Straws, Solids and a Possible Parthenon

I'm trying to brush her hair.  We've got places to go, people to see. She darts over to the straw/pipe cleaner tetrahedron and brings it back to me.

"Mama!"

"What?"

"This tetrahedron does NOT have equal sides."

"What do you mean?"

"Well...[positioning the tetrahedron so that one triangular face is toward her, and pointing through to show the two other triangular faces coming together in the back]...you see these sides are two together, but this one...[losing steam]"

"Those sides are called faces. I think what you're showing me is that there are two faces that look like they're opposite each other, and that there's a third in front that has no match?"

"Yes."

"Well, 'equal faces' or 'equal sides' does not mean there is always a match.  What it means is that each face is the same shape and the same size. [Note to self: How should I really be describing the sides of regular polyhedra?]  For a tetrahedron that means that each face is a triangle shape.  Let's look at the cube...all its faces are squares of the same size, that's what equal means in this case.  It doesn't matter whether there is a match for each side...

"Here, look. Let's count the number of faces of each solid you made with marshmallows and toothpicks...  [counting together, four...six...eight]  It doesn't matter how many faces there are, just that they're all the same.  Hey!  I know, wanna try making an octahedron out of straws to go with our tetrahedron and this cube?

"Mama!"

"What?"

"Let's make a model of the Parthenon out of straws and pipe cleaners!"

"Uh, okay...maybe we should finish building these solids first?  So then we'd have some building blocks to work with?"

"It'll be math and history at the same time!!  That'll be really fun!!"

"You're absolutely right! [rummaging]  Hey, here's that book I got at the library book sale, on buildings of the ancient world.  Wanna see?  Here's the Parthenon."

[Kid, looking at the book, flipping through the pages.]  "Or we could build a castle.  But what would we do for the round towers?"

Never did get her hair brushed.  Didn't really get to building the Parthenon either, but we did build the octahedron and get out the door, eventually. 

This is the first time we've tried making structures with straws and pipe cleaners.  The beauty of platonic solids made with a unit length of 6" or so is that because they're not really, well, 'solid', you easily look through them to the other side which is what prompted the whole exchange, above.  You can also play around with them more easily, experimenting with how they fit together and observing how the relate to each other.   Just as exciting is having them around the house with us, keeping us company.  We've been admiring the toothpick/marshmallow sculptures and solids from last week as well.   

After making all these wonderful structures, it's also been wonderful to share our space with, well, space.  And, I am reminded over and over, that just because I look at something doesn't mean I understand it.  Even for me, as an adult, physically constructing these solids is bringing to light a whole new understanding of structure, relation and order.  As always, this is an amazing (and fun!) learning journey for both of myself and my daughter.