Flexagons · geometry and paper

Flexagons and Me at MoMath

Some time ago I created this new kind of flexagon. I’ve kept the secret to myself long enough that I’m ready to share it. The Museum of Mathematics is hosting my reveal through their events program, via zoom, this coming Thursday, August 12 at 6::30. flexagon.momath.org. I want everyone to join me there.

There are many different kinds of flexagons. All of them can be folded into different configurations to reveal hidden sides and to show different patterning. I am enthralled by this genre of paper folding.

Some flexagons are quite tricky to fold. I think of this one that I’ve made as being elegant because it’s super easy to fold. It’s one of those things, that after you know it, you wonder why hadn’t you figured this out yourself.

I want everyone who likes my work to sign up for this event! It’s only $10 to join, and you can have your friends and family sitting with you with the same link. What’s even better is that proceeds will be benefiting the museum itself.

I’ve wanted to do this at MoMath because, throughout the lock-down, I’ve been so impressed by how MoMath kept up their programing via zoom, with programs for everyone from young children to senior citizens. The wide range of people they supported with their programs was truly impressive, and quite affordable including many free events, and lots of $5 sale events.

Oh, one more thing.

I’m making a graphic available for people to decorate. I designed this graphic specifically for my flexagon. I’m not sure if the museum will be distributing it (I think they will), but if not, I will make it available directly for people who sign up.

Gather together a couple of sheets of regular copy paper, glue stick, scissors, scrap paper, and four paper clips.

Be there or be square.

It would mean the world to me.


geometry and paper · Math with Art Supplies

Revisiting the Gryobifastigium

A couple of years ago I wrote about a shape with the wild name gyrobigastigium. I made and sent off a a collection of them to a group show. After they were returned they were boxed up and and tucked away. Recently I was feeling a bit of sadness that all the thoughts and ponderings and joy that this shape brought to me had also gone into deep storage.

I found the box, opened it, and began to move the solids around.

Many gyrobifastigium

These solids were as every bit as engaging as I had remembered them to be.

A few days later I saw, on Twitter,a thread written by Dr, Martin Skrodzk announcing that the German Mathematical Society had put out a call for papers for an on-line mini symposium called “Mathematics and Arts.” https://twitter.com/ICERM/status/1417941320409264128?s=20

Having just been forlorn, thinking about my shapes, I decided to submit. I had to write an abstract. I’m not really sure what mathematicians want to see in an abstract, so I asked some questions and wrote something.

My submission was accepted!

The symposium happens between Sept 27 and October 1. I think I saw, somewhere on their website that registration is free for teachers. Not 100% sure of that, but am checking. 

If you are interested, here’s the PDF of what I wrote. It’s a short, fun read. I hope you take a look.





Book Art · Workshops

Well, that was fun…

Taught the first set of the in this series of cool Zoom paper engineering classes for Center for Book Arts.

Was trying something new, so I was very nervous. What I did differently in this class was, instead of filling the time with lots of instruction, I showed one thing. Okay, maybe two, but the second thing was a variation of the first. The structure was a pop-up that was made by using a constraint, which guided the way the paper moved. After showing a few things, we worked on what I taught, then worked pretty much independently for quite a while before I started teaching again.

I was able to share some of my favorite tips about decoration, showed more variation on the same structure, and then it was time for show and tell.

My favorite thing that I worked on was a second version of a lollipop farm. It opens really well, making it look like lollipops are emerging from the earth. People tried out all sorts of inventive ideas of their own, going in directions that would have never occurred to me.

I very much wanted people to enjoy the relaxed, playful nature of the class. A number participants were people who had worked with me on-line before. One person was a far more accomplished artist than me. One person knew me from following this blog (hi Leslie!), and the rest were taking a chance. Everyone seemed really happy. Then most of them signed up for another class in this series, so, yeah, I guess they enjoyed what we did together.

Next set of classes will be making the Magnificent Unlikely Pop-Up Bird. There will be an evening option and an afternoon option. What I like about this bird is that its wings are a canvas for decoration. I use cut paper, Prismacolor pencils, and, sometimes, gold sticker paper to create these. Participants will print out their own pdf template, which they will then personalize. People will be using their own materials, or they can choose to buy a packet from me for the class.

If anyone is interested in joining me for the Magnificent Bird project, I will teaching it on Monday evening EST, July 19, and Thursday afternoon EST July 29.

Hope you’re all having a good summer. I am. 🙂


Constraints applied to Paper

Video Link of this Fireworks card

After a whirlwind of teaching multi-session workshops, this summer I’m turning my attention to single session summer classes at the Center for Books Arts. There are certain moveable constructions that are so simply ingenious and full of possibilities that I personally continually revisit them but rarely teach. I decided that summer should be low stress, so I thought it would be fun to pick out some of these favorite paper-engineered structures to show.

Joke’s on me!

I tend to forget that teaching something requires a clarity that is different than when I make something on my own. I’ve been spending days and days reworking templates on strategies.

Coming up this week (classes whose registrations, at the moment, are so small that if anyone wants to be in an intimate class, this is the week to join in) is one of the sweetest, most elegant structures one can do that is both surprising and accessible – by which I mean it’s a good one to teach to children. The one characteristic that I particularly like is that the paper engineering is one that uses a constraint. The colors can be wild, but the paper is controlled.

Here’s what I mean.

Here are some unconstrainted strips of paper just glued to the page. The way that they are they would just wiggle freely. See the paper behind with the holes? The paper will be threaded through the holes to create what I am going for.

In this case, what I’ve made is something like a lollipop farm.

Here’s another…

Waiting to Bloom

Above is the closed version of this card.

Below is the open version


I can have fun with these all day long. They give me a great excuse to use up lots of these gorgeous bits of cut paper I keep around.

I make these abstract cards.

Closed above, open below

These are such a great fun. I’m looking forward to teaching these this week, as I am always delighted to see how other people choose to use something that I find to be enchanting.