A bonus project on a Zometool icosahedron

We’ve done two projects on platonic solids recently:

Talking about Angles in Platonic Solids

Following up on our angles in platonic solids project

In the last project my younger son explored two different kinds of “golden rectangles” inside of the icosahedron. I thought it would be fun to try to fill in the entire shape with the rectangles, so today the boys took on that challenge.

Here’s their discussion of the shape made by filling in all of the large golden rectangles in the icosahedron:

Next we turned to the shape made by filling in the smaller golden rectangles. These were a little harder to make. Since the first shape took a bit longer to make than we expected, we only filled in 10 of these rectangles and avoided the problem of dealing with ones that overlapped.

To wrap up we removed the struts from the original icosahedron to get a better view of the shape formed by the rectangles:

Definitely a fun project. As always, it is incredible how easy (and fun!) it is to explore 3d shapes with a Zometool set.


Following up on our “angles in Platonic solids” project

Yesterday we did a fun project on angles in Platonic solids:

Talking about Angles in Platonic Solids

We ended up getting a really neat comment from Allen Knutson on that project. He said:

“You should look for the three orthogonal golden rectangles in an icosahedron! They’re easy to see in a Skwish toy.”

My older son was working on a different math project today, so I had my younger son build an icosahedron out of zome and look for those rectangles. Here’s what he had to say after building the shape:

During his description he found a second rectangle. So, off camera, he filled in that rectangle and then had a bit more to say:

So, thanks to Allen Knutson for the comment that inspired this project, and thanks (as always!) to Zometool for making it so easy to get kids talking about math!

Talking about angles in Platonic solids

My younger son wanted to do a Zometool project today and since my older son is currently learning about the dot product, I thought it would be fun to talk about angles in some platonic solids.

This idea turned out to be one that was better in my mind than it was in practice – ha! – but it was still a nice project even though it got a bit messy.

We started by talking about angles in a cube:

Next we moved to the octahedron:

Here we go through the steps to calculate the angle between two faces in the octahedron:

Finally, we wrap up by looking at the fun surprise that a hypercube has a 30-60-90 triangle hiding in it! My younger son got a little confused about how to find the lengths of some of the vectors we were looking at, so we went slow. It is really fun to see how some relatively simple ideas let you explore hard to visualize objects like a 4-dimensional cube!

Exploring an amazing tweet from John Carlos Baez with my younger son

I saw an incredible tweet from John Carlos Baez last week:

Here’s the picture in case the tweet isn’t embedding all that well for you:


I thought exploring some of these shapes would make a great project for kids, so I began by asking my son (in 7th grade) for his thoughts on the shapes he was seeing:

Next we built a few of the cubes from our Zometool set and talked about some of the shapes. First, though, I asked my son to give his definition of what an n-dimensional cube was:

Finally, we played around by a different version of a 4-dimensional cube – “Hypercube B” by Bathsheba Grossman. This amazing version of the hypercube makes amazing shadows and my son was able to find a projection that was a little closer to the projection of the 4d cube in Baez’s tweet:

Also, here’s a video I made a while back showing some other (almost freaky) 2d projections from our Zometool model of Hypercube B:

Definitely a fun project – thanks to John Carlos Baez for sharing some of his ideas about higher dimensional cubes on twitter!

Finding the volume of a rhombic dodecahedron with our zometool set

Yesterday we did a neat project inspired by a tweet from Alex Kontorovich:

Sharing a 3d geometry idea from Alex Kontorovich with kids via zometool

At the end of that project a question about finding the volume of a rhombic dodecahedron came up. Since I was going to be out this morning (and my older son was working on a calculus project) I asked my younger son to play around with the Zometool set and see if he could actually find the volume.

Fortunately he was able to – here’s how he described his work:

Sharing a 3d geometry idea from Alex Kontorovich with kids via Zometool

I saw an interesting tweet from Alex Kontorovich earlier this week:

We’ve looked at but the Cuboctahedron and the Rhombic dodecahedron before, but I thought it would be fun to revisit the shapes. I also hoped that we’d be able to recreate the shape in the picture with our Zometool set.

So, first we built a cuboctahedron and the boys talked about what they saw in the shape:

At the end of the last video the boys thought that the dual of the cuboctahedron would possibly also be another cuboctahedron. Off camera we built the dual, and happily were able to recreate the shape from Kontorovich’s shape!

They were a little worried that we didn’t have the “true” dual, but I think they came around to believing that these two shapes were indeed duals:

Definitely a fun project – it is always fun to see what you can make with a Zometool set. Maybe tomorrow we’ll revisit an old project of finding the volume of a rhombic dodecahedron. That’s another project which Zometool really brings a lot to the table.

A fun creation with our facets

My older son is working on a different math project this morning, so once again my younger son was working along. While cleaning up a little bit yesterday we found our old collection of “facets” – so I asked my son to build something for the Family Math project today.

He built a really neat shape:

We have done two previous projects with the facets (including making a big circle 🙂

Our Facets have arrived!

Our second facets project!

They are definitely fun to play around with!