Behind the Scenes #4: The Hexaflexagon

You've got to be kidding me... I thought this was DESIGN class, not ALGEBRA!

Let's face it, you don't need a proper introduction. I've already made three of these, you know how it goes by now...I hope. Anyways, this final installation of Behind the Scenes deals with the shape I decided to make for my final portfolio, which usually goes by the name of 'The Hexaflexagon.' It's essentially a hexagon shape that consists of three sides, but you're only able to see two of these sides at a time, and you can cycle between the sides by flexing the shape. Sound confusing? It's a little hard to explain it entirely, but the preliminary work that went into creating this thing is not worth passing up.

What have we got here?

I started out with a simple sketch of a hexagon, and began marking the dimensions, side lengths, and congruent angles across the shape - and yes, if you couldn't tell already, this type of portfolio involved a lot of math to perfect. For one, to make sure that the size of my project fell within the guidelines of the rubric, I solved for the dimensions of the smallest possible hexaflexagon and the largest possible hexaflexagon that could be made for this project. Then, after creating these mock-ups and deciding on a final size, I began to sketch out where I wanted my portfolio pieces to go. This, inevitably, lead to even more math, as I had to figure out the largest possible square, the largest possible 2:1 rectangle, and the largest possible 3:1 rectangle that could fit diagonally in a rhombus with a side length of 8 inches. Although the process was a little rough, to say the least, I did end up calculating all of these dimensions, meaning that laying out my pieces should be smooth sailing from here.