Next picture. Now they are radiant from the center out. They radiate energy out. The same phenomena, same A and B, rearrangeable in space. Brings about completely different energy conditions. This began to really get me. And you realize if you took the center of gravity of each of those A's and B's, the center of gravity's are deployed in this picture, in the first one they are conserved. I don't know whether you've ever seen X-ray diffraction where you hit metals and so forth, and you really can see these displacements take place like that.

Now I'm going to talk some more about these A's and B's. They are very, very fascinating. I found then, what I was putting together was this group right here, and they can be put together two ways. Here's an A and an A. But the B has been put here. In this hand I've got an A and an A base to base and the B is out here. An A and an A you can put them that way, but the point is, when you then turn them like this you find that they are, this is an isosceles here, the isosceles in a number of different directions. This is an isosceles triangle. So they are rotatable. They are a right angle, a right angle, a right angle. Three sets of right angles in the inside here, which allows changing the right angles around because that is an octahedronal center. You realize how rotatable that is. And they're all these isosceles forms, so that they can really be changed around.

Now, the next thing about those A's and B's. You can go on and make all, and I have, I've made all of the geometries there are. But when I handed those to you, if you'll look at them carefully you'll see that there is also, a little line, a curved line in there as they come together here would you come take this one and pass it around? This then, this point is the center of the spheres in closest packing, and these are spheres in closest packing. You'll see how much of the what some of them, part of them, occur in the space, and part of them are inside the spheres. And so, as they keep coming together, they continually put spheres together. Now, the next thing I discovered which was really I told you then, this fills all space, the rhombic dodecahedron, and it's face, it's mid-face is at the point of tangency between the adjacent spheres in closest packing. And then I found this extraordinary thing. I can make this into an octahedron. Because of all those different 90 degrees. I can rotate this piece around an incredible number of ways, and this thing fits down into the rhombic dodecahedron here, so this is what I call the "coupler," between any two spheres. It is also all space filling just as the rhombic dodecahedron is. You'll see the two spheres kissing one another in here. So it's volume consists now of each one of those is 1/24th of a tetrahedron, and there are obviously 3,6,12 and 12 there are 24 of them which is the same as one tetrahedron, isn't it? There are twenty four of them, so it's back to our friend unity like the tetrahedron. And, I call this the coupler. And I find then what it does, now you're going to see a series of pictures where, you can rotate, you can make these in different colors the A's and the B's, to see what you're getting. But the numbers of rotations in place within the coupler, seem to be very close to the same number as the periodic table of the atoms it looks like it's 92 rearrangements within it.

Next picture please. I'm just going to show these to you fast so that you can have a little feeling. Oh, there you are looking at the octahedron one half of the octahedron is broken up into the A's and B's, the top part.

Next picture. At the upper right hand then, is an A and the white is a B. The only difference between these is another unit of altitude with the same base. As long as you have the same base, and increase one unit of altitude, then each is always the same fraction. So the orange, then, is one unit more of altitude, and the black is the top of the tetrahedron. Then it goes another one, and another one, always the same increments, therefore the volumes are always the same. They get thinner and thinner and thinner. We find then, energies that are putting on a conductor like this, really tend to keep going the waves going outwardly , and out, getting flatter and flatter, getting more and more parallel to the conductor itself, and then trying to precess off of it. This is one of the problems with conductors.

I want you to understand, how a wave, because this can act as an energy input, each one of those a wave going on a conductor system. You don't have to get very much altitude then, and they seem to be absolutely parallel.

Next picture please. I'm just showing A's and B's a little closer here. Next picture. And there we are seeing, I put together, I handed to you just a minute ago, three of them. And, this is the negative A B. Because one is a positive and one is a negative which way I do it. You can fill all space with the negative one. These are very extraordinary tetra, because you remember a regular tetrahedron can't fill all space, but this one can fill all space. Or the positive can, or they can do it together. And I call this there are two ways of putting the six together positive and negative. They can go this really long way, and they I call these the SYTE the little one is a MYTE, and these are the SYTES. And you can see them in the two different arrangements. And, they fill all space. So here, if we're using a Quanta as unity where tetrahedron now must be 24, and octahedron is 4 x 24, that's 72 and so forth, we then find, that these have a basic unit of 6 6 quanta. This is very interesting to have six quanta, because we found there were 6 quanta when we spoke about the basic putting the proton and the neutron coming together around the two models and we got the "sixness" the basic six quanta. There are six quanta in there, and they will fill all space, both positive and negative, so that they do all the tricks you can possibly do.

Next picture please. These pictures just go on making sytes and mytes.

Next picture, please. This was part of the rhombic dodecahedron. I found I could open it and fold it, putting tapes to the edges, and they would all fold together again.

Next picture. There's the coupler. Next picture.

Now, that's the way you could make either a positive or a negative. You must start with two A's and then either a B on the right side or B on the left side.

Next picture. And I'll identify then where the rhombic dodecahedron is, you can see on each vertex of the vector equilibrium, and then where the coupler occurs. Now there is going to be a series of these.

Next picture. where you see your spheres at the center.

Next picture. Next picture. Not very sharp.

Next picture. These are beginning to show you some of the strange combinations that begin to occur with your reds and blues. At some places they are conducting, at sometimes they are not conducting. Sometimes they are fortifying, sometimes they are subtracting, and so forth.

Next picture. Next picture. I'm going to just keep right on with you, just a little flick because there is a whole series of them.

Next picture. I made a series of all the possible combinations. These are all in the Synergetics book.

Next picture. And there is an analysis of each one, how the energy values are, and what it does in the way of shunting, blocking, conducting or not conducting.

Next picture. Just keep it on please. I would like to go through this series quite rapidly, you can just do it at will. The quicker you do it the more rhythm you get out of it.

Now, I'm just going, quickly that's the end of the A's and B's.

But into some studies of the complexes of the octahedron and tetrahedron, which I made.

Next picture. If you look at the complex of a big vector equilibrium made of octahedra and tetrahedra this is a two frequency. You'll find that there are very different aspects of them. You are going to see five different aspects.

Next picture. You see through it in quite different ways.

Next picture. Next picture. Keep right on. Next.

Now, keep on, next picture please. This is getting into when I began to find the great strength you get in such trusses. This is in North Carolina State back in the early 50's. And we found that they make very, very powerful structures. And,

Next picture. Then we began to get into fascinating mathematics. If you'll remove my head from the picture. These are octahedra and tetrahedra in complex trusses made out of single sheets of paper, strips of paper that you find that you can triangulate it and they simply come together.

Next picture. Next picture. And this one is done with a single set of wires and so you make it with bed springs and so forth. The wires can coil and let you make them.

Next picture. Next picture again. These are out of Linus Pauling's book. Next picture. You can see the chemists paying great attention to these things.

Next picture. Next picture. Now we are coming back to joints of the octahedron-tetrahedron trusses. Since the rhombic dodeca occurs, we found where the twelve radii come together, these are then the perpendiculars to where all those lines come in. This then, becomes a very natural joint for, so you'll find a number of studies of that going on here.

Next picture. There is a this thing comes apart in one, two, three, four in these four parts and you, may I have the picture back please, and you can see it open like that where the faces, then, and the perpendiculars coming in.

Next picture. And here is one with crevices, and you can find that all of these things can be brought together.

Next picture. It was along these lines that I made the truss, this is in the beginning of my studies for what became the Ford Motor Company's Dome.

Next picture. Where we made our struts out of sheet aluminum, just angled, and found that the angles could overlap. Around the vector equilibrium's twelve vertexes, there is a turbining. I've showed you where balls can get to two layers begin to turbine, so literally these surfaces turbine around one on top of the other. So it was possible to have them overlap and just turbine on one another.

Next picture (From the technician "That's the last picture).Very good.

In the coupler that I in the asymmetrical octahedron, and being an octahedron has really very interesting properties of octahedron. The mathematical properties. You are used to the x, y, z coordinates and to the fact that if you get into cartography and so forth, you would find that the latitude/longitude grids anything that happens in one octant of the x,y,z coordinates tells all the mathematical stories things upside down, reverse and so forth they go positive and negative, but all the number relationships are all covered by your octant. I find this of great importance because I would like to really know why that is. Can I give any kind of a mathematical, geometrical proof of why that would be so. And I find it really quite interesting, because you and I know, then, the tetrahedron is then the minimum system dividing Universe into insideness and outsideness, the minimum structural system, and it is then, has it's four sides so that there really are only total systems really only requires four facets to tell the whole story. And I am going to then look at an octahedron where we'll have, this is a solid sheet , and then find that this is a solid sheet here, and this is a solid sheet here, and this is a solid sheet here, so you can make the octahedron with four triangles with single-bonded instead of in the tetrahedron the four triangles are edge bonded doubled bonded, and here, this is single bonding. And, yet, they really cover the whole story. So it goes plus, minus, plus, minus, and that's exactly the way the we get into our trigonometry now our trigonometric tables. This being a plus, and a minus, a plus and a minus. We're going around any one point, the main, the clock you get going around the point there is plus, minus, plus, minus this is your straight trigonometric basis for doing everything.

Now, I found it very interesting to get into that, because then the this octant, I was able to when I was trying to find out how many different relationships exist in there, this did come into play in a very big way. Now, the next thing I would like to talk about in that relationship is something I have come to in numbers. When we do our spherical trigonometry, I'm going to talk about spherical trig with you a little more. I mentioned it quite a lot the other night, and I pointed out that when we were brought to trigonometry we were bothered by the idea that signs and cosines, the trigonometric functions, were fractions, and that the fractions were seemingly different phenomena of edges and then angles, but I've shown you then if you start with wholeness, if you start with Universe and System, then there are the central angles and the surface angles, and one of the things that I discovered that I found was fascinating as I did those great circles, that I showed you, as I went from the four great circles, the angles in there when I spun it where you went where a line went altitude of a triangle and altitude of a square and altitude of a triangle it only went through two sets of vertices when I spun it where the altitude of the triangle was 54°44', and the altitude of the square was 70 degrees and 32 minutes, and the triangle 54°44' again. We'll just look at those. Looking at the vector equilibrium, when I spun it on these six, there are twelve vertices so there are six axes, this is the one that went altitude of a square, and then altitude of a triangle, and then altitude of a triangle. Now, in doing that, we have, I said this altitude here is 70 degrees 32 minutes which is an interesting number because I am also familiar with the dihedral angle of the tetrahedron. And this is 54°44'. and this is 54°44' again. Altitude of the triangle. Those numbers are interesting as I think about 60 as being the normal angle. So let me take 60 in relation to 54°44', and that's 6 and 5-4=1, and 9-4=5, and there we are 5 degrees and 16 minutes. Two times 5 degrees and l6 minutes should be 10 degrees and 32 minutes, so it is very interesting, 60 plus l0 degrees and 32 minutes is 70°32'. So if I use 5 degrees and 16 minutes, as a basic increment this one is saying minus one, minus one, plus two or it goes plus two, minus one, minus one... plus two, minus one, minus one as it goes around. That I found very typical, and when we went then, from this first phase of the vector equilibrium to where I made the, we got this set the six great circles which we did get from this when I did that, you'll find it dividing the surface of the there is also the oh yes the three great circles, which are those of the cube, and the three great circles of the cube come about from the three square faces and they do this. They never get into the triangles, they only get into the squares.