Skewb Ultimate Tutorial

Here, front and center, is the Skewb Ultimate, supported by its dodecahedral friends, the Kilominx and the Megaminx.

Like both of those puzzles, it's a Rubik's Cube-inspired 3D twisty puzzle based on the marvelous dodecahedron, the Platonic solid that has 12 identical, regular pentagons for sides. If you're a math geek, you gotta love a regular dodecahedron (and the regular pentagon, for that matter) because the Golden Ratio, φ, drips out of them every-which-way. No doubt that's connected to the fact that φ (phi), which is to 1 what 1+φ is to φ, is exactly equal to one plus the square root of five, all divided by two. Look it up for yourself. This isn't a math essay. We're talking about the Skewb Ultimate.

The other puzzles the Skewb Ultimate is related to are the Skewb and the Skewb Diamond, which I discussed in some prior tutorials. I mentioned that the Skewb family of puzzles basically take the shape of one of the regular, face-turning puzzles, like Rubik's Cube or the FTO, and change the direction of the cuts so that the pieces turn diagonally and each move twists half of the puzzle.

Instead of 12 faces that all turn around their own center, the Skewb Ultimate is cut in half four ways, with the cuts running across its faces in different directions and dividing each face into similar groups of pieces – three corners and an edge. But one of the corner pieces on each side is also an edge piece between two adjacent sides, so that two large pentagonal sides meet at each edge and two smaller rhombuses join them in a corner at each end; so, a four-colored piece. The other two corners on each side really are just corners, with three similar but rotated trapezoids coming together at each vertex. These funky shapes mean it's possible to get pieces of the right colors in the right places while having them rotated in the wrong direction. Isn't that fun?

However, solving it is only as difficult as remembering which way to hold the puzzle while executing a series of "down-down-up-up" moves, or (if you do a "y2," 180-degree equatorial rotation between two of those) the so-called Sledgehammer move. Well, almost only as difficult. The first step is a wrinkle unto itself. It kind of makes the puzzle, if you ask me.

Here are examples of the four different ways you can turn a Skewb Ultimate. I'm not bothering with notation on this one. So, either clockwise or counterclockwise, you could twist it along any of these axes:

Before we get into it, though, let's appreciate the unusual color scheme of this puzzle, with a sticker on it that won't let you forget it's manufactured by Mefferts. The colors are a little tricky to tell apart. Like in the sides pictured below, there's a white, gold, purple and blue side, but also a green side and a side that is neither quite light blue nor light green; I suppose you could call it cyan.

Flipped the other way around, we find that there's another blue side, another green, a yellow, a red, a pink and – what's this? another pink? I'm not sure what to call that unless we run with the "cyan" theme and call it magenta.

So a dark blue (indigo?), light blue and cyan; a dark red, light red (pink?) and magenta; a dark green and a light green; and also purple, gold, yellow and white. They're gorgeous colors, to be sure, but not exactly Mefferts' gift to the color-challenged. My ballot in the suggestion box would be to revise this color scheme with more easily distinguishable hues, such as (say) a straight-up black side, gray, and good old orange! Just sayin'.

According to Wiki, the Skewb Ultimate was initially called the Pyraminx Ball. Due to the limited number of pieces and the fact that, like the FTO, each turn takes you right past a side where you can't stop before you get to one where you can – and there are only two other positions where it can stop before coming back to where it started – the number of possible scrambled states is a measly 100,776,960. Grubiks tells us the Skewb Ultimate was invented in 2000 by Tony Fisher and that Mefferts' first edition of it had only six colors, meaning opposite sides were colored the same, which I suppose made the puzzle even easier. Also, Mefferts initially misspelled the word "Ultimate," a misprint that probably makes the unopened OG model a valuable collectors' item. Finally, Grubiks informs us that while the Skewb Ultimate isn't a sanctioned speed-solving event, the record time for solving it is unofficially 4.67 seconds. For what it's worth.

Here we are, all scrambled. I just tried to make a random-ish series of turns among all different axes. If there's a scramble generator for this puzzle, I don't know about it; and I don't know what other puzzle's notation would apply so you could use that puzzle's scrambler. Just do your best not to accidentally solve the puzzle while you're trying to scramble it. Good luck.

STEP 1. Make a yellow and dark-blue cross. This is the step that isn't all about algorithms; you have to reason it out and intuitively apply a few general procedures. The goal here is to take this yellow and dark-blue edge and surround it, in the correct orientation, with the four three-sided corner pieces that feature those two colors. Also, pay attention to the two shades of red on the rhomboid corners at the ends of the edge piece; for the cross to be correct, the trapezoidal corners need to line up with those as well. Here, for example, there's a yellow-pink corner at bottom left and a yellow-red corner at the right. Unfortunately, they're both oriented the wrong way and, more concerningly, they're on the dark-blue side of the edge.

Here, you can see I twisted the lower hemisphere to bring that yellow-pink corner to the right, under the dark green-magenta edge. If you squint a bit, you can see that dark-blue edge at left.

Next, I twist the side of the puzzle that pivots around the yellow-pink corner in the direction that will put the yellow side in line to dial into place. And dial it I do.

Then I twist the red-yellow corner into position to dial into its place. And dial it I do.

Checking the blue side of the edge, I find the blue-red corner is already where it belongs, but oriented incorrectly.

Take note of which direction it needs to rotate to face the right direction – in this case, to the left. Naturally, this means you need to rotate that corner to the right on the bottom layer (always the opposite direction).

Then twist the side that pivots around that corner so that the red and blue sides will match up with the edge when you dial it back in; and dial it back in.

Again, if we dial the pink-blue corner into place, we find that it's oriented incorrectly.

So, we dial it out in the opposite direction to the way you'd rotate it for it to be oriented correctly; pivot a whole hemisphere around it; dial it back in to place; and then restore the corner that was displaced by that pivot move.

Voila! You have a yellow and blue (and pink and red) cross!

Now put the yellow-blue edge at the bottom of the puzzle and move on to ...

STEP 2. Solve the top corners. Eventually, the edge opposite yellow-dark blue will be white-light blue (shown here, obviously not in the correct spot).

Consequently, the adjacent corners need to end up with their light-blue and white sides up. But to start, those four corners could be aimed in any direction. With the yellow-dark-blue edge oriented down and and a pentagonal face at front, check whether you have a pair of either white or light-blue "headlights" at either right or left. If not, aim one "headlight" to the right, like the one on the green-white corner below:

Then repeat the "down-down-up-up" algorithm, alternating from right to left, and pivoting around the corners closest to top front on each side.

While I didn't immediately reach a state that had light-blue or white headlights, I eventually got there by repeating this pattern. See below, with the two light-blue "headlights" shown here.

Putting the headlights to the right, then, repeat that down-down-up-up pattern one more time. Result (viewed from above): all four white and light-blue corners correctly oriented and facing up.

STEP 3. Move that white and light-blue center to the top. Still with the yellow and dark-blue edge facing down, find the edge that should end up at the opposite end; here it is, at front.

Put it at the back and do the Sledgehammer pattern – that's the same old down-down-up-up, followed by a y2 move (a 180-degree, equatorial turn), and repeated from the other side. What this move does is cycles three edges, from back to top, from top to front and from front to back. At the same time, it rotates each of those edges 90 degrees counterclockwise. The initial result, viewed from above:

Well, that's the blue-white edge on top, all right. Unfortunately, the counterclockwise-rotation part of the Sledgehammer algorithm flipped it the wrong way around. To fix that, you need to do another Sledgehammer to get the blue-white edge off the top again, then rotate it to the back and do one more Sledgehammer to put blue-white on top, the right way around:

Gosh, that's beautiful. And now we hit STEP 4: Solve the remaining centers. Strange but true, at this point all the corners are correct, and you should have maybe four, but ideally three edges to cycle into place using – you guessed it! – the Sledgehammer pattern. Start by putting the first two centers (yellow-dark blue and white-light blue) at right and left; that way, nothing that happens from here forward can touch them. Also, if one of the other centers is solved, put it at the bottom, edge-down. Again, the Sledgehammer pattern, complete with that equatorial rotation in the middle, will leave the bottom edge untouched. But it will cycle the back, top and front edges from back to top, top to front and front to back, while also rotating them counterclockwise. So you might have to repeat the Sledgehammer a few times to get them where you want them, the way you want them. Just don't do a "y2" between Slegehammers; only as part of the algorithm itself. Got it?

So here's "before and after" my first Slegehammer cycle, starting with yellow at left, white at right, and ending vicey-versey:

One result was an additional solved edge, which I then put at bottom to keep it safe while continuing to work on the remaining three edges:

After some number of Sledgehammer moves – I can't remember how many; my photography is somehow failing to remind me) I realized I had solved the third-to-last edge, but the two remaining edges were flipped around backwards – one of two possible parity cases that may require special attention.

As these were adjacent centers, the solution was to put the parity edges at the back and the top (solved centers at bottom and front) and do two Sledgehammer moves – again, being careful not to do a y2 rotation between them! – and this was the result:

To solve the parity case where the two rotated edges are on opposite sides of the Skewb, just do two Sledgehammer moves (again, without a y2 rotation between them; only as part of the pattern itself!) to get into the adjacent-edges parity case, then do what I did above. It doesn't matter how the puzzle is oriented as long as yellow and white stay at left and right.

So there it is. And again, I'm helping myself as much as you (if not more) by making a record of this solution method, but one of several for this puzzle and the "beginners' method" at that, because of the same reasons I shared in my Skewb Diamond tutorial. It's an attractive puzzle. It feels nice in the hands. It turns with a satisfying clicking sound. It doesn't put up much of a fight when you set your mind to solving it. The hardest thing about coming to grips with it is keeping track of which corners your "down-down-up-up" moves are meant to pivot around. Once you've drilled that into your mind, the only parts that require deep thought are solving the initial cross and deciding how best to cycle the last few centers. When you mess up, you get more practice. And more practice is definitely needed when, the longer I spend away from this puzzle, the more likely I am to need to relearn how to solve it. Keep the brain supple and flexible. Strive for variety in your puzzling exercises!