This month I have finally finished a project I started many years ago and I wanted to share a picture of the two pieces that both sprung out from the same basic question. That question was: “Can I weave two (or three) dodecedrons into each other such that it preserves the five-fold rotational axes of symmetry of a single dodecahedron?” The answer is No, I cannot (yet), but in the process of trying to answer it I discovered something else entirely, and then by extrapolation (from a rhombic dodecahedron to a rhombic tricontahedron) yet another thing. Those two things I call Triaxiallia 12 and Triaxialla 30 respectively, and are developed from the nets you see in this image below.

You can see how the same rhombic tile is repeated to form a continuous pattern over the polyhedron, but the eagle-eyed among you may notice that the edges don’t always quite link up. As a result, 6 of the faces of Triaxiallia 30 have a different weaving pattern, that allowed me to preserve quite a lot of symmetry and allow the cage-like structures to adhere to a over-under-over-under weaving pattern across the entire surface. Sometimes they come together as 4 lines rather than 3, and as your eye is drawn round it presents a nice little diversion every so often. This is a natural consequence of taking a pattern that can tile a 2D place and wrapping it round a 3D object, and although its note quite what I had in mind, I was very pleased when I discovered it!

I started Triaxillia 12 (below right) September 2018 and finished it at the start of 2020, worked on a few other things for a while and then started Triaxiallia 30 (below left) towards the end of 2020, eventually calling it done a week or two ago. It’s an unusual mix of emotions to finish a personal project after such a long time, veering between relief, satisfaction, the inevitable angst any creator feels when their perfect ideal is rendered in an imperfect world, pride and The Void. I don’t know how else to describe The Void other than the newly created space in your brain that briefly exists after a task is completed, but it quickly gets filled with more Stuff To Do. I also want to state for the record that I could have continued to finesse both of these pieces for many many more hours but I was so far into diminishing returns territory that even I couldn’t tell if I was making things better or worse anymore, which is a good time to stop.

Watch this space for the thing that almost immediately filled The Void!