Our goal is to make an ornament that looks something like this:

The name for a polyhedron with 20 congruent equilateral triangles for faces is a regular icosahedron! It is one of the five Platonic solids, which we will learn about.

The ornament is made of 20 “winged” equilateral triangles—the wings are glued together. You can hang it by sticking a threaded needle through a glued-together wing and making a loop.

To start, get an 11 by 8.5 inch piece of card stock and Xerox onto it this drawing:

Click the image to print it!

If you want to decorate the equilateral triangles with holiday drawings, it is easier to do it now.

Before you cut out the circles, using the point of a compass, score along the three sides of each triangle. Then cut out the circles.

You will need some quick-drying glue for the next part. We have also used small clamps to hold the glued edges together. This makes the task easier, but it is not a requirement.

Here are the steps for putting it together:

Take 5 of the triangular pieces you have prepared and glue them together as shown below.

Attach 5 more triangles to the piece you created in step 1 as shown by the green triangles in the image below.

Now attach 5 more triangles to the ones you attatched in step 2 as shown by the orange triangles in the image below. Then glue the sides together as shown.

Take the last 5 triangles and glue them together as shown below.

Attach the cap you just created to the rest of the ornament. You have now created an awesome icosahedron holiday ornament!

One more thing!

If you have only eight “winged” equilateral triangles, say four each of two different colors, you may make an octahedral ornament. (A regular octahedron, a polyhedron with eight equilateral triangles for faces, is also a Platonic solid. “Regular” means that all its sides are congruent, the same size and shape.)

Here is an octahedral ornament: