There’s a rabbit hole of of making 3D shapes that I’ve stumbled into…
This week I have the good fortune of being able to talk to people, via zoom, at the German Mathematical Society’s 2021 Minisymposium “Mathematics and Arts, about the gyrobifastigium polyhedron. Since there are specific ways solid shapes are talked about it was suggested that I define some of the classifications. No fun in that, unless I can manage to physically toss around some of the supporting actors. There is a certain exclusive club of shapes that my shape belongs to, so I got to work on creating a few samples
My little quest started out as a disaster. The polyhedron friends of my shape looked incredibly shabby.
This story has a happy ending. Things are looking good. Here’s what changed.
This one photo shows more than it lets on, about paper, tabs, and designs.
First the paper. Tried out all sorts. Hands down winner was Hammermill Premium Cardstock, 110 lb, 199gsm.
Notice the tabs on my pattern for the shape. (I’ve learned to call these shapes the net of the shape.) Unlike anything you will find on the sadly misled internet images for nets, putting a generous tab on each raw edge elevates the final product into the upper bracket of awesomeness.
Finally, I needed a dash a beauty that came easy. Messed around in Photoshop, and made some dreamy washes.
Every single fold line has a score line pressed into it – I used a ball point to press in the score line, which is nice because I could see where I had already scored. Until the ink ran out. But that was okay. I managed.
Now this is important. I prepared for the gluing by making those tab folds really sharp, pressing down with a bone folder or the back of a scissors, which ever I found first. This helped make the edges of my shape look and feel really really good.
I used straight PVA for an adhesive on most the tabs, applied thinly with a flat brush. I tried out Elmer’s School Glue. Didn’t like it at all because it took too long to dry. My patience has limits.
The results, finally, were glorious.
I actually couldn’t sleep one night this week because I wanted to play with my new shapes. Finally came back downstairs and messed around with them for a while. Then I could sleep.
Now I will tell you that you didn’t have to read anything I wrote above because it’s all here in a video.
Now if you must start making your own nets, there’s a very cool video that you can watch next, made by my math friend Mark Kaercher, who just happened to post this about this earlier today. Gotta love these synchronicities.
Here’s my little exclusive club of shapes, the cube, the hexagonal and triangular prisms, the truncated octahedron, and, my hero, the gyrobifastigium. What these shapes have in common is that they are the only five regular polyhedra that can tile space. An exclusive club indeed.
One thing kept bothering me about these shapes. I could make them all play together nicely, with the exception of the truncated octahedron, because it was just so darn big. You see, I wanted all the edges of all the shapes to be the same sides, and since the truncated octahedron has so many faces, it just turns out to be really big. Does not play well with others…
Then it occurred to me that maybe…maybe….
…the four other shapes might like to be stored inside the big one.
There they are, one set, all tucked away.