Master Pyraminx Tutorial

In my Pyraminx tutorial, I described the three-layer tetrahedron puzzle as a sort of warm-up to a round of practice with Rubik's Cube-type 3D scrambles. With the Master Pyraminx, a four-layer tetrahedron, the game is really on, with an interesting and diverting puzzle that will definitely take more than one second and change to solve. Here it is, in the foreground:

According to Ruwix, the Master Pyraminx first came out in 2002 but was mainly a collector's item until a Chinese manufacturer, ShengShou, started mass producing them in 2016. Analogous to leveling up from the 3x3x3 Rubik's Cube to the 4x4x4 Master Cube, the Master Pyraminx (according to Grubiks) has about 217 quadrillion possible configurations – although Grubiks also claims the original Pyraminx has 75 million possible combinations, which is far higher than the estimate I cribbed from Wikipedia for my Pyraminx tutorial. Since solving the Master P. isn't a sanctioned competition, there are no official records but, again pace Grubiks, the unofficial record for the fastest solve goes to Fedor Abaev of Russia, 18.01 seconds.

It is genuinely a bigger and more complex puzzle. Here's one way to slice it, from the tippy-tip corner (so trivial that my favorite scrambler doesn't even bother to include corner moves in its scrambling notation) down to a second, third and fourth layer.

Let the two pictures above soak in for a moment. There's something different about this four-layer tetrahedron. Not only does each side have three second-layer "centers" that travel with their adjacent corners on two-layer moves, but also a fourth center, right in the middle of the third layer, which travels with three-layer moves. In the Pyraminx tutorial, I inaccurately described the corner-adjacent centers as having a single color. Technically, they're attached as a single piece to the centers on two adjacent sides, making them three-colored pieces just like the corners; but this fourth, more central center really is a one-color piece, and in the solution described below, it ends up being the last piece of the puzzle to find its way home.

Meanwhile, each edge has three pieces you're going to need to slot into place with the right colors facing the right way. But all three edge pieces are not the same. The "middle edge" piece anchors its side in a way that means you'll need to solve it first, before handling the two "side edge" pieces. And because the two side-edge pieces need to approach their slots from different directions, it actually is possible to get them flipped around the wrong way, which really means they're on the wrong side of the center-edge. It's a case of "just because they're the same color doesn't mean they're interchangeable."

So, here's the scrambler for the Master Pyraminx on the puzzle scrambling website that I prefer. Haven't you bookmarked it yet?

It's got this over my second-favorite puzzle-scrambling website: There actually is a Master Pyraminx scrambler on it. (It's worth noting, though, that you have to go back to the Ruwix scrambler for the 8-, 9- 10- and 11-cubes because Cubing-dot-net only goes up to the 7-cube. So, keep this one bookmarked, too.) The drawback to Cubing-dot-net's Master Pyraminx scrambler is the notation, which absolutely drives me nuts. The capital letters stand for two-layer turns; three-layer turns are lowercase, as you can see if you tap on the individual steps in the scramble algorithm and look at the image of how each step should look. My brain persistently wants to flip this around, but the results are lousy. I almost have to mutter aloud what each step is. And what's going to make this tutorial difficult is that you'll need to move fluidly between two- and three-layer moves throughout your solve.

So, let's get this straight. By the notation of the scrambler pictured above, this is a u move. (Always start your scramble with green at front, yellow down).

This, then, is a u' ("you prime") move:

Here's an r move (oh, how I hate this notation), and just trust me but r' twists the same three layers in the opposite direction:

Here's an l move (that's a lowercase ell, mind you), and I trust you can suss out what an l' move is:

And finally, shooting down from above, here's a b move (and again, bear in mind there's also a b'):

But wait! There's more! Here's the capital U move, which is to say, a two-layer corner turn (and from here on, I'm not going to show examples of the "prime" moves, which go counterclockwise when viewed point-on).

An R move:

An L move:

And a B move:

I really, really hate this notation. I'd rather see the wide (3 layer) moves be capitalized and the not-so-wide (2 layer) moves done in lowercase, or maybe a "2L" vs. "3L" type of notation to distinguish between them. But it is what it is.

And now, before we get into steps to solve this thing, here's the scramble pattern provided above, in real life:

You might start to get the impression this is going to be a long tutorial. I won't lie to you. I shot over 100 pictures for this. So far so good. Let's get solving!

Step 1. Match up the corners on all four sides. You can do this with capital-letter or lowercase moves, your choice, so long as it ends up like this. Trust me, the blue and yellow sides are similarly matched up.

Step 2. Choose one side to face down (in this instance, I plumped for yellow). Then put the middle-edge pieces where they belong on the bottom layer. So, for example, find the red-yellow middle-edge at the front, between the red and green sides; there's a red-blue piece where it belongs, at the lower left. (I'm holding it at this angle so you can see both pieces.)

Twist that red-yellow middle-edge into position so the yellow side (i.e. the color that should face down) is at front over the slot where it belongs.

Then do the following variation on the general theme of "down, down, up, up." In this case, the moves are l r' l' r. Coming in from the right, that would be r' l r l'. But note that whichever way this "down, down, up, up" ditty plays out, the component moves alternate between left and right, starting on the side containing the piece in question. And for this step, all the moves are three-layer moves because it's that middle piece you're trying to slot into place.

Note that at the end of this pattern, everything is the same except those two pieces have been swapped, and the yellow-red middle-edge is properly placed between the two yellow-red corners.

Keep doing this until the bottom-layer middle-edges are correctly placed on all three sides. If you find a bottom-color middle edge on the wrong bottom edge, swap it with a dummy edge to get it out of there, then put it where it belongs. I'll spare you the photography I shot of doing this to the other two yellow middle-edges. When you've got all the bottom-layer middle-edges done, you can move on to ...

Step 3. Dial in the bottom-layer side-edges. So, this awkward camera angle is meant to show the red-yellow edge piece, toward the top of the edge at front, which will need to go where that red-green edge is at the bottom right.

Why this slot and not where the red-blue edge is? Well, because if you brought it in from the other direction, it would end up red-side-down. Clearly, it's going to be a three-layer move to get it into that bottom edge. So, that's the play you need to make. With the red side at front (go by the bottom corners) and yellow down, do that "down, down, up, up" maneuver – again, starting from the side the relevant piece is on and alternating between left and right; but this time, also alternating between 2- and 3-layer moves, always with the slot in question at the tip of the move. So, below, that would be l R' l' R:

Observe how, at the end of that pattern, the yellow-red edge to the right of center is now in place. Now here's an example of where you'll lead with a two-layer move from the left. We're trying to get the blue-yellow piece, below center on the front edge, into where the yellow-green edge is lurking at right.

The version of "down, down, up, up" in this instance translates to L r' L' r:

Again, it ends as desired, with the blue-yellow side-edge now correctly positioned and oriented at the left of center on the bottom front edge. Another variation comes in from the right, like the yellow-green side-edge toward the top of the front edge, which ought to be where the red-yellow edge is at the lower left:

Bear in mind, you might have to twist the top two or three layers a bit to get this piece into position to go where it needs to go. But once the move is set up, "down, down, up, up" will take the form of r' L r L':

Of course, there's also the possibility of a short-long-short-long maneuver from the right, which would be R' l R l', but I didn't take a picture of that. Let's just say we've made our way around the bottom edges and the bottom layer is done. Even the center-center is done, which doesn't always happen (though it did in my example solve); in fact, that's going to be a problem later.

But let's call this step a success and move on to Step 4: Permutating the middle-edges of the other three sides. This picture, looking down on the upper three sides, illustrates our predicament. The green-blue middle-edge, at top, is where it belongs between the blue-green corners. However, the red-blue middle-edge, at left, and the green-red one, at right, are swapped. What, oh, what shall we do?

With those two edges at right and left of front, do a down-down-up-up maneuver, alternating left and right, all three-layer moves. Here I started from the right, so it was an r' l r l' move.

Hang on, we're not finished yet. After these moves, as you can see above, we've broken the bottom layer, with a chunk out of the bottom swapped with a chunk out of the left side. So now, twist that chunk out of the way (a u' move here):

Then dial the other side up from the bottom (an l' move here):

Twist that out-of-the-way chunk of the bottom layer back in (a u move here):

And dial it back down (an l move here).

Finally, twist the top layers as needed to find that (for example) the blue-red middle-edge is correctly aligned, as compared to the blue-red bottom corner, as are the other middle-edges. If all three edges were out of place at the start of this step, you may have to do it a couple times. But remember this "out-up-in-down" pattern; it's another theme on which you'll play variations as this solve unfolds.

Step 5. Solve the lower side-edge pieces on the upper three sides. Here's another awkward, top-down camera angle. I'd like to draw your attention to the edge between the two blue-red corners at left, where there's a red-green side-edge piece. Meanwhile, at right, there's a red-blue side-edge that's correctly positioned to drop into that slot.

Putting red at front, dial that slot down (here an L move):

Then dial in the correct edge piece from the other side (here an r' move):

Put the edge back where it belongs (here an L'):

And dial the other side back up as well (here an r). The camera angle allows you to appreciate that the blue-red edge ended up where it belongs; however; you may notice that a yellow piece broke free of the bottom and is now at the upper right. That means there's a bit more work to do.

See the yellow piece at the upper right? That needs to go back into the slot where there's a red-green edge at the moment.

Dial that piece out of the way (here a U move). Then dial the slot where it goes up (here an r), put the problem piece in (U') and dial it back down (r') – again, that "out-up-in-down" pattern.

I didn't get pictures of it, but a situation may arise where you need to swap a side-edge piece between two below-center edge positions. There's a method to it that you can probably figure out based on the procedures laid out above, but beware: it doesn't just swap two edge pieces, but it creates a cycle between three pieces, including one of the bottom side-edges. You might be just as far ahead to use the step just described to swap the problem piece with a "dummy" piece from higher up, then repeating the step to put the problem piece where it really belongs.

Suppose we've solved all those below-middle side-edges. What you'll probably see at this point is a mostly solved puzzle, except for above-middle side-edges that need to be cycled between the upper three sides, and at least three of the center-centers.

Step 6. With all the corners aligned on all sides, take a strategic look at those last three edges, and note which direction you'd have to twist the top to get those edges where they belong by the shortest route. Like, in this picture, that would be a counterclockwise (u') move.

Now think to yourself that in this step, the word "twist" in the pattern "up-twist-down-twist-up-twist-down" means the opposite direction to that shortest-way-round; in this example, clockwise. Got it? The "twist" in this recipe means the direction of the long way around. And that means, in this example, r U r' U r U r', at the end of which those last three edges will be correctly permutated.

Step 6-1/2. Ideally, you'll just have the four center-centers left to solve. But there's a parity case that often comes up, where one of the centers is already solved, like this yellow side that I warned you about earlier.

Before you can move on to the final, solving-the-centers move, you need to deal with this parity. No worries, there's an algorithm for that. This time the pattern is "down-twist-up-twist-down-twist-up-twist," starting with the problem side down; only instead of two-layer twists like in Step 6 proper, you're doing 3-layer twists; and instead of the "twist" moves taking the "long way around" direction toward the side each center belongs to, they go in the "shortest path" direction. In the example below, I goofed and made my "twist" moves in the "long way around" direction, which led straight back to a similar parity. But here's how it looked anyway: a series of moves that, in this case, were r' u r u r' u r u.

At the end, you then need to do a two-layer move to restore the top corners to their proper sides (here a u' move). And as you can see, my mistake led to another parity, only with the solved center on the green side.

Anyway, now you have to re-do Step 6 again (that's the up-twist-down-twist-up-twist-down one), starting by eyeballing those last three edges to see which direction "twist" means; and again, that's the "long-way-around-to-their-matching-sides" direction. Let's skip from the eyeballing stage to completion:

In my photography, I apparently skipped over redoing the parity algorithm (6.5) and went right on to Step 7: Permutating the true centers. With all four centers out of place, choose two that need to swap centers between themselves, like the red and green sides pictured here; put one at front and one facing down.

Then do "down-down-up-up," alternating between right and left – three times. All three-layer moves!

Whew! It's great to see a puzzle coming together. Even though there's a lot of "down-down-up-up" and "out-up-in-down" and "up-twist-down-twist" or "down-twist-up-twist" going on in this puzzle, there's something satisfying about solving the Master Pyraminx that rises above just hammering it with a handful of rote algorithms. At each step, you need to strategize a bit to make sure the right piece ends up in the right slot, facing the right way around, and that you don't break something already solved without fixing it again. Meanwhile your mind teems with questions like "is that up then down, or down then up?" and "Which way does that twist go again?" and "How the hell do I get that from there to here?"

One more reason I'm pleased with this puzzle is that it's slipped out of my hands a couple of times and taken a hard fall to an even harder floor, scattering pieces in all directions ... and amazingly, I was able to snap those pieces back on. It's not solid plastic. Each red, yellow, green and blue bit can snap off and on again, with a little care. I'm so relieved that my Master Pyraminx wasn't totaled. And truly, it remains a fun puzzle to play with.

Now what do you think? Was this tutorial worth shooting over 100 photos? I didn't use all of them. But quite nearly! Tune in another time for a word on that weird-looking gizmo to the left of the Kilominx and Pyraminx in this series of pictures. It's called the Pyraminx Edge, and I recently adopted it into my menagerie of twisty games. Not to spoil it too much (I hope), its solution is almost entirely a series of "down-down-up-up" moves. I believe the term high-level cubers use for that powerful move is the Sledgehammer; it has many more applications, as we'll see in future tutorials.