Mathematicians 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.
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