Art and Math · geometry and paper · Paper Toy



gyrobifastigium (plural gyrobifastigia or gyrobifastigiums)

  1. A polyhedral solid formed by joining two face-regular triangular prisms along corresponding square faces, giving a quarter-turn to one prism. It is noted for being one of the few regular polyhedra that packs in three dimensions.
Zhen Xian Bao

Zhen Xian Bao Gone Wild

In the book arts studio at The Center for Book Arts
In the book arts studio at The Center for Book Arts

Just came back from teaching a two-day workshop at The Center for Book Arts in NYC. One of the many reasons why it’s such a great place to teach is that there are enough materials around for classes to scavenge from (drawers of well labeled colorful and printed paper scraps, rolls of book cloth, shelves of random, unusual papers) that when I get to the point in our project where people can make their own choices of how to proceed I get to be surprised.

Barbara's Zhen Xian Bao
Barbara’s Zhen Xian Bao

After Barbara put on a bright orange cover, she was considering how the leaf paper would work with on the thread book. My thought is that these books are a celebration of personal choices so I was happy to see her bold preferences all combined altogether.

Karen's Book
Karen’s Book

Although my classes starts out with people using my papers (which is the executive decision that I impose because the patterns on the paper help in guiding accurate folding) it’s always fun to see what choices people make when they take charge. Look how border around the edges of the collapsed boxes brighten the whole interior.

Karen's Thread Book, closed
Karen’s Thread Book, closed

Love this choice of chartreuse book cloth cover with bright yellow ribbon.

Rita's Twist boxes
Rita’s Twist boxes

Here, Rita used her scraps to decorate the twist boxes in a way that made the box feel like flower petals unfolding as the twist box opens. I’ve only thought of using these scraps at the top edge, but this other choice now makes more sense to me.

Vince's Big Box in Purple
Vince’s Big Box in Purple

Vince came to the class already having high comfort level with box folding. He made this incredibly dramatice big box layer out of some very cool looking purple/brown paper, not at all following my suggestions on how to construct this layer. Instead, he built on something else I showed him, just in passing, to create a veritable cavern in his book’s interior.

Nancy's Choices
Nancy’s Choices

I had a couple of people in the class who played in the rabbit hole of choices for so long that I didn’t get to see the final product put together. Nancy found all sorts of great scraps, then worked on all sorts of inspiring and unusual pairing and arrangements, both graphically and structurally. I hope I get to see how this one as it comes together.

Side View of Dana's Book
Side View of Dana’s Book

The surprises kept coming. Dana’s book, when closed looked like a yummy sandwich. The interior, well, I would need a dozen photos of this one to really show it off. Here’s a couple:

Dana's Chinese Thread Book/Zhen Xian Bao
Dana’s Chinese Thread Book/Zhen Xian Bao

Dana’s has a great eye for combinations. While the rest of us were carefully considering our decisions Dana was cutting and glueing up a storm. So much fun to see.

Dana's Zhen Xian Bao/ Chinese Thread book, open center
Dana’s Zhen Xian Bao/ Chinese Thread book, open center

Notice the pink cover. This was from a stack on from CBA’s shelf. Worked perfectly with the book.

Flower Top Box
Flower Top Box

There is so much to go over in these classes that I make it optional to learnthe flower-top box. Still, everyone in this group made one.

While I was teaching this class I noticed a woman who was in the bindery, looking at the show in the gallery and watching our work in the class. When we broke for lunch she and I spoke for a few minutes. Turns out she had recently moved from Switzerland to Canada, and had taken a class in Canada on how to make these Zhen Xian Bao structures. She expressed a frustration about the fact that the class had been taught using inches as the unit of measurement, which was not used to having been raised using the metric system. I wanted to give her the measurements that we used in class, which doesn’t rely on inches or units, but, instead, on parts of a square, but she already knew what I was talking about, explaining she understands the way that “Paula does it. ” Evidently she’s watched my tutorials, knows “Paula” but didn’t realize, until I said it, that I was the Paula that she was referring to. This made us both very happy. A wonderful moment. I found a nice note from her today in my inbox.

What a great couple of days!


design · geometry and paper · geometry and paperfolding

Pattern by Rotation

Twist Boxes
Two Twist Boxes

A bit of eye candy tonight.

Here’s the birds eye view of two collapsed twist boxes . What’s wild about these is that they are made from nearly the exact piece of paper.

Patterned Paper
Patterned Paper

Here’s the paper they were made from. Can you see the difference between them?

What’s going on is that the pattern is shifted by just a small amount.  This small shift makes a big difference in the pattern that is created by the folds that rotate the design on the paper.

Here’s another fun rotation.

I have four of these little squares. I can put them together so that the design is rotated around a specific corner. Like this:

Rotation #1
Rotation #1

A design pops out! When I rotate the design around another point, another design pop-out.

and another…

and since this square has four corners there is another design for these rotations to make, but this is all for now.

I should be prepping for the Center For Book Arts class that I am teaching on Thursday and Friday, on how to make Zhen Xian Bao.,,

Good thing I’ve got tomorrow. Have been spending way to much time rotating things.


Workshop Prep

Sourcing Materials

Mohawk-Keaykolour Sample pack
Mohawk-Keaykolour Sample pack

If anything gets me out of the business of doing workshops before I’m ready, it will be the shifting ground of finding the materials that I need for my workshops. Not only have places vanished that I used to just stop by and get materials (ExPedex), not only have some of the materials that I’ve loved and relied on change dramatically for the worse (UHU Glue sticks) but the papers that I rely on the most have at least doubled in price. No exaggeration AT LEAST doubled in price. Even at these elevated prices I feel lucky to get what I want. Sometimes I don’t get lucky.

Blue Copy Paper
Blue Copy Paper

Yesterday I got lucky. I needed some bright blue copy paper. I checked on-line at Staples. It said they were out of stock. I checked Amazon. Yesterday I couldn’t find this on Amazon unless I bought it by the case (over $100). I checked the Mohawk paper site. Nothing. Checked Walmart. They had it, but it was about $34.00. I used to pay about $9.00 for this paper. Since I needed some other things, I drove an hour to Saratoga Spring Staples. They had it on the shelf for about $16.49. But then today I checked Amazon again and they had a comparable paper by Astrobright for a better value, $14.99 for 650 sheets. If I had used Astrobright as part of my search I would have found it, but I didn’t know to do that.

Card Stock and Cover STock, white
Card Stock and Cover Stock, white

I made a mistake on one purchase because I wasn’t clear about the difference between 67lb cover stock and 65lb card stock . I’m clear now. It’s not a huge mistake, and I will use what I bought, but I don’t want to make this mistake again.

Let me explain. It would seem the the 67lb is heavier than the 65lb, but you can’t go by that. For a better weight comparison you have to look at the g/m-squared weight. You will notice that the 65lb is heavier. While this seems to make so sense, it has to do with the fact that the card stock pound measure is determined by a different base than the cover stock pound measure. Yes this is sounds crazy, but remember this is the land of inches and feet,

It’s not the weight of the paper that bothers me: it’s the feel of it. I like the toothiness of the COVER weight paper, because I like that crayons and colored pencils feel better to use on the toothier paper. The cover weight cost about about $3.00 less than the card weight.

What’s uncomfortable about these Staples purchases, though, is that the instore prices were more expensive  than the on-line prices. In-store the items were about 15% more than on-line.

from Nicole's papercrafting collection
from Nicole’s papercrafting collection

I made a stop at AC Moore too. I happened to see pack of 50 sheets of 65Lb card weight paper on sale from from Nicole’s papercrafting collection, for $3.33. There are five colors to a pack, which comes to about 7 cents a sheet, which is about standard. What attracted to these is that I liked the selection of curated colors in each pack. I will probably buy these again. I can get curated colors of Astrobright colored paper,  (for closer to 10 cents a sheet) but I like the Nicole’s colors better.

The downside of the Nicole paper was that it kept jamming in my copy machine. Not all but some, which is an oddity for my machine

Stardream Paper
Stardream Paper is a place I’ve frequently bought paper from, especially when I’m looking for Stardream paper.

Also, I’ve been happy to discover I can buy full sheets of paper, without having to buy a full box, from Mohawk at  I’ve invested heavily in buying many of their sample books, like the one in the photo at the top of this post. I absolutely love buying the papers that I’ve been getting from Mohawk.

My biggest problem has been glue sticks. I am not happy with any glue stick choices.

sing Gel Markers when they were good, 2013
sing Gel Markers when they were good, 2013

I used to buy some cool colored pencils by Crayola (Fx pencils) that worked great on black paper. Then they disappeared from the market. Then I bought Crayon Gel Markers for black paper projects, but then they stopped working well. I now use Prismacolor pencils with kids when we are using black paper, but I still miss great Gel Markers.

I used to also do many projects using 36″ shoelace tipped yarn. My supplier stopped selling them, and any others that I found were more expensive, but worse than that, were not made of the lovely, thick soft yarn that I was used to. Now when I want to use yarn with kids I nailpolish the tips myself. It works.

There’s probably more to be wistful about, but it’s time for me to get back to prep work for this weekend’s workshop.