Helen’s Book

The Art Of Paper Craft by Helen Hiebert

No question about it: Helen Hiebert put together a book, The Art of Paper Craft, that is a must-have instant-classic for people who love working with paper. I am pleased to be one of her contributors, and am happy to have the project of mine which she included in print, out in the world.

Oh, so much to unpack here.

I met Helen in NYC before the turn of the century, In 2002 she included some of my work in her first (?) book, Paper Illuminated. She and I had both moved out of NYC, she to Colorado, I to Upstate New York. We did not stay in touch. One day in 2017 Helen reached out to me, not knowing that this was when things were changing for me, when my focus was starting to shift, when I could spend time in my studio and be in touch with people again.

A place to perform, But how does this stage stand up?

It’s not that I hadn’t been working. While my husband and were raising our children, my creative focus was on designing projects for schools. At the same time we had some tough issues to deal with here at home. I had no time to keep in touch with people. The project of mine that Helen shows in her book was designed in 2012, during a time when I was just trying to get through the day. I love this project. It is a perfect example of the work that is most important to me.

A view showing the side supports
A view showing the side supports

It’s a stage. Children are quick to play make-believe, to enact stories that they know or that they make up. Having a stage to interact with can ignite and focus their imaginations.

Here’s what I love about this stage: It can be large or small, it can be made out of a wide variety of materials, the side supports are also pockets which can hold puppets or scripts, it can fold up flat to be put away for another day and it is almost ridiculously easy to make. Extra bonus: there are oh so many to decorate the structures: drawings, stickers, collage, bling.

Kindergarteners, 2012

I love this project because anyone can make anywhere, making it any size, using available materials. It can be plain and small or large and fancy. And now this project is out in the world in a larger way that I ever suspected it would be.

Thanks, Helen.

I have to mention that my name enjoys being in the company of the other names on page 276 of The Art of Paper Craft.

Congratulations to the world, for now having Helen Hiebert’s beautiful book in it.

Frieze Groups

Frieze Symmetry, intro #3: Square Bases & Gyration Points

I am going to be writing about what’s missing from everything I’ve looked at about learning the seven frieze groups.

It  has to do with two tools: square bases and gyration points.

To get started, I emphatically want to say that the easiest way to understand the frieze groups is to make them yourself.

A good way to construct frieze patterns is to move around simple paper shapes.

A note about simple shapes:  For the purpose of learning frieze patterns, the unit shapes should not have lines of symmetry which are parallel to or perpendicular to the horizon.  I’ve created a file of shapes that can be altered so that their horizontal and vertical lines of symmetries are disrupted. This can be done by slightly tilting the shapes, cutting out bits to make regular shapes less symmetrical, or strategically adding color or other shapes to the shapes.  A standard circle paper punches is also a good tool to use for the purpose of disrupting the symmetry of a regular shape. For examples, see the image below

It’s not that using symmetrical shapes for frieze pattern is a bad thing. Just the opposite is true. It’s just now, when first learning about the different symmetry groups that it’s preferable to avoid the confusion that can come with using shapes which have their own embedded horizontal and vertical symmetries.

The way to handle the unit shapes is to mount each of them on a square base, preferably one that is transparent. Skeptical? You will be convinced. I am certain of it. Eventually you will be able see the squares in your mind’s eye, but to start out, the squares are like training wheels.

For the rest of this post my shapes will  be attached to a square base. Think about this:

  • it’s the underlying base that moves horizontally to create the frieze.
  • It’s the shapes that are attached to the base that create the design.

My squares are made from a mostly transparent drafting film.

Here are some units glued to the square bases:

The only rule with the square base is that one side always remains parallel to horizon line of the frieze. This infers that the two of the sides of the square are always perpendicular to the horizon line.

Overlaps, extreme spacing, vertical reflections, horizontal reflections, and 180 degree rotations. which are the defining characteristics of frieze patterns, will work out just fine with the square base, as all of these changes do keep a side of the square base parallel to the horizon line.

Repeated Tilted Square
Repeated Tilted Square

If a design is made with an asymmetrically tilted square, the square base square doesn’t tilt, rather just the repeating unit is tilted.

If the shape overhangs the base, that’s not a problem. Let it overhang in any direction.

If the shape is so big that it obliterates the square, use a bigger square.

Now it’s time to talk about gyration points.

As I sifted through lots of examples of friezes that didn’t seem to correspond to each other, I finally realized that recognizing the role of gyration points in frieze patterns is essential. Gyration points are like the secret that nobody talks about

If you don’t know what a gyration point is, well, it’s a term that I also just learned.  The concept of what it is, however, has been one of my favorite visual playthings for many years. I just didn’t know what it was called.

Simply put, it’s a point around which an object is rotated which is not  located in the center of the object.

For instance, the sun is a gyration point of the earth, since the earth rotates around it.

A gyration point is a hard concept to immediately internalize and accept as important. Don’t worry if it feels fuzzy right now. If you follow along with these posts it will become clear.

Here’s some visuals that are intended to get things started.

In the image above, the same shape is rotated, but each pair is rotated around a different center, each creating a look that is different than the rest.

Now here are these same pairs, each creating a frieze pattern:

Friezes symmetry with gyration point
Friezes symmetries with gyration points

Varying the gyration point creates completely different visuals. Be sure to squint when looking at the bottom frieze and you will see a zig-zag pop out.

Here’s a video, repeating everything I’ve just written. I think that seeing the transformation happen on video makes a more convincing case for using a square base, and better illustrates gyration points.


The first two posts in this introduction are :

With any luck, I’ll be posting about the seven frieze groups before too long. It’s a linear process. 🙂

summer art/math

Making Game Cards with Kindergarteners

5 year-olds in the summertime could use a bit of number play. Get them invested, make it a game, get them coming back for more.

Numbers PDF   

Kent Haines wrote about a card game that he played with his daughter using a deck of cards. No point in spending two bucks on a deck of cards when there’s twenty 5 year-olds looking for something to do, right? We started out making our own deck by coloring in numbers 1 – 10. Of course I couldn’t find the perfect typeface so I made one I liked.

We did the coloring as sort of side project to other activities, so a took a few sessions to color enough for forty cards, which was my goal. Full disclosure: I probably did about 10 of them myself.

Next, kids put the “right” number of plant items with the numerals. I photographed them, then put them through my graphic program.

I printed and cut out the cards at home, then we played!

My rules for the game were a bit different than Kent’s, though we both start our games with laying out ten cards (two rows of five each), and the ultimate goals of our games are the same, which, as Kent points out, is to give children practice with counting, cardinality and comparing numbers.

In my version of the game I make sure that all ten numbers are in front of the child, but hidden, and in scrambled order. A random card gets turned over then it’s up to the child to determine where it goes in the number line up. The card that’s now bumped out of its own starting place gets turned over and the child decides where it needs to go, and so on.  If it turns out that two cards just switch places so that there is now no new card looking for a new place, the child can turn over a random card. This sounds confusing until you play, then it makes perfect sense.

There is no winning or losing, just finishing. Sometimes the kids played in pairs, some were slow and thoughtful, some were super fast, but they all loved the game. YAY! And they recognized the cards that they had in hand in making, and loved this connection. Too much fun.

Since we are moving the cards around I’m calling this version of Kent’s game “Recycle.” So PC.

Here’s a couple of video clips:


Addendum April 10, 2020


Here’s the a PDF of deck of recycle cards 2 types that we made, that you can print out to use or to use to make your own.

geometry and paper · holiday project · Ornament · Paper Ornament · Uncategorized

Round-up of Holiday Season Projects

A Bevy of Paper globes
A Bevy of Paper globes Directions at

Making things out of paper seems to be something we do during the holiday season.

Here’s some projects that I’ve written about with links to the full posts that explain them, that seem appropriate for the season.

This first one, the Spiraling Ornaments was surprisingly well-liked. All year, when I visited different places, I’d see ones that people I know had made.

Video tutorial (not mine) for Kaleidocycle



Here’s a template for a kaleidocycle. Not particularly holiday-ish, but fun and colorful, folds into something like the image below. More about this at



Next, directions for a six-sided snowflake. My big tip is to use paper napkins, as they already are the right shape: no extra prep needed! Also, paper napkins cut quite easily. They are perfect for snowflakes.

how to make a paper snowflake


If you want to understand how the cuts of your snowflakes affect the final design, see below:



Festive Jumping Jacks are quite fun. I’ve made these with kids just a few times, as all the knot tying makes this an intense project for anything more than a small group, but so worth the effort!

Jumping Jumping Jack

To work out how to make these you might have to look at a few posts, which are all listed at

The stars below are tricky to make, until you get the hang of them. I still have the ones I made on display from last year.

The original post contains a good bit of discussion about the geometry embedded in these shapes.

Finally, making little books with stories or messages is always worth doing.

Origami books made from a multiple folded papers, to create a Star Book and a Cascading Book, aka Origami Caterpillar Book
Origami books made from a multiple folded papers, to create a Star Book and a Cascading Book, aka Origami Caterpillar Book

Here’s a post that can get you started on some simple books to make with kids

For more an overwhelming amount of other book ideas, check out what I’ve tagged as making books with children

There you have it. Enough to do to keep you out of trouble at least until January.