Making Spheres From Cubes

Realization through visualization

The silvery thing in the photo above looks like a Christmas ornament. It is, in fact, a scale model of a sculpture now gracing the Engineering Quad at Texas A&M University. The sculpture, in gleaming stainless steel, is a repeating geometric pattern that makes a sphere from cubes. That’s clever. But also buried in the myriad of shapes along the way is a Texas star. Very clever.

I don’t go around photographing scale models. I took this photo because I helped get this project built. But before we got to that point somebody had to make heads or tails of just what the artist was trying to do. I have been reading fabrication blueprints for over 40 years. Yet, I could only look at the prints from our customer and say, “Well, isn’t that nice.” So it fell on our company’s Vice President of Design, a guy who has forgotten more about custom metal fabrication than I will ever know, to come up with the above scale model. I’m going to let how he came up with this be his little secret and move on to my small contribution to this project.

Most of my projects go into private industry. Private competitive industry. Our customers don’t want mug shots of their tanks, vessels, gantries, mix trucks and process piping in the wild. It’s not secret stuff; it’s just proprietary stuff. But I sometimes land a project that goes into the public domain. This is one of those.

I avoid art projects like the plague. But this one was different. Unlike other art projects, it wasn’t a fabrication problem. A wizened, bespectacled welder in a leather apron wasn’t going to solve this one. It was a manufacturing problem.

It was a manufacturing problem for the very reason that the sculpture was an array of regular shapes. This was the goal of the artist, Olafur Eliasson of Studio Olafur Eliasson. He wanted five geometric shapes in the sculpture. He began with a cube—as far from a sphere as you can get. Cutting the cube into a diamond gave triangles and hexagons. Arranging five diamonds around an axis yielded circles and pentagons—and the Texas star. Assembling the stars gets you a sphere. The sphere, I might add, needed to be twenty feet in diameter. And it needed to be open to reveal triangular mirror panels inside. (Olafur Eliasson loves putting mirrors in public art.) That is to say that the sculpture was the framework of those geometric shapes—not the solids. Here is a picture of our framework prototypes:

Getting the basics right. It starts with parts.

On to the manufacturing problem. You might not have enough psilocybin on hand to know how to transform a cube into a sphere. But, tripped out or not, you do know how a dozen small mistakes can add up to one big mistake. So I’ll begin there. We needed to start with the smallest plane geometry feature in the sculpture and build all the other shapes from it. That was the triangle. From there we needed to make the smallest, most logical assembly component possible. That was a diamond. These needed to go into the largest shipping piece possible. (Assuming you are shipping by truck.) That’s your star.

Our mantra became “Triangles make diamonds. Diamonds makes stars.” So we began with 360 pesky triangles. Pesky? Pesky because they all needed to be almost identical. That’s the problem. You can never make two things identical. Any two things you try to make identical will vary just a bit from each other. It doesn’t matter why, they just will. So our triangles were going to vary. The trick is managing variance enough to keep it from adding up. In manufacturing you set up a means to check your parameters. Any number of gages and fixtures tell you that your parts are right. Other fixtures and jigs ensure your assemblies go together.

Now… this is easy in a world that comes together in right angles. If you are sitting in a room right now, look around. It’s all right angles. The planar floor is horizontal. The planar walls are vertical. Those two things come together at a right angle. The corners where the walls come together? Right angles. The four corners of the doors and doorframe? Right angles. It is no accident that we’ve built our world on this theme. Euclid made it easy for us. And that was the problem. Diamonds have no right angles. A prototype of ours looked like this:

Our diamond-in-the-rough prototype

So how do you fixture it? I puzzled over that for awhile. A few of us did. We hatched three or four schemes—all bad. And it looked for awhile like this was going to end up a fabrication issue after all. But plumb bobs and levels and chalk lines on the floor were not going to let us meet our schedule. We needed to build diamonds fast and without variables.

Of course, you clever kids in the front row are already on this. (Well done!) And that’s the answer I crawled to. The artist had started with a cube. A cube! You know, a special geometric solid in which all of the corners are right angles and all the sides are the same length. And that was the key to the project. So after we all banged our heads together for awhile, I finally managed to come up with this fixture:

A diamond inside of a cube

Of course, the fixture doesn’t matter. What matters is that it ensures that the assembly goes together. In our case, we had to bring 180 mating surfaces together using almost 1100 screws. In most welded structures that involves a lot of prying and pounding. This assembly, though, went together in our shop like LEGOs® and looked like this:

Our final shop check

Exactly what are the details that make this work? Well, if I told you that you could build your own stainless steel sculpture, twenty feet in diameter, in your own backyard, replete with repeating patterns of cubes, triangles and circles. That would make Studio Olafur Eliasson unhappy. That would make my employer unhappy. And that would stop me from getting to share once in awhile. You wouldn’t want that, would you?

Anyway, our project manager was on the job site in College Station to make sure everything went well. He was kind enough to share this photo of the sculpture freshly installed on the university’s Engineering Quad:

Studio Olafur Eliasson sculpture installed at Texas A&M University. (Photo by Kevin Stout)

If you want more,  here is a link to TAMU’s web page for the finished quad:

And, here is a link to a great photo: iBeam Systems

(At the iBeam link, You can select a tab named Timelapse. From there you can set up a timelapse from July 21 through August 14 to see our part of the project being erected. Or, there is link to the righthand side of the timelapse page that let’s you download that timeframe.)


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