I’m ending this series of posts on hexagon-flexagon with images of work done by students in Michele Gannon’s art classes in the Adirondacks.  I taught the students how to do the paper-folding. Michelle’s considerable artistic influence supported the students’ creative output.  Each of images that I am showcasing here is followed by the same image in different configuration on the same structure. Notice how the patterns change.

This lovely design was created with Prismacolor pencils. Some, but not all, of the Prismacolors show up well on black paper.

This next set shows a really simple design that works really well, as the look of it changes dramatically when the image is flexed.


Since each hexagon-flexagon has three distinct surfaces to design and decorate I  brought in a variety of novel tools to help motivate the students to keep working. In the photos below the students used my Chinese Dragon paper punch. Paper punches are a great motivational tool, and the dragon is the most popular of all that I have.

By the way, the students that made these images were about eleven years old.

I like the way the relationship between the dragons changes when the flexagon flexes.

Another tool that makes a big hit with students is Crayon Gel Markers. These markers take about 15 seconds to fully show up on the paper, thus adding a bit a magic to the process of decorating.

I also use some of the Crayon colored pencils. Only some of them work well on black paper. I used to be able to find Crayona FX (?) pencils that worked on black paper, but I haven’t seen them around for awhile.

I have to say that that only reason that I felt comfortable teaching this structure to these students is that I knew I would be working with small groups. I don’t think that I had more than 10 or 12 students in each class.  The fact is, the folding  for this structure is so specific, that I doubt I could successfully teach it to large classes. But I think it would be a great project to teach to home schoolers, or in an after school art class.

The hexagon below has a completely different look when it’s flexed.

The middle circle totally changes, and that white line becomes a whole different thing, too.

These were so much fun to teach.  It’s a real pleasure to watch the expressions on the students’ faces when they see their own design be transformed when the hexagon flexes. That’ s my favorite part of the process, too.

Related posts:

Intro to hexagon-flexagons

Fractions Flexagaon

How to Make a Hexagon-Flexagon

Forest of Flexagons

April 28, 2011


I don’t often have the chance to make flexagons with a class. But recently, Mrs. Schroeder, who works with an artistic group of fifth graders, asked me to plan a project with these students that could showcase their creative energies while still requiring that they use research skills.

Mrs. Schroeder chose Adirondack trees as the object of research. Each student was assigned their own individual tree. They were then asked to research such things as the tree’s  habitat, uses of its wood, characteristics  (the look of the bark, shapes of the leaves, etc) and its latin name .

Making flexagons to house these research facts was my idea. Here’s my instructional  PDF for Flexagon Squared.

Flexagon about Easter White Pine

For the uninitiated, a Flexagon is a paper structure whose surfaces rotate in unexpected ways when the folds in the paper are flexed.

Flexagon flexing

There are many shapes and styles of flexagons. The ones pictured here are based on a square.

Flexagon about Shagbark hickory1

Ok, I know it doesn’t look  like a square, but imagine unfolding the lime green paper….Flexagon about Shagbark Hickory, flexing

…now, here it is, half-way unfolded….

Flexagon about Shagbark hickory, Flexed

…and all the way unfolded.  There are still surfaces on this one flexagon that remain unseen.

Flexagon showing White Ash Tree

The French teacher at this school saw this project and was tres impressed by the work of these energetic and talented students. In addition to the fine work done by the fifth graders,  I told her that the secret to the success of this project was Mrs. Schroeder. She kept the class on task, and raised the bar high for research, spelling, and presentation.  Mrs. S.  remained consistently positive with and respectful to the students while staying clear in her intentions that they produce. It was really great observing how responsive these young people were to meeting Mrs. Schroeder’s standards.

My part in this project mostly consisted of providing instruction on how to construct the flexagon, and providing colorful papers and compelling materials to support motivation and inspiration.

dotted Flexagon

I hope to put together a set of directions on how to make this structure.

Flexagon showing uses of wood

But for now, please enjoy just looking.

Flexagon about Red Maple Tree

Addendum: here’s my instructional  PDF for Flexagon Squared.