This is a follow-up to my paper toy 'ible. I looked for sliceforms on this site and did find a few but not enough. As a geometry teacher of many years, I know how important playing with shapes is to a student's understanding of shapes.

In this instructable, I want to show you how to design and produce a few simple shapes that you can play with afterwards--or share with a child who can play with it. (I gave my paper toy sample to an adult to give to her children. She did show it to them but refused to let them keep it. She loved playing with it too much.)

Once you have built a few of these, you should start to feel capable of trying to design a few of your own. Don't be surprised if they come out nothing like you expected--especially on the first try.

Step 1: Print Some Graph Paper on Cardstock

As with all sliceforms, you need to use something a little thicker than copy paper. I use cardstock because I have a lot of it and it comes in a lot of fun colors. You can use 'cover stock' which is just a little lighter than cardstock. You can use sheet of plastic--but it is hard to print on plastic. Tracing your design onto the plastic with a permanent marker works well. Then you can erase marks left behind with rubbing alcohol.

Print a few sheets of graph paper. I don't bother with just printing a single sheet because when I start playing with my math, I tend to get a little carried away.

There are a lot of graph paper generators available on the internet so if you want a different size grid, you can easily find one.

graph paper quarter inch.pdf
Download

Step 2: Decide on a Shape to Work With

There is no right shape to work with but there are easier ones than others. Let's start simple. If you made my last paper toy, you made a 3 dimensional cylinder but cutting oval slices.

Let's try to make a square prism (box kind of shape for non-technical people). We will need some rectangle pieces. This is really easy to draw on the graph paper you already printed. I drew a bunch of the same size rectangles--I chose to make them 6 squares by 4 squares. I like a small pocket sized toy. It is not critical that you use this size--just make them all the same as each other.

I then drew in the lines to mark where I would cut my slits. These should be only half the height of the rectangle you started with. This is why I chose an even number of squares on the grid. I chose to use 5 slots per piece so I spaced my lines on every other grid line. If you space the marks closer, you will end up with a more solid toy; farther apart and the toy will be more open. I usually use an odd number of slits on each piece--my weird OCD. You can try an even number if you want to.

After I drew a couple of pieces, I was pretty sure I could cut the rest even without drawing the lines. It took less time that way.

Step 3: Cutting Your Pieces

As with most sliceforms, cutting has to be done carefully. If you leave a jagged edge, the paper will catch. Try for smooth cuts.

Cut all the pieces apart and then start on the slits. Cut the slits in one smooth motion if possible. You need to cut just to the left of the mark and also just to the right of the mark. There should be a thin (1 mms wide) strip that curls up a little. Pinch off this strip to leave a small gap in the paper.

Step 4: Attaching Pieces Together

Now for the fun part--putting it together so you can see how it works.

Half of the pieces will have the slits point up; half will point down. I used 2 different colors because I like the effect when you play with the toy. Start with one piece of each color. Slide the pieces using the last slot on each piece. Add a few more of one color but be sure to offset each piece one slot from the previous one. Flip the thing over and work with the other color--again offset each piece. Keep doing this until you use up all your pieces.

The video is a bit rough. It is hard to hold the camera and the toy at the same time.

Step 5: A More Challenging Shape

Grab another sheet of graph paper. This time, I decided to draw triangles and they will be of several different sizes. I start with the largest one--it will end up in the center of my toy. I mark where the slits will go. The graph paper allows me to measure half way up the piece without a ruler and it keeps me going at a right angle to the bottom edge. I marked the center slot and then equally spaced ones on either side (an odd number of slots).

I used a slope of 2 and drew the 2 sides of my triangle. The base is 12 units wide. From the top to the base (altitude) is also 12 units.

The next slices will end up going on either side of this center piece. They will be a little smaller than the original piece. I chose to follow the same angle I used for my original piece--just a bit smaller. The height of this triangle should match the height of the original piece at the location of the slot it will fit into. Make 2 of these. Space the slot marks at the same distances as you used on the first piece.

Mine is 10 units wide and 10 units tall.

Make a third piece. This one should match the height of the original triangle at the location of the next slot. Again, make 2 of these pieces. You will probably not have room to place as many slots as on the first piece. This is ok. Keep the same distances e apart.

Continue in this manner until you have made enough pieces to fill all the slots of the original piece. The farther out from the center slot that you get, the fewer slots you will make in these new pieces.

Copy all the triangular pieces but make their slots go in the opposite direction. Cut out all the pieces and their slots.

Arrange the pieces on your work space in the order they will be assembled with the tallest piece in the middle and the shortest on both ends. It is easiest to start with the 2 middle pieces--one opening at the top, the other opening from the bottom.

Step 6: Komodo Dragon

This is a non-geometric sliceform I made when my son was in elementary school. He was doing a report on komodo dragons. He made a life sized picture of one on a 6 foot long piece of paper. I made this little 3D one. Sorry but I am out of komodo colored paper--this color will have to do.

Because I made the nose portion narrower than the body, this one does not collapse nicely. If you want to fiddle with it, just remove the one top piece.