3D Hexaflexagons
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So I was talking to my friend Trent and we were just brainstorming and talking about cool ideas when I was reminded of this object that I own:
This is an Origami 3D Hexaflexagon with some of M.C. Escher’s tessellations printed on it. I bought it from a bookstore that was going out of business a few years ago in the hopes of one day figuring out something cool to do with it….looks like today’s the day.
The object is made of 6 tetrahedra (a triangular pyramid where all the faces are the same) where each face is an isosceles triangle whose base and height are the same. These 6 tetrahedra are joined at the edges where the bases of the isosceles triangles meet.
The fun thing about this object is as you start pushing and pulling its faces its corners start to rotate and it looks like it’s turning itself inside out. But what’s really happening is that the edges are simply bending back and forth. It’s really interesting how these simple movements in unison can look like something much more complex.
So anyway, I wanted to reverse engineer this object and come up with a way to produce my own. The simplest way (outside of copying the paper net of the object I started with) would be to 3D model a tetrahedron, print it out 6 times, and tape it together.
This turned out pretty nicely, and lead to a lot of brainstorming for what could maybe be done with this object next. I think I’d like to put electronics in it eventually and have them do some fun things. Here are some sketches of what that might look like one day:
I then started modeling a larger version of this tetrahedron that would be held together with hinges instead of tape and did a little test print.
This went….okay. The screws are a little bit too long for the space allotted so that makes everything a little bit unpolished, but otherwise most of the tolerances were pretty good. I think if I can get screws that are better sized then I’d be ready to keep adjusting the model and print out a full 3D Hexaflexagon. I’d also like to add sockets for small magnets eventually so it really clicks into each position.
And finally for now, I decided to bust out the sewing machine and make a 3D Hexaflexagon pillow. Templating the shape out of 2D fabric lead me to break it down differently than I do when thinking in 3D software. Instead of being made of 6 tetrahedra, here I made it out of 12 rhombuses (or 2 isosceles triangles touching base to base). This is also a rough prototype sort of thing, but I might try to make a nicer larger one or something in the future.
So that’s been my exploration of 3D Hexaflexagons so far. They’re a really fun shape that I bet could make some really interesting objects. I hope to do more with them in the future.