Painting a Pentahedroid

Painting a pentahedroid with pencils and ping-pong balls.

The simplest regular 3D solid is the tetrahedron.

Have you ever seen a  bubble with sharp edges? Let’s make one.

I couldn’t sleep tonight, so I took apart an old tootsie roll I found lurking in a drawer and stripped the cotton off 6 swabs and stuck them into the pieces of the tootsie roll to make a tetrahedron. You don’t have to make a perfect tetrahedron for this to work.

Now find a container deep enough to dunk the tetrahedron like a donut. Put water in it and add some soap. Dunk the tetrahedron. If you do it right, you will be surprised to see the 3-space projection of a 4-D hyper-tetrahedron (a pentahedroid) appear as the soap film, moving through time, balances forces and achieves stability, anchored to the tetrahedron as a base.

(Can you guess what happens next if you touch the bottom of the swab tetrahedron to the surface of the soapy water one more time, and then lift it? No?  Why don’t you try it out? Hint: I don’t mean the bubble will pop.)

If you click the picture above to enlarge it, you can clearly see the edges of the soap film, straight and sharp, connecting the four corners of the swab tetrahedron to a point at the center of the artifact. The tetrahedral symmetry of the soapfilm recalls to mind the bonding symmetry of the Carbon atom. Cute, ain’t it?

It also happens to be part of why diamond is so strong. What we call diamond is just an allotrope of carbon, a giant polycarbonate molecule with each carbon atom, ideally, bonded to 4 other carbon atoms.

We used to think the only way you could make diamond was to either (a) be Superman’s best friend, so he could crush a chunk of coal into one for you, or (b) look for places where carbonaceous material got squeezed really hard, and probably at high temperature too.

Now, there are lots of ways to make diamond. It’s been done with high pressure (had to build a machine for that; superman was out of town that year), explosions, ultrasonic cavatation, and chemical vapor deposition. We can even “dope” diamond with impurities and make diamond transistors which can operate at higher temperatures. Fact is, synthetic diamond is used to make heat sinks to conduct heat away from high power transistors and semiconductor lasers; diamond makes an excellent material for this because it is a superb conductor of heat but does not conduct electricity in a pure undoped state.

Truly we live in an age of marvels. When I took my electronics classes as an undergraduate heat sinks were made of aluminum. Now we can afford to make them from diamond. All of diamond’s unique properties stem from that tetrahedral bond structure.

There is another important thing to remember about carbon. It is the element all life on earth is built around. Those bonding angles make possible a dazzling multiplicity of molecular configurations, which includes, among them, DNA.  Everything is connected. You can look at a pile of sticks and a bit of soap and uncover the basic symmetries of the molecules of life. We are surrounded by wonders. –MRK

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4 Responses to “Painting a Pentahedroid”

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