. There are other pictures of these. Here we're doing that in a really rather open frame so that you can see the vector equilibrium with its triangles the octahedron on the left, and the concave vector equilibrium on the right.

Next picture. Now we can see two vector equilibria coming together with one another. I've showed you the square faces come to one another, and that there is an octahedron between the two. Remember that? That then left a space on the outside, so that there is an external and internal octahedron in relation to the vector equilibrium.

Next picture. Now, what you are seeing there are a number of the actual ping pong balls. In the lower right hand side are the concave octahedra, in the lower middle right side are the concave vector equilibria. So you put the little triangular windows of both together, making the edges match, and together they come to create, then, holes that fill all space. But you get an aggregate of balls, where you see the convexity of it on the outside, you're seeing only the concave side. This looks very much as if, I don't know if you you must have done it, picking up fossils where clams have been fossilized into clay. And the clam died in between because the two clam shells came apart, so what you see is the concave side of the shell in the clay matrix. That's what it looks like. But you keep putting these together and they keep filling all space, but the outer group will always be in the concave side. So what we are now seeing is really very interesting. There is some relationship between spaces and spheres. And remember that there were nests that you didn't use because the aggregate of the three only let you use one set of the nests at a time. There is an alternate set of nests which are also then these spaces that are in there, and there are two kinds the octahedron and the vector equilibrium.