How to Solve a Pyraminx - Step-by-Step Course

Before you start

Take the pyramid in your hand - the best way to learn is to repeat the moves on a real puzzle. You can rotate the animations in the course: drag the pyramid with your finger or mouse.

What a Pyraminx is made of

The Pyraminx has four faces in four colours and three kinds of pieces:

• 4 tips - small triangles on the vertices. They turn in place and do not move anything else.
• 4 centres - bigger pieces right below the tips, each with three colours. They also always stay at their vertex and only turn.
• 6 edges - pieces in the middle of each edge of the pyramid, two colours each. They are the only pieces that really travel around the puzzle.

That is where the simplicity comes from: the tips and centres are set without thinking, and solving comes down to the 6 edges. The whole pyramid has 933,120 possible positions (not counting the tips) and from any of them it can be solved in at most 11 moves - the 3x3 cube has 43 quintillion of them.

How to hold it

Throughout the course hold the pyramid with the yellow face down and the green face towards you. One vertex is then on top, and the two other sides - red and blue - are at the back. The animations are the same, but remember that this is only a convention: you can start with any colour.

The method has four parts: tips (stage 2), centres (stage 3), the bottom layer (stage 4) and the last three edges (stage 5). The first two stages need no algorithms.

1Move notation

On a cube you turn faces, on a Pyraminx - vertices. Each vertex has a letter:

• U - top (up),
• L - front left, R - front right,
• B - back, at the bottom at the back.

A capital letter, e.g. R, means a turn of the two layers at that vertex (the tip together with the layer below it) by one third of a turn clockwise when you look straight at that vertex. An apostrophe (R', read “R prime”) is a turn in the opposite direction. A lowercase letter (r) turns the tip only. Click a move below to see it on the pyramid:

Watch out for the direction: “clockwise” is judged while looking at the given vertex. For U you look from above, for L and R from the front and below, and for B from the back. That is why L and R turn “in opposite directions”, even though both are clockwise. A two in the notation (U2) is not needed - two turns one way are the same as one turn the other way.

y is a rotation of the whole pyramid in your hands around the top vertex - nothing gets solved, only the side you have at the front changes. The yellow face stays on the bottom. In the course you use it to bring the right spot in front of you.

The most important sequence of the course is R U R': right vertex, top, right back again. Repeat it a few times on a real pyramid until your hand remembers the move.

2Tips

Goal: every tip in the colours of the centre right below it.

A tip has three colours and only three possible positions. Look at the centre below it: it has the same three colours. Turn the tip with your fingers (u, l, r or b) until both are lined up the same way - colour next to colour. Do this for all four vertices.

The tips are not tied to the rest of the puzzle: none of the later moves messes them up, because they turn together with their layer. But if you ever turn one by accident, just fix it with your fingers - at any moment.

3Centres

Goal: three centres of one colour on every face. Yellow ones on the bottom.

The three bottom vertices (L, R and B) each have one centre with a yellow sticker. Turn each of these vertices (L, R, B - two layers) until its yellow sticker is on the bottom face. Each move turns only one centre, so three moves are enough. The edges move around while you do this - that is fine, they are scrambled anyway for now.

Once the three yellow stickers are on the bottom, the sides line up by themselves: two green centres at the front, two red ones at the back left, two blue ones on the right. The top centre is left - turn the top (U) until its colours match the sides. On every face you will then see three centres of one colour, a triangle-shaped “badge”.

How do you know which centre matches which side? You do not have to check: the centres are attached to their vertices, so when the yellow stickers are on the bottom, the other colours end up on the right sides by themselves. Just check at the end that the three centres on every side are the same colour.

4Bottom layer

Goal: the whole yellow face and the bottom row of every side in one colour. Three edges with yellow need to be inserted.

One edge

Hold the pyramid (rotating with y) so that the spot you want to fill is at the front bottom - between the L and R vertices. The edge that fits there is yellow and the colour of the front face (green in the animations). Find it; it is somewhere in the upper part of the pyramid, i.e. in one of the three edges touching the top vertex. Now:

1. Turn the top (U) until that edge is at the top back - between the two back faces.
2. Look at which side its yellow sticker is on:
   yellow on the right back face - R U R',
   yellow on the left back face - L' U' L.

The edge drops down correctly oriented, and the piece that was there comes up to the top. The other two bottom edges stay untouched.

The edge is on the bottom, but wrong

If the matching edge is in the bottom layer but flipped or in a different spot, take it out first: bring that spot to the front bottom (y) and do R U R'. The edge comes up to the top, and you insert it as above. In the same way you get rid of any edge without yellow that is taking up a spot on the bottom.

All three

After inserting an edge, rotate the pyramid (y) so that the next free spot is at the front, and repeat. The colour you are looking for together with yellow is always the colour of the face you currently have at the front.

Finally, look at the pyramid from underneath: the whole bottom face is yellow, and on every side the bottom row (tip, centre, edge, centre, tip) is one colour.

5Last layer

Goal: a solved pyramid. The three top edges and the top centre are left.

The top centre first

The moves from stage 4 turned the top, so the top centre may have moved out of line with the sides. Turn the top (U) until its colours match the bottom centres again - three centres of one colour on every side. From now on you only turn the top as part of the algorithms.

Edges into place - the cycle

Each of the three top edges has two colours, so you can see straight away where it belongs: where the sides have those two colours. If no edge is in its place, they need to be moved one spot around in a circle. Look at the edge at the front left:

• it belongs at the back - R' L' U' L U R (the edges travel clockwise, looking from above),
• it belongs at the front right - R' U' L' U L R (the other way; this is the same algorithm done backwards).

After the cycle every edge is in its place, but some may be flipped - you will deal with that in a moment. If you happen to use the wrong cycle, nothing breaks: do it once more, and the edges will reach their places the other way round.

Flipped edges

An edge in its place may be flipped - its colours on the wrong sides. Then there are always two flipped edges, and the third one is good. Rotate the pyramid (y) so that the good edge is at the back, and do:

L R' L' R U' R U R'

It is easiest to remember in two halves: L R' L' R (left and right vertex alternately) and U' R U R'. It flips the two front edges, the back one and everything else stay in place.

Done - the pyramid is solved. Your first solves will take a minute or two, and after a dozen or so you will do it without looking at the course.

Cheat sheet: all algorithms

Everything you need to remember in one place. Yellow face on the bottom, green at the front.

Printable cheat sheet (A4 / PDF)

1. Tips - turn each one with your fingers to the colours of the centre below it.
2. Centres - L, R, B until the yellow stickers are on the bottom, then U to the side colours.
3. Bottom layer - free spot at the front bottom (y), turn the edge yellow + front colour to the back with the top: yellow on the right back face R U R', on the left L' U' L. Edge on the bottom but wrong - take it out with R U R'.
4. Last layer - top centre to the sides (U). The front left edge belongs at the back: R' L' U' L U R; at the front right: R' U' L' U L R. Two flipped - good one to the back (y): L R' L' R U' R U R'.

Solve it yourself

A practice simulator. You can scramble the whole pyramid or choose a single stage - then only what you are learning is checked, and in stage 5 you get a pyramid with the bottom layer solved.

Common problems

I did the algorithm and it is worse than before

It is almost always one move in the wrong direction. “Clockwise” is judged while looking at the given vertex - for L and R from the front and below, for B from the back (go back to stage 1 and click those moves). The second cause is the wrong grip: in stage 4 the edge must be at the top back, and in stage 5 the good edge at the back. Do the algorithm slowly, move by move together with the animation.

After the flip algorithm there are still flipped edges

The good edge was not at the back. There are always two flipped edges - the third, good one has to go to the back (rotation y). If after the algorithm the edges look mixed up, first check whether the top centre still matches the sides, fix it with a U move if needed, and do the cycle.

The yellow face is there, but the bottom row of a side does not match

One of the edges with yellow is in the wrong place (its second colour does not match the face). Take it out at the front with R U R' and insert it where its second colour fits.

The centres on one side have different colours

If the three yellow centre stickers are on the bottom, the sides always match. Different colours mean that one of the yellow centres is actually on a side - look over the bottom face again. On a correctly assembled Pyraminx such a position is impossible, unless someone has swapped the stickers.

The tips have gone out of line

The tips turn very easily and are easy to catch with a finger. It does not matter for the rest - fix them at any moment, even at the very end.

The pyramid locks up

Cheap Pyraminxes often get stuck halfway through a move, and clean vertex turns are hard on them. Modern speedcubing models turn smoothly, and magnets pull the layers into place. See Pyraminxes.

How long does it take to learn?

Most people solve the Pyraminx with the course within an hour, and without looking - after a few solves. This method needs about 30-40 moves, which at first gives a minute, and after a few weeks - around ten to twenty seconds.

What next?

Once you can solve the pyramid a few times in a row without looking at the course, start timing your solves. Time every solve and count the average of five - single results vary a lot. The Pyraminx is an official WCA competition event, in which the best competitors get below two seconds.

Faster methods shorten the way: in the L4E method (last four edges) you solve only the centres and one edge, and finish the remaining four with one of a dozen or so algorithms. Competitors add to this planning the whole solve while inspecting the scrambled pyramid.

If you enjoyed turning vertices, the Skewb turns in a similar way, and a bigger challenge is the Master Pyraminx (4 layers). If you do not solve the 3x3 cube yet, this is a good moment - you will find the course below.