Platonic Polyhedra (Fun with 3D Geometry)

Platonic polyhedra sounds so much more sophisticated than 3D shapes, doesn’t it? Actually, in our math history lessons, we found that the 5 now called “Platonic” solids were actually identified by the Pythagoreans (Pythagoras and his students) before Plato’s name became attached to them. Of course, we were not content to see them in a book, we had to construct them. That is only logical to me; otherwise how can you truly understand these figures?

We used this wonderful resource for printable templates:  Platonic Solids Mobile. I printed the nets (as flattened 3D shapes are called)  onto cardstock, then cut and scored them. Scoring makes a huge difference for a mathematical craft like this; it enables you to fold precisely. Just place a ruler along the line to score, and press with the rounded edge of a paperclip. It took patience and white glue to get them to hold together.

Before stringing the mobile, Sprite had to fill out this comparison chart (I created) for analyzing the features of the five figures.  She found it helpful to mark the faces, vertices (tips), and edges to keep track.

Sprite used the diagrams from page 2 of this book excerpt to create a notebooking page which we referred to quite a lot since the names of these figures don’t come too easily. But they are mighty fun to say!

1. icosahedron
2. tetrahedron
3. hexahedron (also known as a cube)
4. dodecahedron
5. octahedron

Putting the mobile together was another mathematical experience. Sprite had to discover which way to shift the strings to balance the mobile.

When we found the perfect arrangement, we taped the strings to the straws.

And here it is, ready for the cats to attack. (That is what happened, you know.)

This whole project was a tangent that I took off on.  Our scheduled reading, the chapter on Pythagoras in Mathematicians are People, Too, is what inspired me. So this was actually a four day activity that was a footnote to our (supposed to be) two week long Pythagoras study. Yeesh!

Living math is so messy! Not just in glue and squares of paper, either. I like things to be linear, but I’m finding that living math is not a neat path from A to B to C and so on. Instead it  jumps ahead to QRS and then circles back to pick up DE and F. So I’m adjusting to this new style and trying to enjoy where it takes us.

We do have an outline, but when we find a mathematical concept we want to veer off track towards, we go ahead. It’s all math, and it doesn’t bother me anymore that the tangents we choose are not in the textbook or not “grade appropriate.”

Later when we study Euler, another mathematician, we’ll revisit these shapes with this chart — Euler’s Formula with Platonic Solids.

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Tagged as: geometry, living math, math