C’mon and Zome, Zome, Zome-a-Zome

Anyone remember the old PBS kid’s show “ZOOM”?  Anybody?  OK, well, this week’s post title pays homage to the theme song which is still burned into my brain decades later. :-)

But today I’m not talking about ZOOM, but rather about Zometool, an incredible building system that allows geometric artists (and crystallographers, and mathematicians, and chemists…) to explore an incredibly rich universe of shapes built on the symmetries of the Platonic Solids.

What is Zometool?

In short, Zometool is a construction toy consisting of nodes and struts which can be connected to form geometric structures.  It’s a lot like the old toy Tinkertoy in this regard, but with one key difference: while Tinkertoy nodes had nine holes along 5 axes in space, Zometool nodes have 62 holes defining 31 different directions in space! (ZOOM and Tinkertoy? Clearly I’m feeling nostalgic for my youth today…!)

There is far more to know about the underlying principles of Zometool than I can cover here, but to give you a little of the flavor…

Zometool Parts in Detail

As the chart below shows, nodes are complex little balls, somewhat like geodesic domes, that have three shapes of hole: triangle, pentagon, and rectangle. Each kind of hole accepts a different family of struts: blue struts go in rectangular holes, red struts go in pentagonal holes, and yellow struts go into triangular holes. (Green struts are a bit of an exception which I’ll get to in a moment…)

Easy, right?  Well, yes and no… You are never in danger of putting the wrong strut in the wrong hole, it’s true.  But 5 minutes of playing around will show you that there are a LOT of possibilities!

Zometool Parts Chart (courtesy of zometool.com)

 

Basics of Zometool Geometry

If you remember the post about the Platonic Solids, you’ll remember that they represent three basic geometries or symmetry groups: tetrahedral, octahedral/cubic, and icosahedral/dodecahedral. The magic of Zometool is that it embodies ALL of these symmetries at the same time. If you imagine using a node as the exact center of the various Platonic solids, the rectangular (blue strut) holes point in the directions of the edge midpoints a dodecahedron or icosahedron; the triangular (yellow strut) holes point in the directions of the vertices of a dodecahedron (or face centers of an icosahedron), and the pentagonal (red strut) holes point in the directions of the face centers of a dodecahedron (or vertices of an icosahedron).

That’s fine for the icosahedron and dodecahedron, but what happened to the poor cube, tetrahedron, and octahedron?

Well, it turns out that the rectangular (blue strut) holes also point in the directions of the face centers of five different cubes (or vertices of five different octahedra), and also in the direction of the face/vertices of ten different sets of tetrahedra.  In fact, this is where the mysterious green struts come in.  Blue struts point in tall the right directions to build cubes, dodecahedra, and icosahedra directly. But despite the 31 different directions available, none of the three basic color struts point in the right directions for the edges of the tetrahedra and octahedra. So, a little later they came up with the green struts, which fit into the pentagonal (red strut) holes but emerge at an angle (not point straight out from the center) — just the correct angle, in fact, to make the edges of tetrahedra and octahedra.  This page shows examples of all of the Platonic solids (any many other basic polyhedra, besides) built out of Zometool.

Zometool as an Exploration Tool for Geometric Artists

If all of this sounds way too complicated to be fun, never fear!  Although there is some very complex geometry available here, it is also the case the you can pick up Zometool and just start connecting nodes and struts and build all sorts of cool shapes without knowing a darn thing about what’s going on!  In fact, these very qualities have led to its heavy use in education. They’re easy enough for kids to immediately start building with, but along the way you can teach all sorts of different geometric concepts.

As for geometric artists — well, speaking for myself, I can spend hours and hours just fiddling around, following my nose, and I have discovered all sorts of possibilities that I never would have stumbled on otherwise. Here is where a few examples and pictures are worth the proverbial thousand words. :-)

The All-Yellow Star

One day I decided to see what would happen if I used only yellow struts of the same length. Along with several other things, I came up with this (half of) a twelve-pointed star with all diamond-shaped faces:

"All Yellow Star" by Phil Webster

 

which tickled me enough that I roughed out a prototype in card stock:

"All Yellow" Star card stock prototype

 

This rough little model continues to get a disproportionate number of admiring comments to this day, so it is high on my list to produce in a more elegant form.

The Dodecahedron Cluster

Another time I was playing around with dodecahedra and came upon this cool way to cluster four of them together:

Cluster of Four Dodecahedra

 

Again, not something I would likely have come upon without my trusty Zometool.

The Inverted Dodecahedron

Finally, I have spent a long, long time exploring the possibilities inherent in the shapes I like to call the “inverted pentagon” and “inverted dodecahedron”. (I don’t think these are “official” names, but they seem very descriptive to me!):

"Inverted" pentagon

"Inverted" Deodecahedron

 

Among the variations I have discovered are this pinwheel:

Inverted Pentagon Pinwheel

 

this “lattice” of repeating inverted dodecahedra:

Inverted Dodecahedron Lattice

 

and this I’m-not-sure-what-to-call-it shape made up of inverted pentagon faces:

Inverted Pentagon Shape

 

If You Like What You See…

That old ZOOM theme song ended with “If you like what you see, turn off the TV, and go DO IT!” So, if you feel like playing with some Zoomtool, consider picking up any of the wide variety of Zometool Kits available on Amazon, and go DO IT. :-) Anyone who sends me a picture of a Zometool creation will get their name and picture featured in a future post!

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About Phil Webster

Phil is the creator of GeometricArts.com. You can reach him on the Contact page.
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