Next picture. I'm doing some I want you to think of a big tetrahedron now in which something else is going on. There is a center of gravity there is a center of the base triangle, you can see that. Above it, there is a point, and that is the center of gravity of the tetrahedron. That's where the one quarter tetrahedron comes into it, and above it, an equal increment there is a vertex of a one-eighth octahedron, which is superimposed can you get me out of the picture, I'd like every bit that we can get of the picture that we are looking at there. There is, then, a tetrahedron, and it encloses with the same common base, a one-eighth octahedron and enclosed within it is a one-quarter tetrahedron. Now a one-eighth octahedron has a volume of 2, remember, an octahedron has a volume of four so one eighth turns out to be 2. And the one quarter tetrahedron, then, has a volume of where the one-eighth octahedron is two, and the tetrahedron, itself, in this case, I'm going to make it a volume of 4 where the volume of the tetrahedron is 4, the one-eighth octahedron will have a volume of 2, it has the same base as the big tetrahedron, but half the altitude, and the one-quarter tetrahedron has one quarter the altitude and the same base, so it is if the big tetrahedron is 4, the small tetrahedron is 2, and the bottom one is 1. That is, the volume of the one-eighth octahedron turns out to be exactly twice the volume of the one-quarter tetrahedron. One-eighth octahedron is twice that of one quarter tetrahedron.

Next picture please. We're going to have some very interesting things showing up here. Now I've got four black one-quarter tetrahedra coming out of the big tetrahedron.

Next picture. Now, there is a regular one-quarter tetrahedron. And as you know the regular equilateral triangle has three perpendicular bisectors. I'm taking a plane perpendicular to the base plane, three three such planes and chopping, they come down to the perpendicular bisectors, and they cut the one-quarter tetrahedron into six parts. Remember, if I stepped tetrahedron up to having a volume of 4, for convenience, and we made, then, the one-eighth octahedron a volume of 2, and we made the one-quarter tetrahedron a volume of one. I'll now chop these all up into units, so that each one will be one-sixth of one. For a moment I'm going to multiply everything now. So each one of these blacks would be 1/24th of a tetrahedron. There were four faces, and they break into six parts it is 1/24th of a tetrahedron. And I call that unity. Then the tetrahedron has 24 and all the other numbers multiply the same way.

Next picture. That 1/24th of a tetrahedron is a very interesting thing, because you can make it out of one triangle. I have the dimensions over there. It is not a right triangle, but it is a triangle and so you can fold it up out of one triangle. When you fold a tetrahedron out of one triangle into a tetrahedron then it has, for instance, you can take an equilateral triangle, bisect its edges, interconnect, and you get four triangles and then you fold on those truncated corners and you get (a tetrahedron). So when you do, energies that would bounce around inside of a triangle then keep bouncing around inside the tetrahedron. So, this is an asymmetrical tetrahedron that is folded out of all one triangle. And therefore it is an energy inhibitor. It will hold energy bouncing around on the side of it.

Next picture please. Now, move my head out. You'll see the one-quarter tetrahedron and there are on its sides there, excuse me, we have not done this here properly, so that I'm going to ask you to go back, if you will remember where I had that black skeleton where I had the tetrahedron, and under the eighth octahedron and under it the quarter tetrahedron and there were a whole lot of little lines there. I not only took this vertical plane of cleavage of the perpendicular bisectors of the quarter tetrahedron, but also of the one-eighth octahedron, so it too broke into six parts. But because the one-eighth octahedron had the volume of 2 and the one-quarter tetrahedron had the volume of 1. When I took one away from the other, one is under the other, then what the difference the space between the one-quarter tetrahedron and the one-eighth octahedron is also one. Because it's total volume is two and the thing enclosed is one, so the space between them is one. So then when I have these vertical planes cutting both the one superimposed on the other, the perpendicular bisectors of the base triangle, each one breaks into six, and the six ones on the

Next picture, I'm going to have, the top ones will be gray and the bottom ones are going to be black. That's what you're seeing there on the lower left-hand side, are the gray ones that lay on top of the black ones. And they will fold in on top of it, and

Next picture. There they are the greasy are on top of the blacks. Can you see them there in the lower left hand corner? And each one the gray is exactly the same volume as the black one. In other words the space between the one-quarter tetrahedron and the one-eighth octahedron was equal to one total volume being two which was the volume of the one-eighth octahedron. So, I find then, that the, if I'm going to call then the black 1/24th, I'm going to also then, and let them be unity, so that would make the tetrahedron, it will have to be 24, and then we find that each gray there and each black have a volume of l. So what you're looking at is a set of 6 sitting on top of 6. The volume of 12 involved in what you're looking at there. These are very asymmetrical. These are what I have here laying on the table. There is 1/6th of a quarter tetrahedron. I call that an "A". And here is a sixth of the 1/8th octahedron sitting on it, and it's a "B". They are obviously very different shapes. And we call this the "A Quanta Module" and the "B Quanta Module" because remember then that octahedron and tetrahedron do fill all space. And when we break them up, both "A" we get something common to both tetrahedron and octahedron, you suddenly can make all the geometries. The "A Quanta" and "B Quanta" these two alone complement one other to make all the geometries. So they've got to be very, very, very important. This is one of the most important of all the discoveries I ever made.

I'd like to just pass that to you, and hand it around so that you can get a little feeling of it.

And now the next picture, there you'll see two one-quarter tetrahedra fractionated which equals one one-eight octahedron.

Next picture. Now I am making a large, you're doubling the size of a one-eighth octahedron. On the lower right hand side you'll see a one-eighth octahedron, and I have put three of those on the corners of the thing on the left. I'm doubling the size of the one-eighth octahedron. And you'll see then there is that one-eighth octahedron in each corner, and then there is one sitting on top of it there. You can see six one-eighth octahedra there. But you remove those three top ones,

Next picture, and you'll find that you have what was inside there was a tetrahedron. Now, this is now a new, this is the one-eighth no this is a one-quarter tetrahedron doubled in size, and in order to make it you'd have to take, you have three regular one-quarter tetrahedra on the corners, and then inside them, you start piling you remember, now, the blacks are the A's, so there is A, A, and then the B. A,A,B. But I found that that space, in which they are. Notice, you've got a three-pointed star here haven't you? Of greenness. So I'm going to be able to take those A's and B's out of that space and rearrange them so they don't look like that at all, but they'll still fill the same space. In other words, they are reorientable within the same space.

Next picture. Now, there are the same ones, but their narrow ends are in and they were not that way at all before. To find, then, they are all radiant from the center, do you notice. Can you go back one picture? This one where they are radiant from the mid-edge inwardly. They are butt-end, they are putting their energies inwardly.