Here, have a rabbit hole.

While I was shoveling out tidying up my study, I came across this:

I have no memory of where this came from — an attachment from a book perhaps? — but I know exactly what it is: the instructions and explanation for folding the now-lost strip into a hexahexaflexagon.

What is a flexagon, you ask, and how does it get to be hexahexa? I’m glad you asked.

First rabbit hole: Wikipedia.

I discovered these things when I was a teenager, and I’m pretty sure I came across them in a book by Martin Gardner, he of Scientific American fame. They were super-cool, and I taught all my friends how to make them. I even taught a seminar on them at the Governor’s Honors Program one summer a quarter of a century ago, since GHPers are all fabulous little nerds, even if they weren’t math majors.

Here are two good websites with instructions:

• https://www.instructables.com/Hexaflexagons/

• https://mathequalslove.net/hexaflexagons/

So let’s make one, shall we?

I constructed my own strip (Pixelmator Pro, highly recommended: create a triangle, duplicate duplicate duplicate, distribute, situate, group, duplicate, flip, align).

I cut it out and colored it.

Well, I put some colored dots on it. I folded it — making a couple of mistakes along the way; remember, it’s been decades — et voilà:

It is very small, but still as satisfying as I recall to keep that thing flexing and rotating. It’s kind of the original fidget spinner.

Want to see one in action? Here you go. (Beware: the first couple of videos I checked were making a hexaflexagon, with three faces, not a hexahexaflexagon, with six (like mine). For your own rabbit hole, find those instructions and make a hexaflexagon before moving up.

The main problem is that even a sheet of legal size paper is not long enough to make a decent size flexagon, so if you want a larger one you have to print out, cut, and glue multiple strips.

Which I’m not going to do at the moment.

Go, play with the rabbit hole — it’s a great opportunity for some TASK AVOIDANCE.