# Revisiting 5 tetrahedrons in a dodecahedron

After procrastinating for ages, I finally got around to ordering more green Zometool struts last week. The new pieces arrived yesterday which meant today’s project was going to involve green Zometool struts one way or another.

Flipping open our Zome Geometry book . . . .

I stumbled on a great project – building the surface formed by five tetrahedrons in a dodecahedron.  Here’s an old tweet from the American Mathematical Society that shows this shape:

That tweet inspired an old project where we actually built the tetrahedrons inside of the dodecahedron:

Five Tetrahedrons in a Dodecahedron

Now we had enough green pieces to actually build the surface!  It was a fun -though very challenging – project.    One challenge that we’d not encountered before was that the pieces of this surface can only be built if the pieces are in a specific orientation.  Even with the clear instructions in the Zome Geometry book, figuring out that orientation took a while.

But . . . we did it!

After we finished the build the kids had lots of great things to say about the shapes.  We started off the conversation by looking at the AMS tweet:

Next up – their thoughts while holding the shape in their hands:

After that short discussion, we moved to the floor to look at one tetrahedron inside of a dodecahedron:

Finally, during the build the boys noticed an interesting shape that lived inside of intersection of the 5 tetrahedrons. It turns out that this shape is pretty cool, too. It is an Archimedian Solid known as the Rhombicosidodecahedron

The shape that my older son references in the video is the shape we made in this project:

A Stellated 120 cell made from our Zometool set

So, a super fun project. I’m really excited to have a bunch of green struts now – can’t wait to see what other projects we can work on using the new pieces!

## 2 thoughts on “Revisiting 5 tetrahedrons in a dodecahedron”

1. Jacob Rus says:

Did you guys notice that the last shape you made is basically the same shape as the Zometool balls themselves? If you made enough of those you might be able to use them for making supersized Zome shapes.

(Actually I think to get exactly the same shape as the tiny Zome balls you might want to use the next size up of blue struts as the sides of the triangles, turning all the squares into rectangles.)

2. (Notice that with this shape you have a face perpendicular to every hole direction in the Zome system.)