No place like dome

Yesterday was the 20/12. Nobody had realised that this was a particularly auspicious date until after we had decided to hold the event about to be described; at the time we were planning it, all that mattered was that people seemed to be available at the time (although that didn’t stop outside agents imposing meetings upon some of our number at the last minute).

During one particular morning tea conversation, it was revealed that our department has a geodesic dome kit, which (a) had not been assembled for ages, (b) was good fun to assemble, and (c) was unlikely to be assembled in our new location due to the lack of large open spaces. Thus it was that we decided to have a ceremonial end-of-year dome-assembling picnic (unfortunately the picnic idea fizzled out and ended up inside because, summer notwithstanding, there was a freezing wind howling around our plaza).

Of course, this event was not without crises and chaos; the most significant of which was that we couldn’t actually find the kit.

Aaaagh.

Fortunately I was able to work out what was needed and that we had enough pieces of each of two approximately correct lengths of dowel to make a small geodesic dome. With equipment assembled we went outside and did battle with the elements — and my assembly instructions (I’ve only ever made a tiny model, and that was 20 years ago) — and eventually succeeded in building a 2-frequency dome.

And the significance of 20/12?

Well, the geodesic dome is based on an icosahedron, which is a shape that has 20 triangular faces and 12 vertices (corners). If you look very closely at the picture at right, you may be able to make out the top 5 triangles of the (half) icosahedron, by looking at the green triangles that meet at the top. There are then 10 half triangles (also green) around the base, some with their apexes* pointing upwards, and some with their apexes (not shown) pointing downwards). The 2-frequency geodesic dome is obtained by dividing the triangles of the icosahedron into four smaller triangles (the blue sticks) by halving the sides of the original green triangle. The extra vertices are then projected onto a sphere.

The bigger and more spectacular 3-frequency geodesic dome is obtained by dividing the sides of the green triangles into 3, thus getting 9 smaller triangles. That particular dome needs sticks of three different lengths … and I couldn’t wing it with the equipment we had (and I’m not sure we would have had enough people to manage the job).

It’d be nice to find the proper kit, though, and build the big one sometime, somewhere; it just won’t be in anyone’s new tiny office!

* My Oxford dictionary lists “apexes” before “apices”.