folding · Paper Toy

Six-fold, flat-fold, Paper-fold

Paper Folding the Ferozkah Jaali
Paper Folding the Ferozkah Jaali

I found a fold.

If paperfolding graps your attention, prepare to be overwhelmed.  There’s three things to unpack here: the fold, the pattern on the fold, and how they interact.

I had been wondering if I could fold a tetrahedron out of a rectangle.

Tetrahedrons and other shapes
tetrahedrons and other shapes

Turns out, yes. I can make a tetrahedron with a square base or a triangular base out of the same piece of paper using the same folds in different ways.

Looks like a fish
Looks like a fish

Then I started seeing that I could make other shapes out of the same pieces of paper using the same folds differently.

Some shapes are flat, others are dimensional.

I’ve been playing with these all week, and I am still finding different shapes that these folds create.

 

I’ve also been drawing this six-fold pattern from Islamic Geometry called the Ferozkoh Jaali. It occurred to me that it would go perfectly with the folds I was making.

detail of Ferozkah Jaali
detail of Ferozkah Jaali

 

This is just a small portion of the pattern. I’ve been coloringing copies of these in all week, trying to get to know the shapes.

Here’s the fold that I’m using:

 

Mountain and Valley folds
Mountain and Valley folds

It’s four mountain folds (diagonals) and two valley folds (horizontal and vertical) that are created around equilateral triangles. Oh, and there’s a slice in the middle. One horizontal slice.

Now here’s the first wonderful thing about using this image with my folds:

No matter how you use the creases (which are around the equilateral triangles) , the pattern lines up. In the photo above, a corner is peeking through that slice in the paper, and, look, the pattern lines up.

Equilateral triangle(s)
Equilateral triangle(s)

I printed the design on the fronts and backs of my papers, and look, when the paper wraps around itself, the pattern lines up.

Now there is one more thing to mention. Hold on to your seats. This is wonderful. But, first, here’s the foundation of the image I created, first by hand, then on the computer, because I needed the precision of the computer image.

Six-fold-geometry
Six-fold-geometry

Okay, so as I’ve been folding and refolding and refolding again, and finding different shapes all the time, the last final amazing thing that I noticed (and this makes so much sense) ….

Some heart shapes?
Some heart shapes?

…is that every shape I make with these folds can is echoed somewhere in the lines of the  geometric drawing that is printed on the paper.

This makes me so happy, well, I can’t even describe it.

Another heart shape
Another heart shape

Well, there you have it. Hope you love it as much as I do.

covered with NOT geometry
covered with NOT geometry

Oh, and just in case you’re wondering, I think this fold looks good with just about anything on it.

Am seriously considering making a bunch of these and offering them for sale, probably through Etsy. Stay tuned….

 

 

 

geometry and paper · geometry and paperfolding · Paper Toy

A Cool Adobe-Illustrator Artboards Thing

To be two cubes
To be two cubes

I wanted to transfer this image to a big piece of paper. Way too big for my printer. It’s just under 24 square inches.

One the way to being two cubes
One the way to being two cubes

I made the pattern with the intention that it would fold into two cubes. BTW, I recently learned that the correct term to use here is net:” A pattern that you can cut and fold to make a model of a solid shape. This is a net of a cube.” (quoteth from the internet)

While I was scheming how to break the net into prints that I could piece back together, it occurred to me to just overlap the artboards in Illustrator. Set them up to be negative one inches apart. Here’s a snip of what the Illustrator workspace looked:

Six overlapping artboards in the Adobe Illustrator workspace
Six overlapping artboards in the Adobe Illustrator workspace

All I did, after setting up the six artboards was to overlay my net onto the artboards. No figuring, no scheming, just laid it right on top. Honestly I didn’t know what would happen. Would the overlapped parts not print? Just didn’t know.

Amazing. Everything printed everywhere. What I mean is that the parts of the image that were on the overlap printed on both papers. This made it really easy to piece together. Of course the best use of this technology is to print Happy Birthday banners. But what I did was piece them together, cover the back of the paper with blue crayon, and, using a ballpoint pen, trace over the lines to transfer to my larger paper.

net of the Cubes, cut out

I didn’t take any more photos of the process, but here’s my fully cut out net.

On the way to cubeness

The blue crayon showed up just enough, but what was really great is that the force of the tracing created score lines, making this easy to fold.

Weighted by a train
Weighted by a train

Here’s the cube. Hard to imagine how that image becomes these two two-inch cubes. So I made a video:

 

Arts in Education · Book Art · Flexagons · group project · Paper Toy

5th Graders’ Kaleidocycles of the Bill of Rights

Piling Kaleidocycles
Piling Kaleidocycles

They did it! This group of fifth grades did this hand-lettering kaleidocycle class project! I described the details of this project a few posts back so check out that post for more details. Here’s the general gist: After introducing the project, which is a 3D paper construction with rotating faces that will be graced with references to the Bill of Rights, students were given pages of letter fonts to choose from.

Tracing

Using the windows of the library as light boxes, students traced out letters to created one phrase each that described one of the first ten constitutional amendments, aka The Bill of Rights.

At the window

Every single student was highly engaged. Really.

Within two class sessions the students produced something that I could take home and scan into my computer . I won’t lie..scanning and cleaning up their work took time. Above you can compare what they gave me, on the left, to what I ended up with on the right. Some pages required much more work than others. The middle example above was so easy to work with that next time I will encourage students to just give me outlines. The most time-consuming letters to work with were those that were colored in and touching other letters. I moved things around a bit, like in the top example you can see I centered the word “OF.”

I brought home their work, scanned them into my graphics program, cleaned them up and laid them into a kaleidocylce template. Brought them back for students to cut around the perimeter and score.

Scoring the paper
Scoring the paper

Students made score lines so that the paper would fold easily and accurately. Scoring is generally done with bone folders but we used glitter pens to score the lines. They worked great, and kids were excited to be using the gel pens.

Assembling the Kaleidocylce

Then came the folding and gluing. I didn’t take many pictures of this process as I was, like, really really occupied helping move this process along.

One of four faces of the Kaleidocycle
One of four faces of the Kaleidocycle

This project turned out so well. Not everyone had a chance to finish up and decorate, but the wonderful school librarian will be able to help with the few than still need finishing.

Kaleidocycle yellow borders
Kaleidocycle yellow borders

Students enjoyed individualizing their own kaleidocycles.

Another side
Another side

I tried to get them to use completely different color schemes on each face, so that the differences between the four rotation of faces were dramatic. Students didn’t much listen to my suggestions.

Here’s one of their kaleidocycles in action:

I consider this project a great success. I got to talk to the students about design, about hand lettering, and they got to work with some cool geometry. I’d even go so far as to say that they are also much more familiar with the Bill of Rights , as they were constantly asking each other, which one do you have, which one is yours, and talking about their own.  I have to say that at first the students were confused about what I was asking them to do, after which the librarian told me that doing a group project was pretty much out of their experience, so the concept was hard to grasp at first.

One thing that made this possible was that this was a small class, just 12 students. I often work with 60 to 70 students in a grade level: I wouldn’t do this project with a big group. OH, but it was so delightful doing this with a small group.

Tower of Kaleidocycles
Tower of Kaleidocycles

Do I get to pick a favorite project of my teaching season? Yes? This is it.

For more about all this take a look at these posts:

https://bookzoompa.wordpress.com/2017/02/19/kaleidocycles-and-tetrahedrons/

and

https://bookzoompa.wordpress.com/2017/03/19/designing-a-seriously-fun-project/

Book Art · Box · Paper Toy · Uncategorized

Four Squares, Each Folded like an 8-cut Pizza

 

Here’s something that can only be described as playful.

img_20161205_161942.jpg

It’s four squares, which have been folded into eights, like an 8-cut pizza. I made this as a sample book when I was teaching the Book Arts at Bancroft series of classes at the Bancroft Library here in Salem.  I would teach eight classes in the fall and eight more classes in the spring, to groups of 3rd and 4th graders. I did this for ten years. It was a really great program, funded by New York State Council on the Art Decentralization Program.  No one was in charge of me so I did whatever projects I felt like doing with these kids. This was when my own children were as young as they come, so this book arts program kept me thinking about the arts at time when I would have otherwise been thinking only about laundry, meals and bedtime.
img_20161205_161718.jpgThis way of folding squares and then just connecting them together is an idea I came across during a day that I passed at the Patents Office in NYC long ago, before the internet. I’d go up there now and then,  into this great cavernous room on the west side of Manhattan and just looked through cool stuff. I’m pretty sure that this way of folding was in a folding toy section, patented by a woman from Israel. There were some great drawings with the patent (which I copied and probably still have).

img_20161205_162118.jpg

When I did this with kids during my book arts workshop I was aware of one big obstacle: There are 64 distinct areas to decorate. Since the charm of this structure is finding all sorts of different configurations to display it in, it seemed to me that the patterns should be varied on each facet. But, 64? That’s a lot of designs. I had the kids for 90 minutes. Could they fill the papers? How could I facilitate this?

img_20161205_161851.jpg

We spent the first 25 minutes making the structure. 65 minutes left. 64 areas to fill.

img_20161205_161655.jpgWhat I did was prepare 64 notecoards, each with a different design. The children sat in a big circle, each with a  marking tool. Each note card had a different design suggestion on it. Kids were not bound by my suggestions, but they would have only about a minute to decorate one of the triangular areas, then they would pass their marker and note card to the person to their left and receive a new suggestion and marker.img_20161205_161641.jpg

I’m usually not so regimented with my classes, timing things in short intervals and making commands, but this time it was great fun.

img_20161205_161918.jpg

So, got that? Four squares folded pizza-style and linked together and decorated. Then filled with designs.