Five Intersecting Tetrahedra: Step by Step

As you know, one of my other hobbies is origami (see my first post if you missed it). You probably also know that I'm a math professor - what you may not know is that math and origami are tightly linked.

One of the books that I bought a year and half ago has proven to be a great classroom reference: Project Origami: Activities for Exploring Mathematics by Thomas Hull. Hull's book is full of origami and mathematical projects, spanning a variety of mathematical topics including geometry, calculus, graph theory, etc.

Within the book, Hull provides instructions for one of his most famous models - the Five Intersecting Tetrahedra.

A year ago, I folded the Five Intersecting Tetrahedra with decent results. However, I'm a bit of a perfectionist when it comes to my models, so I wasn't entirely happy with the results. With that, I decided to fold the model again...

I started with 10 sheets of origami paper (10x10).

The first step is to cut each of the squares into thirds and then fold a model known as Francis Ow's 60 degree unit.

After folding all 30 units, it's time to begin the construction process. First, form a tetrahedron (a pyramid with a triangular base).

Then, weave a second tetrahedron into the model. Then weave a third tetrahedron into the model. (Note: don't try to make the full tetrahedra and then weave it in - you have to weave each individual edge and then connect the corners within the model - I found it easier to "balance" the model on an open cup when trying to weave the first three tetrahedrons together.)

After weaving the first three together, the worst of the model is over! If you've done it correctly, there's basically only one way to weave the final two tetrahedra models in. The beauty of the model is that the entire thing is held together on its own - NO TAPE or glue is needed if you fold (and assemble) the model carefully!

Think you can do it? Thomas Hull has made the instructions available for free on his website.