Honeycombs

I was reading a bit more on tilings of 3 space and found these two neat pages on Wikipedia that were related to our tilings with truncated octahedrons:

The “Bitruncated Cubic Honeycomb” article on Wikipedia

The “Cubic Honeycomb” article on Wikipedia

I was a little more interested in the topic than usual since my younger son had made a new “smushed” truncated octahedron after we finished yesterday’s project:

yesterday’s project is here:

Tiling 3 dimensional space with our Zometool set

For today’s project we built some more of the shapes that my younger son built yesterday and explored if these shapes could also tile space. Here is their description of the shape and how it is similar to and different from yesterday’s “smushed” truncated octahedron:

Next we looked at how the “smushed” truncated octahedron and the new shape tiled space:

Finally, I showed the boys the two Wikipedia pages from above so that they could see all of the incredible honeycomb patterns:

So, a fun project inspired by my son just playing around. 3D tiling / honeycomb patterns are really neat!

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Comments

2 Comments so far. Leave a comment below.
  1. Years ago I worked with a class of Pre-K students whose teacher had treated them to an extended study of dinosaurs. Those very young children were able to rattle off a list the long, tongue twisting creature names that I couldn’t even pronounce. Hearing your boys say the names of the honeycomb shapes reminded me that even though we don’t generally teach youngsters these words, that they are certainly capable of saying and using them.

    I am wondering if you could help me out with thinking and talking about shapes in math. For a long time I struggled with making sense of how to explicitly understand the connection between building patterns and doing math. Finally I’ve become comfortable with understanding this connection as being one that we make, in other words I’m of the mind that the math in patterns exist only when we see and describe it in a mathematical way.This is something that I can do. Now I have the same kinds of questions about shapes.

    I’ve been thinking about this is while I am still thinking about your post, about how to bring math thinking, to young children. I know when you are doing these cubic shapes with your boys that it’s rich in math thinking and that when they are looking at the downloads of Dearing Wang’s geometric stars that this is also math thinking, but I can’t explicitly say why.

    So if I just copy a pattern, no, that’s no math. It takes an understanding, like for every red bead I use 3 blue beads, that makes it make it math If I fill in a star or even make a honeycomb, what is it that makes the activity mathematically relevant? ( Besides my genuine curiosity about this, my hidden agenda in asking this question to figure out how to justify as well as make it meaningful to do this sort of thing with students when I do my visiting-artist gig in schools. )

    • The thing that make your question difficult to answer is that I don’t know what I’m doing at all. I just like doing math projects with the boys – usually non-standard / non school math stuff – and it goes wherever it goes.

      I did really enjoy the coloring activities at the family math nights we did, and the kids seemed to really like coming to the front to talk about the patterns and shapes that they had colored. But then again, maybe they just liked talking into the microphone!

      The only thing I’m pretty sure about is that if you have neat math-related activities, kids will really enjoy them.

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