Two years later he began his search for a three-dimensional, seven-sided sculpture. After much trial and error, failure after failure, and months and months of effort, he eventually discovered something, the likes of which this world has never seen before: a new geometric form with seven equal faces. In the history of mankind this geometry has never appeared on the earth before.

Even though Frank found a new geometric form, the significance of the form was unknown. (Rudolf Steiner said that “geometry was knowledge which man himself apparently produces, but its significance is completely independent of him.”) Since its discovery, Frank devoted himself to discovering the potential meanings of this form, and almost ten years of work have led him to see how it relates to the human heart, to the geometry of the Earth, to sacred architecture, and to inspiring others about the awe-inspiring connection between seemingly abstract geometries and the dynamism of life.

See also the “About” post for more information.

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Friday, August 13th, 6-8pm

ISIP, 6241 palma St., Poblacion, Makati (near Ateneo Rockwell)

P500 (P200 for teachers and students)

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http://www.youtube.com/watch?v=_ujfk4fhYi4

www.youtube.com/watch?v=_ujfk4fhYi4

www.youtube.com/watch?v=-CPAVD7bfWs

www.youtube.com/watch?v=HmcXKtPxR9E

www.youtube.com/watch?v=C5b_1BQzKTI

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Frank has been given the opportunity to test the new device at Environment Ventures Marketing, Inc. in the Philippines during the month of August. He has been invited for the first time free access to a professional laboratory environment which includes scientists, engineers, fabricators, and machines to produce and test many of his ideas.

The results of some of these studies and test data will be presented at the Annual Conference of the Biodynamic Association, Sept.30-Oct 3 in New York.

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Seth: When did you begin to work with Platonic forms?

Frank: When I took Consciousness Studies, in the platonic forms section that Patricia Dickson taught. That was my first introduction to platonic forms. I had never seen them before.

How long ago was that?

One and a half years ago. [In 2000.]

And how is the form you work with related to platonic forms?

Well, there are five platonic forms and they have equal angles and equal surfaces. The thing about mine is that the surfaces are equal and in the platonic forms their surfaces are equal. The Saturn form is a semi-polyhedral form, in that all of the polygons aren’t the same. There are two different kinds of polygons: four equilateral triangles and three quadrilaterals, which makes seven.

The thing is that there hasn’t been a seven-sided polyhedron that has equal surfaces in any of the research. There is nothing in the books, in planar geometry, solid geometry, in the artistic or in the science literature. There has never been a seven-sided object with equal surfaces. And that is what is significant about this.

Is that what you set out to do?

No, no. After seeing the seals and capitals at the Goetheanum in 1997, I was inspired. I was told they were powerful forms; they were spiritual forms, which really interested me. But no matter where I looked in the books or in the Goetheanum, I never found any three-dimensional sculptures [of a seven-sided form]. They were always either one-dimensional or two-dimensional. I thought, “gee since I have this sculptural background I have to make one that is three-dimensional.” And I didn’t do it for two years. I wanted to do it but I didn’t have time. I was teaching college, I was busy, or whatever. When I took Consciousness Studies and the platonic forms were taught, I thought “this is my time to do this.” I started just before Christmas. I wanted to make a seven-sided object. Everything I did failed; I couldn’t do it. I did it with measurements. I tried to do it scientifically. I measured them. I took the seven-sided form in two dimensions and tried to put it in three dimensions and it didn’t work I tried to take seven sticks of the same length and put them in a piece of clay and measure them. It didn’t work. I tried to take seven balls and push them together with a piece of clay in the center, that didn’t work. A whole bunch of things that I tired–forget it, they didn’t work.

So then I decided to approach it artistically, which is the way I was trained. When I did I came up with a seven-sided form and I did about three or four of them and I finally refined it until it was quite nice. I showed that to Dennis Klocek and Patricia Dickson and they were really surprised at the shape. So Dennis said something to me that probably started the whole thing; he said to me, “Can you make that objective?” Then I said, ‘Well what do you mean objective?’ He answered, “That’s subjective”. And what that means is that it is artistic. But can I take it back into science. Can I take it from art to science? A month or so later I came up with the seven-sided form. It has seven sides, with forty-two triangles exactly the same size. Their surface areas are equal, and each one of those has six triangles which are exactly the same size, which together becomes a seven sided object. The only problem is that there are different shapes in there. So what I realized is that I needed to reduce the six to three. So I reduced the six triangles to three triangles, and I came up with four shapes that had three triangles, and three shapes that had four triangles. I thought “What is this all about?” So I decided to pour plaster into the form in equal amounts, then I took those forms out and glued them back together. And I came up with the Saturn form. I found that it had seven surfaces with equal area, and seven points, and it has seven edges. It was this beautiful semi-pyramid shape. It came out way beyond my expectations. The seven-sided form was absolutely beautiful. And neither Dennis nor I could find this shape anywhere in the literature. I went to Sacramento State and Davis and went through all the libraries and books for a couple days and found nothing like it. So then Dennis said that if it was possible to put it into a cube, then it is really significant. If you can relate it to the Platonic forms then it is really significant. So I put it into all the Platonic forms, and it fit. Not only did it go into the cube, but also it went into all five of the platonic forms–all the five Platonic forms has this form in it. That is significant. That’s what really got me into working more with this form, because there was so much coming from it.

Why do you continue to work with this form?

There is also a second part to this. After I discovered the form, I applied what Dennis Klocek had presented in his class on alchemy. I could have stopped with the seven-sided form and said, “this is beautiful and here it is,” but because of listening to his lecturing I know that alchemy works with inner work as well as with outer work. So I decided to take this alchemy and apply it to sculpture. So I took the process of alchemy and applied it to the form, and it just expanded the form into other beautiful forms that I am still working with today. To this very day I am still working with alchemy.

Are you aware of how your work with this form has affected your inner and outer life?

Yes. As far as the sculptural form itself I have developed the capacity to see forms without drawing them–nine sided forms, eleven sided forms, thirteen sided forms. I can see them develop in my mind–I can see them without having to actually make them, whereas before I struggled and struggled and struggled to get to that. Now I don’t even need to do that. I can see how these forms come, and I make them. So the process has been really shortened. Also because of seeing and working with the alchemical processes of earth to water and air to fire with my sculptures I also see these processes in my life. If I have a problem in my life, or a question in my life, or I don’t understand something in my life, I can take that ‘not understanding’ and put it through the same process I put sculptures through and I get really clear images of what to do and how to deal with situations. I can apply the alchemical processes that I learned through form to my inner work.

Wonderful!

Yeah, it is wonderful! I cannot believe how wonderful this is. You can actually take some material, learn the processes of material transformation and apply it to your inner work. I cannot believe how thankful I am for Dennis presenting alchemy in his class.

Were you aware of this affecting your inner work when you first began?

No, not at all. I had never heard of alchemy before.

Since you first began to work with these forms in the Consciousness Studies class a year and a half ago, how has its affect on your inner life changed since then?

Well, there are a couple of ways; I always “boo-hooed” the idea of destiny. I didn’t relate to it. But I also never could understand why I had certain skills, why I did certain things and why I moved into certain jobs. Why did I have these skills, why did I have these jobs, why did I have these experiences? And all of it now makes sense to me because of this process. I know now why I had these jobs, I know now why I had these skills. I needed them. This was my destiny to do this. And so that has just been a wonderful thing for me to realize. I mean my whole life is just glowing because of this process, and that destiny part is coming together. It’s allowed me to be more comfortable in my life. It also allows me to handle problems better in my life. Also I can lead a more spiritual life because of this, because I realize that these things are coming to me, and I’m at the point now where I’m absolutely dedicating my life to it. I don’t care what the income or the outcome or anything attached to it is. I’m doing it and I will continue to do it until it stops–and that I didn’t have before.

Do you find the forms that you work with in natural phenomenon?

The seven-sided form I haven’t found anywhere in nature except when a vortex forms in water. I noticed that the angles were very similar. When I put this form into the water process, from earth to water, I made the Saturn form out of wire and put into water and spun it with an electric drill, and there were unbelievable vortexes created by this form. I designed a propeller later, and the propeller outperforms any of the propellers I tested with those little model boats that go ninety miles an hour. I tested it at the same scale with these high-performance propellers and it outperforms them. But since I have moved on into the air process of reversal, and I haven’t gone back to the propeller idea since, but I plan to go back to it.

Do you find that these forms relate to social life?

Well this form is the most unbelievable Christian symbol I’ve ever seen. It has three crosses and four triangles. The four seasons, the four directions, the four elements, and the three crosses of the crucifixion. The crosses and the triangles are exactly the same square area. And right in the middle of the form is the Star of David. It has twelve edges, so there is the zodiac. It has seven points and seven surfaces. Even at one point there is the Christian shield that many people have in the past put the cross on the shield. I know there is also a second Star of David in here, that is larger, and I am very interested in seeing it’s proportion. The reason I haven’t done it yet is because I can’t go to fast with these things. There is a speed that I could go, but I have to constantly slow it down because it is so overwhelming. I don’t get any rest. If I have a question I go to sleep with it, I wake up, and within three hours I have answers. I can go to books and my dream tells me what page, and I go to that page and there’s the answer. So I have to be very careful, because it is just happening so fast. But this in a church would be just unbelievable. You could design buildings based on these proportions. There are at least nine golden proportions in this object, which is significant because the golden proportion is from the great geometrist in the sky–it is found throughout all of nature.

Have you seen any relation between these forms and the forms of world events?

I have put the seven-sided form into the sphere. Rudolf Steiner said in the third to the last lecture before he died that there was a semi-tetrahedron in the middle of the earth. And so I took this form, and I took exactly the points he indicated, and put the form into a scale model of the earth, and all the points hit exactly where he said they would hit, which was shocking. Now, he said that there was a pyramid like form in the middle of the earth, but at the time that he was saying this there wasn’t this seven sided form. It wasn’t here. But there was a tetrahedron, so he said it was a semi-tetrahedron. And the Saturn form is a semi-tetrahedron, except it has seven points. And one of the things that has always intrigued me was why did he go to the tetrahedron, which has four points, whereas all throughout his seals and his capitals he always dealt with seven. Why didn’t he deal with the seven in the middle of the earth, because all the seals and all the capitals are dealing with the evolution of the earth? The only thing I can think of is that there wasn’t a seven sided object then. But the seven sided object that came through this work fits where he says.

And then when I did an inversion of this form, which was the fire process in alchemy, I came up with the double-sided heart, the inverted heart, which I call Venus. This is exactly what his Venus seal is; two hearts inverted. So because of that process, whatever Steiner says I never hesitate to think that he may be right. But before I used to question everything he said. Oh my gosh now come on, what is this you know? But now my attitude is completely changed, because he saw the Saturn form turn into Venus without doing it. Somehow he didn’t do it–I had to do it, and it took me a year and a half to do it, and it came out exactly like he was saying, but he didn’t go through this process that I went through. If you look at Steiner’s seals the Saturn form evolves into the Venus form, which is two hearts. How did he know that if you invert the [seven-sided] Saturn form it turns into the Venus form, which is two hearts. Do you see two hearts in here?

No.

Neither did I. But I did the inversion process, the transformation, and that what came out. That beautiful heart shaped form came out–and it is all based on objectivity. There is no subjectivity in this. It’s all based on science. The curves are measured to be geometrically perfect, from the Saturn form being inverted. When you invert something you turn it inside out continuously. So you measure the movement and the movement is the dynamicness within a static form.

Why is this seven-sided form so meaningful to you?

First off, it has never been here before. That’s kind of cool. Then, when I put it into the alchemical process I discover so much about the form and about myself and about everything else. And I continue with the alchemical process. In other words I put it back into earth again, and then back into water. Then I’ll reverse it, and so forth, all the way around. And I will continue to do this–like Dennis says, you can continue to do this. You can have a new earth after taking it through the whole process. I am finding out directly that that is true, so I don’t know where I am going to stop. I study the data, then I see what is changing, then I see what is reversing, and then I see what is transforming. And what has transformed I put back into earth again, which is data, the facts. And I’ll study the measurements and so forth, and I’ll see what is changing and then I’ll reverse that. Also because this form is new, everything that comes from it is new. All of my forms are new. Not because of me, but because of the original form.

Will your work with these forms affect your architectural work?

Absolutely. You could make some unbelievable buildings using these forms. It is amazing how beautiful these building could be.

How do you see your work with these forms, and platonic forms, developing in the future?

I don’t really have an idea.

You are working a lot on the relationship between the seven-sided form and the earth, though, right?

I am working on its relationship to the earth and there is something there. I don’t know what it is but I am going to see if it evolves into something real. I don’t know how long that will take but I am going to work on it.

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Frank says:

When I was at the Goetheanum, I saw the Saturn form in two dimensions. Then I saw the seven sided Saturn column. When I saw that I liked the sculptural quality. I thought, man that is cool! And I thought I would make that in three dimensions.

So let me show you the original forms. It is interesting because it shows you how primitively I started.

This is a picture of the Saturn capital at the Goetheanum. That was the beginning.

[Frank thought about the seven-sided nature of the capitals and wondered if there was a three dimensional form that would be seven sided that he could relate to the capitals.]

[His first attempt involved trying to place seven sticks into a ball of mud so that the angles between all the sticks was equal.]

That’s what I started out with. Can you believe it? Seven sticks in a piece of mud.

Then I tried to put seven circles together on a ball. I tried all kinds of things. I had a lot of stuff, which didn’t work. But the main thing that happened is that when I put seven spheres together, and put a piece of clay in the middle, I got this. And I was happy with that. I really was. But there are gaps. I didn’t like the gaps–see this big thick part right here? I didn’t want a big thick part, I wanted seven! But this wasn’t what I was after.

So what I did was I took a ball of clay, and I carved out seven pieces–and that is the Saturn form. I did other things, but this is basically what I came up with.

And that one I put hula-hoops on it and did it this way and increased it and used these holes to do different things.

Then I enlarged it, and I got this real ugly thing.

So then I found out that if I made the good sides–there was one that had a good side here–I made seven of those, and I came up with this. You can see that they are similar. This first one is very subjective. What I did is carved out seven equal volumes, and wherever they met, instead of having a gap, I made a straight line. And when I made a straight line, I came up with threes and fours. So three and four was seven–I should have known. But I didn’t.

Then I put that form through a rigor by making all the triangles the same size, and I got this beautiful shape. I just love this thing. I found it was so interesting because they didn’t look equal.

So what I did is I flattened these out–I made each pair of triangles flatten into one triangle. Then I poured plaster into it and got this. This is the seven-sided object. Objective, perfect surface areas, and all those lines are significant, that you see on there. Absolutely perfect.

So then I pushed all the points to planes, and I got this. This is a fourteen sided object. It hasn’t ever been seen before.

Then I turned the Saturn form inside out and I got that. And this you can take apart and you can see that there is a Saturn inside it and outside it. If you take the Saturn form and turn it inside out, you get this shape, whose inside negative space is exactly the Saturn form.

Then I took the Saturn apart into three pieces.

Then I did a study that I learned from a book by Paul Shautz, who was a Swiss, where he did an inversion of the cube. So I took the same idea that he had, and I did it to the Saturn form. I inverted it, and got this. That’s the inversion of the Saturn form. Paul Shautz was the guy who made the Oloid. He did an inversion of a geometrically symmetric shape. But the Saturn form is asymmetrical. So inversion of an asymmetrical shape, creates retrogrades, and the retrogrades are what you see here. [This is the Venus form.]

And the one thing that I forgot to tell you–when I took it into the water process, what was changing, I found that there was a seven sided bubble. I dipped a wire-frame model of the Saturn into soap, and this is the bubble that came in the middle of the form.

Then I took this back into the water process, and dipped this into soap, and got that shape, which is another Christian symbol, which is a fish, or a flame.

This is what happens when I put it into air–it becomes linear, and this is inside out. And what I discovered inside the form is that there is a beautiful bell shape, if I spin it. You see the bell? Now this is really cool, let me show you this. So inside out you see a bell right? And right side out, you see the same bell. Look! That’s the same bell. Inside. And I didn’t know any of this a year ago. None of it.

Then of course that is the new earth. That is eight Saturns in a cube–they all fit in a cube. So it is a compound of eight.

And this one I wanted to see how many Saturns it would take to make a loop, and I found that it would take sixteen Saturns to make a loop. I connected all the edges and got this beautiful architectural form. That could be a building.

Now this is my latest. This is the closest that I have ever come to a real human being, myself, making objective art that has never been seen before. This has never been seen. No one has ever made this. This is based on the cube and the Saturn form in it. This is eight Saturn forms. This one uses only the base of the Saturn form, not the quadrilaterals. What is amazing is that in this, is a perfect octahedron. The way I discovered that was to put an octahedron in it. It fits right there, see it? But it has all these forms from the triangles coming out in this beautiful relationship. And this is just what it looks like half done. So does that help?

They are beautiful aren’t they? And I try to make them nice. They are only studies, but I try to make them nice. I could try to make them even nicer but I try to have a balance and not be to finicky. And the thing is I have to study. I have to read. I have to see what is going on in other books and see what other people have done, so I can learn more, and relate to it in new ways. So I am reading constantly, all the time. Sacred geometry books and all kinds of stuff.

Reversed-x All2-x Threepiece2-x Fish2-x Carvedout2-x Carvedout-x Reversed2-x Threepiece-x Objectified2-x Venusbig-x Saturncapital-x Reversedlines-x Point2plane-x Venusheld-x Threepiece1-x Sevencircles-x Saturnschematic-x Saturn2-x Bubbles-x Sticks-x Subjective-x 8saturnsnew-x Venus-x All-x Venusheld2-x Balls-x Objectified3-x Venus3-x 8saturns-x Venusdrawing-x Venus2-x Saturnlooped-x Venusheld3-x Objectified-x Frankportrait-x Fish-x Saturndrawing-x Saturnfromvesica-x Subjective2-x Carvedout3-x Saturn-x Point2plane2-x

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This sequence was also physically constructed. Click the images for larger views. Notice how the small yellow tetrahedron’s top point moves upward in four successive stages, each of which is constructed as a separate model. The chestahedron form arises when the small yellow tetrahedron’s top point has moved to the midpoint between its original position and the top of the large tetrahedron.

If you click the images below you will get a more detailed description of the sequence and its significance.

GoldBell Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Tetrahedron Sequence 1 Tetrahedron Sequence 2 Stages of unfolding the tetrahedron Stellated Octahedron 1 Stellated Octahedron 2 Stellated Octahedron 3 Stellated Octahedron 4 Frank Working

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Frank has utilized the unique geometry of the chestahedron (a volume made of 7 faces of equal area, the red shape above) to design a cap for underwater oil leaks, such as the recent spill off the coast of Louisiana.  The design incorporates safeguards against the formation of ice crystals by including heating elements, having multiple sites for gas to collect, pressure-release valves for accumulated gas, and most importantly, the geometric design itself, which passively facilitates the separation of the gas from the oil.   The main flaw of the failed pyramidal design used by BP in the Gulf oil spill had to do with the fact that the oil was collected only at the top of the structure, and in one spot only, where the gases also built up.  By separating the gases from the oil and providing multiple sites for the collection and release of gases, while simultaneously collecting oil from the bottom, this cap design could provide a useful template for future underwater oil leaks.

Watch Frank explain his design in the two videos below:

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