Mathematical Problems, 2 - The Tetrahedron Path

In this article, I want to provide another puzzle, and the solution to it (you'll need to look closely at the diagram below to understand the solution).  This follows on from my previous post, which was a puzzle about a spider and a cube.  The spider was a mathematical spider, and she wanted to walk around all 12 edges of a cube, in both directions (i.e. from left to right and then right to left) in a single continuous path, without getting stuck or having to turn around completely.  In the original puzzle (devised in a BBC Micro maths adventure game), you had to tell the spider to turn either left or right at each corner.  Now I'm a little older, I use a pen and paper and a diagram...

Following on from the cube, I set myself the challenge of doing the same for a tetrahedron.  I can't say if it was significantly harder or easier, perhaps a little easier with fewer edges to follow, but here's the solution.  The path through the letters goes along each edge twice, once in one direction and then later in the opposite direction, starting and finishing at the same point.

My next post will be a brief discussion on how to calculate a very approximate value of pi from first principles (by which I mean a few diagrams and some basic geometry).  After that, I'll use a different method to get the value of pi, and we'll see how that goes.  If you're looking for more information about tetrahedra, I can recommend this post where I calculate the tetrahedral bond angle.

Here's my solution to the tetrahedron path puzzle: follow the letters in sequence.