We've been exploring platonic solids around our house lately. We've made them using toothpicks and marshmallows. We've made them with straws and pipe cleaners. We're even in the process of building a house using straw and pipe cleaner cubes as the building blocks.
Both myself and the kid are learning a lot through the making process, but also from the the fact that we've filled our living environment with the structures. Because they're so open, there are all sorts of relationships within the solids themselves that we observe by simply walking through a room on the way to somewhere else. This is one more great example of environment being an effective teaching and learning tool.
The kid is definitely interested in all this, but me? I have to say that I'm a bit obsessed. Questions keep coming up, and they are loud ones that are demanding answers. Luckily, an office supply store near us had bags of 100 brightly colored straws on sale for $1.00 a bag, so we've got enough supplies to go on for a while.
Here is the dodecahedron I made from 6" straws and some pipe cleaners. Twelve pentagonal faces, 30 edges and 20 vertices. (I know because I counted, multiple times. Sometimes the things that seem the easiest on paper are actually the hardest to figure out in real life.)
And here it is compared to three other platonic solids: a cube, a tetrahedron, and an octahedron, also made with 6" straws and some pipe cleaners.
Wowsa. Not only is the dodecahedron much bigger, it's also really obvious that its not strong enough (using these materials) to hold its shape.
Here is what happened when I cut the straws in half and made another:
It supports itself much better and feels and looks, well, more solid than the first. Here it is in relation to the other solids:
Interesting! Remember, three of the solids shown are made with six inch edges and the dodecahedron is made with three inch edges.
Have you ever noticed that when you see illustrations of platonic solids that they all appear to be about the same size? Here's an example (source):
Or, this (source):
I never would have observed this if I hadn't built a 3D model. Score another point for hands-on learning!
I wonder what will happen when I try the last platonic solid, the icosahedron? Even though it has eight more faces than the dodecahedron the faces are triangles. I'm thinking that even with using 6" straws the end result won't be as cumbersome. Wish me luck!