Gyrobifastigium

Noun

gyrobifastigium (plural gyrobifastigia or gyrobifastigiums)

A polyhedral solid formed by joining two face-regular triangular prisms along corresponding square faces, giving a quarter-turn to one prism. It is noted for being one of the few regular polyhedra that packs in three dimensions.

Its name enchanted me. I had this moment of deciding whether or not to follow this curiosity. It seemed silly, even to me, to dedicate a good bit of time to a shape just because of its name. While I was considering just ignoring it I felt an arthritis-like pain inflame my left thumb. Arthritis is not a thing for me, but for a moment it was like I was being reminded that there will come a time that if I want to hold my own gyrobifastigium that it will likely be hard to impossible to get someone to help me with it. No putting it off. Can’t trust the future for this. The exploration began.

Gyrobifastigium-Net (note: that web address brings you right back to this blog page)

It took quite a number of tries to settle on a net that suited me. It was a tricky structure to glue together so my net went through a number of unanticipated changes. Then I had to find paper that was just right. Some papers were too thin, others too thick. Couldn’t find one that was just right. Finally decided to use one that was more weighty than regular copy paper, but not a cover weight paper. Used ARJOWIGGINS KEAYKOLOUR VELLUM SEAL 80T 27.5X39.3 184M (120 GSM 700X1000), which was too light to make the feel of what I wanted, but that was a solvable problem.

These shapes have eight faces. I glued extra paper to half of the faces. This gave me the feel that I wanted. Naturally, I had to color in lots and lots of squares and triangles so I could choose what to use.

I colored four times as many units than I actually used. This sounds reasonable to me.

One of the many interesting things about this shape is that it tiles space, meaning they can all fit together to fill a space without any space between them. Think of a cube or a brick: they can completely fill up a space without leaving gaps. As this space-packing thing is big deal, it became evident early on that I needed to make many of them so I could check out how they fit together. I didn’t go overboard with this. Made somewhere in the area of twenty of them.

The crazy thing is that these gyrobifastigiums aren’t particularly cooperative when it comes to building. Not only that, but the shape of the space they fill is completely defined by the fact that it is this shape that is filling it. I know I didn’t say that in a way that is easily digestable, but think about it. Don’t let me be alone in this space.

I could nudge these shapes into some alternate fun kinds of patterns that have nothing to do with tessellating space, but, still, the shapes are surprisingly uncooperative.

I am shipping two or three artworks off to Dana Hall in Massachusetts this week, for a December show centered around women who are involved in both math and art. They don’t know it yet, but, along with other work, I am sending them these 12 gyrobifastigia to have as a hands-on, build-with-them-yourself piece that students can engage with. I am not going to worry about them getting damaged, not when I can give students the opportunity, the only opportunity that they may ever have, to play with gyrobifastigiums themselves.