(Post edited per Karl's reply below...thanks!)
This is a construct that I discovered on my own, and I have hardly ever seen in other builds. It is constructed entirely of tetrahedrons, hence the name.
This is a tetrahelix of length 3. Notice that the 3 "edges" are marked with white bars and each one is 3 bars long:
Here are the build instructions:
1. Start with 3 tetrahedrons assembled as shown, using all the same color bars except for 3 bars of a different color as displayed here (in white):
2. Add another white bar to the right of the white bar on top, and then complete the tetrahedron to the right.
3. Rotate the entire structure forward so that the white bar closest to you is now on top.
4. Repeat steps 2 and 3 as many times as you'd like. Every 3 tetrahedrons added will add another bar to each of the 3 strings of white bars.
Now for the challenge, which is more of a brainstorming session than a challenge. Using only tetrahelix segments of length 2 or more, what can you come up with as a complex build? Special consideration will be given to 1-axis or 3D symmetry, and no near-misses. Segments can be connected end to end or intersect each other, but no additional bars should be used to make the connections. To give an idea, here is the best I've been able to come up with (a miss, not following my own rules). Granted, I haven't spent much time on this since I created this, and I'm somewhat in a mental block: