A Gift for the Holidays 2025

This is a modular origami model, where small folded pieces tightly connect to each other. It costs next to nothing. It is also very easy to make, either by yourself, or as a fun evening with loved ones. I sometimes make one as a gift.

This year, I’m giving it to you.

Though it’s coloured a little differently, you’ll notice its shape is that of a football. It goes by other names too, but I will forever know it as a Buckyball, because of one afternoon in my senior year in high school.

I had some time to while away, so I slumped in front of the TV and landed midway into a science documentary, just as a mystery was unfolding.

An experiment had yielded what appeared to be new carbon molecules. This is not an everyday occurrence; pure carbon normally shows up in just two stable forms, which we know as diamonds and graphite. Neither of these shows up in discrete packaging, but as a crystal or in stacked layers. Both can go on and on.

This new form of carbon was different. Analysis showed a sharp spike at molecules with 60 carbon atoms, plus a second, smaller peak, at 70 atoms. What was this material? Why those specific numbers?

The show cut to a guy recounting his woes in trying to figure it out. His lightbulb moment came when he recalled a visit to an exhibition some twenty years earlier, which featured a large geodesic dome designed by a Mr. Buckminster Fuller, of whom I knew nothing.

The TV show swerved to Fuller. In the early 1930s, when cars still echoed the carriage, the young inventor designed and built a three-wheeled, window-clad tictac, complete with a rearview periscope. He called it “the car of the future”. By the standards of past, future and time immortal, the car is explosively cute.

The show said that Fuller deliberately collected speeding tickets as a way to record how fast his car could go. A responsible adult would call this reckless. A fact stickler would call it exaggerated. I just thought it was funny. The vehicle never made it past prototype, but many of Fuller’s later designs had, including geodesic structures.

Now we were back to the chemist with those carbon molecules. His dome-inspired epiphany was that the molecule structure was of a closed ball with exactly 60 vertices. This also explained the mystery with the 70-atom molecules: If you break the ball in two, which you will shortly be able to do, you can stuff a belt between the two halves, which contains exactly the ten extra atoms.

Oh, this was satisfying! My thoughts aflame with molecules and speeding tickets, I shut the TV and went to interview for a thing.

At the waiting room was another girl, reading a book. “Are you next?”, I asked, and she answered with a no. It was the briefest of exchanges, but there was openness about her. So I said: “Hey, you want to hear something amazing?”

Still buzzing, I told this absolute stranger everything I had just told you. And just as I had finished, they called me in.

When I came out again, she was still there. Naturally, I asked if it was now her turn. “No, I was already done when you came,”  she said. “I thought I’d wait for you.”

And that’s how I met my best friend.

You Will Need:

12 Origami paper sheets: six colours, two sheets in each colour
A pencil
A compass and a ruler
A pair of scissors

Instructions:

This ball is made of sixty identical pieces, each folded out of an equilateral triangle. Once you get the hang of it, each piece takes about a minute to fold.

To make the triangles, first sketch a circle on the back of the Origami paper. The photos below shows a circle with a 7cm radius. Larger radii will result in models that are bigger but more fragile.

2. Plant your compass (keeping the same radius!) on any point on the circle, and draw an arc so that it intersects the circle in two spots. Picking one of those places as the centre, draw another arc, which will also meet the circle in two spots.

3. Finally, use the compass to mark the remaining spots on the circles that are at radius-distance from the spots already marked. All told, you will have partitioned the circle into six equal arcs.

4. With the ruler, connect the marked spots on the circle to form a Hexagon, and connect opposing spots so that Hexagon now contains six identical equilateral triangles. Cut out those triangles.

Now for the folding. With each triangle, follow the sequence illustrated below. Make sure your folds are sharp.

a. At first, fold the triangle halfway, and open it again. Do this on all three sides. This will mark a central point inside the triangle. Fold each corner down to the middle of the opposing edge, and open them again.

b. Fold each of the corners to that middle point, and open them again. Now, fold a corner to touch the middle of its opposite edge, and then fold outwards at the halfway point. Do this for all three corners so they overlap. Turn over the piece.

c. Fold the corners down tightly. Now, smooth each of the ends of the resulting triangle into a sharp “beak”, so that you get a three-pronged star.

5. To connect two pieces, gently slide one beak so that it inserts inside another. If the folds are sharp, the two pieces will connect tightly at the seam. Repeat this with the same colour five times to close a single ring.

6. Once you have your first ring, start connecting the next five rings around it, like petals. This will result in half the model.

7. The other half gets built in the same way, except that now, the order of the colours in the first half is arranged counterclockwise in the second half. That way, when the two halves connect, antipodal rings will have matching colours.

8. Now, all that’s left is to connect your two halves. There are exactly ten touchpoints. When all have been connected, you will have a tight, elegant model.

Happy Holidays, and a very Happy New Year!