Sunday, December 11, 2011

Art + Math = Magic!! It's a trihexaflexagon!

This is a trihexaflexagon. It's got three sides that each change, or "rotate"once. This is one of the sides and its rotation. Confused?

One of the workshops that I taught at my recent state conference was a hands-on workshop where the participants each learned to make a trihexaflexagon, a tetratetraflexagon, and a kaleidocycle - all a bunch of fun combining art and math.

Last year I posted about these amazing constructions right here. If you want more specific details about the process of creating a flexagon, or how how I got started making them, please check out that post.

My students this year faced several "challenges" on this project. One was to incorporate their name, initials, or some other word on one segment. This was traced in mirror images around the hexagon using carbon paper, resulting in a kaleidoscopic design.

Another "challenge" was to design one side using a ruler to connect corners and then adding additional lines and curves as desired, "flexing" as they drew to make sure their design connected in all rotations.

A third "challenge" was a color challenge. Students needed to color one side of the flexagon using either complementary colors, triadic colors, or, as chosen by both the students below, an analagous color family.

Here's a couple more student examples.

Making these can be a starting point for many lessons. You can teach tessellation, M.C. Escher, and Islamic design, or you can use them to teach color, or symmetry, or many other concepts. And then there's the ruler and construction skills required in building them.

As you know, I'm retiring. But somehow I know this isn't the last time I'll be constructing a flexagon. I'm hooked!! Perhaps you will be, too?


  1. Gosh darnit, Phyl! I flunked every math class from 7th grade on! I will try this but I can feel my jaw clenching! They are so cool looking and I am not a quitter! I'll let you know how they turn out-


  2. Awww, Pat... I admit to being a bit of a math geek as a kid, which I know is a strange combo for the artistic kid. But my big brother was a huge math nut and got me excited about this stuff.
    What you need is to be at one of my hands-on workshops in making these, or meet me 1/2way and I'll teach you! I had a roomful of about over 40 people at my NYSATA workshop, and every single attendee walked out successful, not just with this, but with another flexagon and the beginnings of a 3-D kaleidocycle (don't attempt that one without some serious assistance).

    Would love to have the opportunity to help you out with this someday!

  3. The orange one is marvelous! Great idea!

  4. actually equals ARTMATH..which sounds like a swanky private school :) ha ha These are great!

  5. Wonderful lesson idea, Phyl. I like the larger size of these for some very colorful options. I've really got to try folding some of these myself. I think I am hooked!