How to make an icosahedron

Well, here you have it.

I was having a really hard time focusing on math homework and wasn't hungry, so I had no idea what to do. James suggested that I take a study break to color. He knows I like coloring. So I decided to make a Platonic solid.

Requirements of Platonic solids:

1. All of the sides are identical regular polygons (shapes where all the sides and angles are equal)
2. Each vertex (pointy part) is identical

In other words, they are perfectly symmetrical in pretty much every way.

I made the icosahedron, a 20-sided shape. Some other examples are:

• tetrahedron (triangular pyramid)
• octahedron (8-sided shape; two 4-sided pyramids stuck together)
• dodecahedron (12-sided shape; looks kind of like the one above but is made of pentagons)
• hexahedron (AKA cube)

And... hmmm, I can't think of any more examples. Oh, that's because I've run out of examples! There are only 5 possible Platonic solids in the whole universe! (No, but really.)

And there are only 3 polygons in the universe that could ever be used to make a Platonic solid, which are equilateral triangles, regular pentagons, and squares. If you want to know why, I'll put a link to the explanation later tonight. It is really pretty cool and not even hard to understand.

So the reason I made one of these is that BYU had a 6th-8th grade STEM fair (Science, Technology, Engineering, Math) last weekend. A friend and I volunteered to run a booth and we decided to have the kids color and make Platonic solids. I had a lot of fun actually!

Here's our booth!

Kinda blurry, but it shows stacks of the 5 Platonic solids and a stack of handouts which I made, which were pretty cool if I do say so myself. (They had a picture of Plato on them.) And all the crayons, markers, string, scissors and tape that the Math Education department provided for us. There's also my computer playing a video about Platonic solids. Here it is if you are interested. And taped on the edge of the table are geometry definitions like vertex and polygon.

Here are pictures of the papers and the poster.

I really liked how the poster had the shapes glued to it and hanging off of it from strings. For some reason I didn't get a close-up of them.

I was told that over 250 middle school kids were coming, so we asked for 400 papers. I figured that most would only want 1, but some would want to make all 5. But I really overestimated! I think it's because the kids would get a prize if they visited all the booths so they had to hurry through them. I still have a giant stack of papers even after telling everybody to take extras to make at home! (Because who really wants to make a Platonic solid in their free time right?)

But it was fun to stamp their cute little papers. It was also pretty fun to watch them make the Platonic solids. Some did it very neatly and didn't need help, others just stuck it together willy-nilly and had to take it apart to readjust. Some would spend loads of time coloring, and some even taped a string to it.

Then when I got home, James had cleaned the apartment and put away all the laundry! He is really the best. I guess he's more productive when I'm not there. I fear what will happen when he's gone all day this Saturday.