Pyraminx Tutorial

I've previously started to shoot photos to write this tutorial on a comple occasions, but I kept biffing it and aborting the project. Well, this time I pushed through. Further to my series of tutorials on Rubik's Cube-based 3D scrambler puzzles, here is the base model in the series of tetrahedral puzzles – which means that group of gizmos shaped like a triangular-based pyramid, with four identical, equilateral sides. It's another one of those Platonic solids, you know, like the cube and the dodecahedron, on which see my previous posts on this thread.

The Pyraminx is sort of the 3-layer tetrahedron to the original Rubik's Cube's 3-layer cube. You can twist the tippy-tip corners at all four vertices; that's one layer. You can twist an entire face opposite one of those vertices; that's two layers. And if you wanted to, you could slice-move the middle layer in between, though I don't know of any practical use for that maneuver, so let's forget I mentioned it.

Practically speaking, a U move would be when you twist the top two layers 1/3 turn clockwise (as viewed from above):

And a U' ("you prime") is the same thing, only counterclockwise:

Photographed from overhead, here's a B move, twisting the back two layers clockwise (i.e. viewed from behind), and I'll leave the B' move to your imagination.

R, as you may be able to guess by now, means dialing the two-layer corner at the right 1/3 clockwise as viewed from that side, with the predictable R' going the opposite way.

And L is your move concerning the left corner of the Pyraminx; just guess what L' is.

To be technical, and for scambling purposes, there are also small-letter u, b, r and l moves, going in both directions, but those only affect those tips, which turn independently. You'll see those on the scrambler, but in my opinion, it's up to you whether to bother with them or not.

The Pyraminx dates back to 1981, when a Japanese toy company called Tomy rolled out Uwe Mèffert's design. It has four corner pieces with three colors each, six edges with two colors each and 12 centers with only a single color. There are 933,120 different ways to scramble it, which isn't all that many in the cube-puzzle scheme of things, and consequently it isn't terribly difficult to solve. Remember the "God number?" That's the maximum number of moves for the optimal solution to any configuration of the puzzle. Right? On the original, 3x3x3 Rubik's Cube, it was 20; on the Pyraminx, it's only 11.

World records for the fastest single solve are being broken on a regular basis, it seems, with the top five solves all occurring within the last couple years and all in the 0.73 to 0.84 second range. I said, less than a second. The top five solvers by "Olympic average" (i.e. the average time of five solves, excluding the fastest and slowest times) are all between 1.15 and 1.48 seconds and all within the past two years as well. Don't expect these records to stand for long, ha ha.

There's no shame in taking a few minutes to solve the Pyraminx. Even without going for speed, once you've practiced it a bit, you may find it's all over rather quickly. For me, it's become a puzzle that I scramble at the same time as a bunch of other puzzles and then solve one at a time, from easiest to hardest, and it definitely comes in toward the beginning of the exercise. Kind of a warm up, really.

Here's one of my favorite online scramblers, mapping the way to a random configuration of the Pyraminx. Be sure to start with yellow down and green to the front.

And her's how that scramble looks in real life:

The first thing you can do is realign those tips, that you twisted due to those small-letter steps at the end of the scramble pattern. It's as simple as twisting them 1/3 turn clockwise or counterclockwise, as needed, so they line up with the colors of the center piece on each side. The tips can't escape those centers, making them so trivial that, again, it's up to you whether to even bother scrambling them.

With that preliminary, optional step out of the way, I'll call the next step Step 1. It's the completely intuitive matter of making all three tip-and-center doubles match each of the puzzle's four sides. Exercise your own problem solving skills here. On a bad day, it can't take very long. There are, after all, only four sides to this thing.

Step 2. Pick a side to put at the bottom. I'm not picky about which color to go with; in this instance, I put the yellow side down. Then, twist an edge piece that belongs at bottom front onto the adjacent side; e.g. the yellow-green edge at front left.

Why at front left and not at front right? Well, you've got to think about the fact that you're going to do this move (R in this case), bringing the edge where yellow-green belongs to the opposite side of the front layer (in this case, front right):

... And then you're going to twist the top layers (a U or U' move, in this case U') to put that edge piece in place, like so:

... Before dialing that edge back down to the bottom again:

So, in retrospect, you wanted to position that edge so it would be flipped the right way when you completed this maneuver; i.e. with the green side (i.e. the color of the front side) toward the front, and the yellow (i.e. the color of the bottom side) out of the way. Here's a similar case, where we find a blue-yellow edge that needs to end up yellow-side-down. I've positioned it on the blue side (cf. those two lower corner/center doubles), with the blue side to front and the yellow out of the way.

Now twist the opposite corner up (here an L' move) ...

And dial the correct edge in (here a U move) ...

And send it home to the bottom layer (here an L).

Repeat as necessary until your initial, bottom layer (e.g. yellow) is fully solved, as shown here; then (Step 3) choose one of the remaining, unsolved layers to become the new down side. In this instance, I chose blue.

Continue in the same vein, twisting an edge piece that belongs on the bottom so its other side (here red) finds its center ...

Then dialing the edge where it belongs up on the opposite side of front:

Then doing U or U' to put the correct edge in:

And down:

You may notice from this last picture that I broke a yellow edge somewhere in this process. Nevertheless, I keep working on with the blue side on the bottom for now, putting the blue-green edge above the slot where it belongs, green side forward:

Then do the up-in-down manuever:

And somehow, I find myself only a U move away from having the whole thing solved!

There are some algorithms, if you need them, for cases when you find yourself cycling the same two or three pieces around and around. I used to keep a note of them handy in case I ran into one of those parity issues. I never bothered to learn them by heart, which turned out to be all right because, since I learned how to solve the Master Pyraminx (the 4x4 version of this 3x3 puzzle), I've somehow never encountered a parity case on the vanilla Pyraminx that I couldn't intuitively solve using the steps above. Nevertheless, here are those algorithms in case they can help you:

• Need to flip 2 edges at front: R’ L R L’ U L’ U’ L.
• Edges at R, L and B that need to cycle clockwise: R’ U’ R U’ R’ U’ R
• Edges at ditto that need to cycle counterclockwise: R’ U R U R’ U R

Anyway, I suppose that's an advertisement for standing by until I post my Master Pyraminx tutorial – verily, a case of the higher-level puzzle giving me a better insight into solving the lower-level one. Until now, stay curious, my friends!