Soccer Ball math

Five Triangles posted a neat picture of a standard soccer ball earlier this week:

Seemed like building the shape out of our Zometool set would be a fun exercise after a week of camping, so we gave it a shot this afternoon:

After introducing the problem we started building (off camera).  We’ve done a few other fun exercises with our Zometool set and actually just bought George Hart  and Henri Picciotto’s “Zome Geometry” so the kids are pretty familiar with building structures out of the Zome pieces.  The only trick for this little exercise is that you want to start with edges that are three times the normal length to make the truncation easier.   Also, once you have the icosahedron, it isn’t so obvious where the soccer ball is hiding:

Next we move to the truncation.  Since we started with side lengths that could be easily divided into three parts, truncating the icosahedron isn’t that hard.  It is, however, incredibly interesting to see the “soccer ball” shape emerge from the icosahedron.  The kids were surprised to see that “the pentagons made the hexagons.”  Here’s a peek from about half way through:


After we finished building we did a quick wrap up and talked about a few other questions that we could ask about our new shape – things like the number of edges, or number of pentagons.  I also asked them if they thought the Zometool shape was actually the same shape as the soccer ball and was surprised to hear that they thought it wasn’t.  We talked about that for a bit, too:


All in all a fun little geometry exercise.   Didn’t want to go into too much depth here since they just got back from a week of camping, but even without the depth they seemed to find all of the building to be really engaging.  Thanks to Five Triangles for the inspiration.