How To: Make Icosahedral Planet Ornaments

Make Icosahedral Planet Ornaments

In honor of the new Astronomy World, I thought we should look at a few planetary icosahedrons. The icosahedron is the most round of the Platonic solids with twenty faces, thus has the smallest dihedral angles. This allows it to unfold into a flat map with a reasonably acceptable amount of distortion. In fact, Buckminster Fuller tried to popularize the polyhedral globe/map concept with his Dymaxion Map.

The other advantage of an icosahedral globe is that it's quick and easy to make, only requiring a paper net. Here's a picture of the planetary icosahedra I made last night—in less than a hour.

How to Make Icosahedral Planet Ornaments

Tools and Materials

  • Paper (1 sheet per planet)
  • Scissors or X-Acto knife
  • Templates
  • Glue (I prefer Loctite brand superglue gel for its speed and ease of use)
  • Ornament hooks (if you want to hang them)

How to Make Icosahedral Planet Ornaments

Pick out your celestial template. On the template site, click on one of the planetary net images on the left side. This will take you to a new page where you can download either a .jpg or .pdf. Print out whichever one you prefer. I used glossy photo paper, which looks great and is stiff enough so that the ornament should survive a fair amount of handling.

How to Make Icosahedral Planet Ornaments

Carefully cut out the net.

How to Make Icosahedral Planet Ornaments

Glue the tabs, connecting the net together. You can pre-fold at the lines if you want, but I opted not to in this case. I wanted to let the paper curve, which makes the globe appear more round.

How to Make Icosahedral Planet Ornaments

Keep connecting the tabs with glue.

How to Make Icosahedral Planet Ornaments

Here you see there's only one more top tab to be connected.

How to Make Icosahedral Planet Ornaments

And now the last tab on top has been connected.

How to Make Icosahedral Planet Ornaments

Now it's time to connect the side tab.

How to Make Icosahedral Planet Ornaments

Connect the tabs on the bottom.

How to Make Icosahedral Planet Ornaments

Almost finished.

How to Make Icosahedral Planet Ornaments

And... finished.

How to Make Icosahedral Planet Ornaments

Now I'll make the moon, only to show you how to make the folds crisp, instead of round.

How to Make Icosahedral Planet Ornaments

After cutting out the net use a straight edge as a guide to folding. You could probably fold directly across the straight edge. I instead used a light touch from a knife to slightly weaken where the folds are going to be before folding. You could also use a dead ball point pen to do this.

Start from one angled line on the left, then continue along all of the parallel folds.

How to Make Icosahedral Planet Ornaments

Then do the same thing the other way, making sure to hit all of the folds.

How to Make Icosahedral Planet Ornaments

And finish with the top and bottom lines.

How to Make Icosahedral Planet Ornaments

As you can see below, the folds are now crisp.

How to Make Icosahedral Planet Ornaments

Once you have pre-folded the icosahedron, you can start gluing the tabs together.

How to Make Icosahedral Planet Ornaments

Here's the finished product.

How to Make Icosahedral Planet Ornaments

Notice the difference between the two globes below. They both look great. Folding results in the more mathematically pure form, but takes more work. Letting the paper bend results in a rounder globe and is faster to make.

How to Make Icosahedral Planet Ornaments

Show Off Your Work

If you make the icosahedral planets or any of the other previous Math Craft projects, please share with us by posting to the corkboard. I'd love to see these as Christmas ornaments hanging from a tree, or maybe you can figure out how to make them into usable boxes by adapting them with a lid. Perhaps you have an original project or something you've seen on the web that you'd like to share.

If you like these types of projects, let me know in the comments. If you have any other ideas you would like to pursue, let me know in the forum.

4 Comments

nice. looks simple.

Nice and easy. They look pretty on glossy paper and are about 4 inches in diameter which makes them perfect for ornaments.

I was just about to make my own and set them up as ornaments then make a how-to! cool

Cool. You can probably find some other templates with different shapes and give it a go for a tutorial...I picked the easiest!

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