Oh dear, oh dear - it's very hard to find any hexagons in a solid with only four faces...

You can cut a tetrahedron in half to reveal a square (drag with your mouse to move it):

Here's the half tetrahedron shown as a solid:

And almost the only hexagon I can offer is the outline of this half-tetrahedron that you see when you look straight on at its square face. However, this half tetrahedron is interesting in its own right - you can make two of them as a puzzle to see if anyone can re-assemble them into the tetrahedron. Click here for a net you can print out on paper (you could notice that this net is actually formed from two hexagons).

Even better as a puzzle is to cut this half into half again - the same as dividing the tetrahedron into quarters with two plane cuts at right angles. The model is here is shown with lines indicating the half tetrahedron we had before:

To see how this model can be made with two plane cuts, look directly along the longest side of the blue face triangle - you can see the two plane cuts at right angles to each other, and the model as a square outline occupying a quarter of the outline of the tetrahedron.

Re-assembling four of these into a tetrahedron is quite challenging unless you've seen it before. Click here for a net so you can make your own out of paper.

One further way to find hexagons in a tetrahedron is to chop off all the corners - this solid, called the truncated tetrahedron, has four hexagonal faces and four triangular faces.

(Java applet from LiveGraphics3D)

page date: 18Nov04.      I enjoy correspondence stimulated by this site. You can contact me here.