Dave Radcliffe’s Tetrahedron dissection

Dave Radcliffe posted this interesting request on Twitter today:

I think that a tetrahedron can be dissected into two smaller tetrahedra and two triangular prisms. Am I correct? Can someone draw this?

— David Radcliffe (@daveinstpaul) June 13, 2015

I could sort of picture it and decided to try to build it with our Zometool set. The unfortunate difficulty is that I don’t have a lot of green struts.

Here’s a tetrahedron with side length equal to two long green struts:

 

Here are the two smaller tetrahedrons that we’ll remove for the first part of the dissection:

 

Finally, here’s how to chop up the remaining shape into two triangular prisms, with an extra bonus of me not being able to figure out how to put the shape back together!

 

Interestingly, the triangular prisms here are a shape that we’ve explored previously because they were part of a famous / infamous test question:

Octahedrons Tetrahedrons and the Pyramid Puzzle