Sunday, 20 December 2009

The Tetrahedral Triple-Helix

Tetrahedral triple-helix, Eric Baird 2009Mathematicians playing with geometrical solids tend to concentrate on the finite ones. Those provide a nice satisfying sense of closure, and they're cheaper to build with straws and pipecleaners than the infinite ones.

This is an interesting shape that doesn't fall into that category. It's a simple rigid stack of tetrahedra that generates a "column" with a triple-helix. The odd thing is, you'd expect an architect somewhere to have already used this on a structure somewhere ... but I don't recall ever seeing it.
Maybe I missed it.

The sequence rotates through [~]120 degrees and [nearly] maps onto itself every nine tetrahedra (that is, the tenth [nearly] aligns with the first). If you want to follow one of the spiral arms through a complete [~]360-degree revolution, that takes 9×3=27 tetrahedra, (#28 corresponds to #1) .

Oh, and it has a hole running right down the middle.

I'll try to upload some more images in another post.

1 comment:

Anonymous said...

I "discovered" this while playing with a magnet toy. This is the first I've seen it documented. So simple -- thanks for writing this up!