Hexagon Flexagons, Post #1

My mind has been on math lately: my daughter and son are taking math classes (geometry and pre-calc) which they have found to be challenging. This has gotten me thinking about math. Math can get me thinking about flexagons.

These two Hexagon Flexagons show the same image in different "flexes"

Wikipedia aptly defines flexagons as ”flat models, usually constructed by folding strips of paper, that can be flexed or folded in certain ways to reveal faces besides the two that were originally on the back and front.”  Flexagons were first created in 1939 by Arthur H. Stone, a 23-year-old graduate student from England, in residence at Princeton University on a mathematics fellowship.  Since flexagons can be described in terms of the polygons they are created from, and since creating them requires mathmatical-like precision, these  folding structures, as a group are often thought of in mathmatical terms. However,  the playful surprises that they reveal create a lovely bridge to the arts.

In preparing this post, I looked around the web to see other people have written. Whew.  There are a huge number of sites that feature all sorts of flexagons. My favorite so far is http://britton.disted.camosun.bc.ca/trihexaflexagon/flexagon.html . I like this one because the it has it all:  a video of a hexagon-flexagon in action,  clear  how-to instructions, and a template with compelling graphics.

(Update: here’s  the link to my post and handout on How to Make a Hexagon-Flexagon)

The same hexagon flexagons as in the previous photos, flexed differently

There is so much on the web already about flexagons, but, still,  I want to write some posts about this structure as I have seen very little on the web that shows hand decorated flexagons or that displays this structure in playful postures.

Hexagon Flexagons, in mid-flex

BTW, Hexagon-flexagons are, in my opinion, the perfect thing to give as a gift to math teachers. This year there are a couple of math teachers who deserve my gratitude, so I made a couple of  these structures.

A Gaggle of Hexagon Flexagon

Since I was making some of these structures already, I thought I’d make a few more. I used the same design on each one, which was great because I was able to take one photo that shows all six design configurations that are contained on one hexagon- flexagon.

This photo shows all six designs contained on one Hexagon Flexagon

Writing about this  gives me a great excuse to mention my all time favorite book on paper-folding. I know nothing about the author Eric Kenneway, though I think he might have hailed from Australia (Bronwyn, are you familiar with him?).  His book, Complete Origami, is a resource I  refer to over and over again. I think of it as my magic paper-folding book, because, no matter how often I look at it, I am always finding something that I had not seen before. It’s like it presents ideas to me only after I am ready to see them.

My Favoirte Paper Folding book, "Complete Origami" by Eric Kenneway (the Steinway of Paper Folding Books)

Here’s a peek at the inside of this book:

Eric Kenneway's flexagon directions

As I like presenting directions on standard size copy paper, I will be working on a hexagon-flexagon instruction sheet to post in the next couple of days.  Also, since there are  many reference to hexagon- flexagons as being a mathmatical structure, I hope to post a hexagon-flexagon design that is straight forward and deliberate in graphically asserting a math connection.

For now, though, colorful and playful is all that have to show.

Addendum: here’s my post on How to Make a Hexagon Flexagon