## Saturday, January 14, 2012

### Solids and an Observation on Scale

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!

#### 7 comments:

1. These are so cool! Do you just stick pipe cleaners in the straws to hold the ends together? I must try this!

1. Thanks! They were definitely fun to make.

My strategy is using a straw that is on the narrow side (Starbucks or McD's straws would be too wide, for example). Also, I cut the pipe cleaners in half, then fold both ends about an inch. That double thickness seems to help keep them in place. I used 1/3 of the pipe cleaners when I started, but that was too short -- the straws kept falling off. Also, you only need to fold both ends when you're attatching two straws to make a vertex. When you add a third straw to that vertex, the pipe cleaner that attaches to that point should be unfolded. Otherwise it won't go in.

I've also seen it done by threading a string through all the straws. That requires you to make a 2D net before pulling it all together to make a 3D shape. I'm not a big fan of that b/c really, in my mind, the point of this activity is seeing and experiencing this shape in 3D AS YOU BUILD IT. If you create it in 2D then what's the point? You have a nice solid, but you haven't done any thinking about how many edges come together at the various vertices, for example. Or how may faces share edges, etc. It's the process of building and analyzing as you go that really brings the deepest learning and comprehension. In my mind, at least! ;-)

Hope this helps! :-)

2. There are NO words. You are the coolest. We are headed for a vacation with lots of space once we get there, but very little in the car for building toys. So this is the PERFECT solution.

May you live to be 1000 years old.

Really.

3. Awesome! May I suggest pre-cutting the pipe cleaners and straws before you go? After a lot of experimentation I've found that the ratio of 3" straw to 1/3 of the pipecleaner makes for the sturdiest structure. Happy travels! :-)

4. How do you attach the the corners so neatly together with 3 straws meeting at one point? Could you please make a 'how to' on this? It's really cool how you made the 3D shapes but just not too sure how to attach everything. Sorry for not being too bright. Thank you for the interesting post and your simple ingenuity.

1. Nevermind, I had a look at your previous posts.
And I must say, brilliant blog. Well done!

5. Does anyone have any ideas for a non-pipe cleaner version?

Thanks for reading. I would love to hear your thoughts and comments!