3x3 Shape Mods: Axis, Windmill, Fisher and How to Solve

What is a 3x3 shape mod?

A 3x3 Rubik's Cube has a core with six turning axes. A shape mod uses exactly the same mechanism, but the pieces are cut into different shapes, or the axes are tilted compared with the outer shell. The result:

• The number of pieces, the number of layers and every turn are exactly the same as on a 3x3.
• The pieces are no longer all the same size, so the cube can change shape as you turn it.
• Some centres have a picture or a shape that shows which way they are facing.

Ruwix, a long-running Rubik's Cube guide site, puts the Fisher Cube, Windmill Cube and Axis Cube in the same group: all three are 3x3 cubes whose axes are turned at an angle inside the outer shell (Ruwix).

!A scrambled Windmill Cube, with the pieces out of line making a wonky shape Photo: [Luis Alvaz / Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Cubo_Windmill_revuelto_08.jpg), CC BY-SA 4.0

Popular 3x3 shape mods

Fisher Cube

This is one of the oldest shape mods. According to Ruwix, it was invented by puzzle designer Tony Fisher in the 1980s and is named after him (Ruwix – Fisher Cube).

Ruwix also gives the easiest way to think about it: the Fisher Cube is a 3x3 turned 45 degrees around its vertical axis. That is why the four edges of the middle layer look like centres, and the four side centres look like corners (Ruwix – Fisher Cube).

!The Fisher Cube, a 3x3 turned 45 degrees around its vertical axis Photo: [cubemeister.com / Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Fishers_Cube_orientation_1_cubemeister_com.jpg), CC BY-SA 3.0

Windmill Cube

A 3x3 with cuts running diagonally across the white and yellow faces, so from above it looks like the sails of a windmill. Ruwix calls it a "supercube": the four red, green, blue and orange centres have to face the right way before the cube looks solved (Ruwix). This is where you need the centre algorithms further down.

!A solved Windmill Cube, with the diagonal cuts easy to see Photo: [RealAppleFreak / Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Windmill_Cube_gel%C3%B6st.jpg), CC BY-SA 4.0

Axis Cube

When it is solved, the Axis Cube is a cube. Just one turn and it becomes a strange shape. According to Ruwix, this is a puzzle where every piece has to face the right way, including all six centres (Ruwix). Because every piece has its own shape, the Axis Cube needs more careful looking than the Windmill. On the plus side, the shape itself is your hint: once every piece is in place and facing the right way, it turns back into a cube.

Mastermorphix

A 3x3 cut into a tetrahedron (four triangular faces) with slightly puffed-out faces. Ruwix notes that its four triangular centres have to face the right way, and that it comes in both a four-colour version and a single-colour version (Ruwix).

!The Mastermorphix, a tetrahedron-shaped shape mod with puffed-out faces Photo: [Mietitor17 / Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Pillowed_Mastermorphix_II.jpg), CC0

Mirror Cube and Ghost Cube

The Mirror Cube has every face the same colour, so you solve it by the thickness of each piece. The Ghost Cube still has its layers slightly out of line even when it is solved (Ruwix). Because even the solved state looks off, save the Ghost Cube for last. How to tell the pieces apart on a Mirror Cube is in its own post, the Mirror Cube. For a list of other kinds of cubes, see types of Rubik's Cubes.

How to solve a shape mod: it's still the 3x3 method

You don't need a new method. Just solve it with the same steps you already use in how to solve a 3x3 Rubik's Cube for beginners. If you can't solve a normal 3x3 yet, follow EasyRubic's layer-by-layer step-by-step guide first. The tricky part is working out which piece is which:

1. Find the 8 corners first. A corner always has three sides showing, whatever its shape. On the Fisher Cube, don't mix up the four side centres with corners.
2. Find the 12 edges. An edge has two sides showing. On the Fisher Cube, the four middle-layer edges look like centres.
3. Find the 6 centres. A centre only spins on the spot and never moves to a new place. These are your landmarks.
4. Solve layer by layer as usual, but check the shape after each layer: a piece that is in place but facing the wrong way will make the cube look bumpy.

If your cube has colours, go by the colours. Use the shape only as a check. If your cube is a single colour (Mirror Cube, single-colour Mastermorphix), compare the thickness and length of each piece's sides with the centre next to it.

The turned-centre trap and how to fix it

On a normal 3x3, you can't see which way a centre is facing. On the Windmill, Axis, Fisher or Mastermorphix, the centres have a shape, so you can solve every piece and then find one centre lying sideways, or turned upside down by 180 degrees.

The good news is that the worst case has a limit. Jaap Scherphuis's site, Jaap's Puzzle Page, explains the rule: the total number of quarter turns of the centres always has the same parity (odd or even) as the way the corners are arranged (Jaap's Puzzle Page). Once all the corners and edges are correct, that total has to be even. That means you will only ever see one of two situations:

• One centre turned 180 degrees.
• Two centres each turned 90 degrees (or more centres, but you fix them one pair at a time).

You will never get exactly one centre turned 90 degrees. If that's what you see, look again: there is definitely another centre that is turned too.

A tip to need the algorithms less often: while solving the first and second layers, whenever a side centre is facing the wrong way, turn that face so the centre is right before you put the pieces in. Jaap Scherphuis also points out that if you do this, by the end usually only the top centre needs fixing. The algorithms below keep every corner and edge where it is and only turn centres. If you're not yet used to reading letters like R, L' or U2, see the cube notation page first.

A normal 3x3 has no centre direction, so EasyRubic's cube pictures can't show the centres before and after an algorithm. Instead, compare your cube with the photo of the solved Windmill Cube below: when every centre faces the right way, the diagonal cuts line up with the pieces around them.

One centre turned 180 degrees

Hold the cube so the centre you need to fix is on the top face. You have two choices.

Short algorithm (12 moves), from Jaap's Puzzle Page: R L U2 R' L' U R L U2 R' L' U

Easy-to-remember algorithm (20 moves), from Ruwix: do (R U R' U) 5 times in a row. It's longer, but almost impossible to forget, because it's just one group of four moves repeated.

Both algorithms leave every corner and edge where it is, and only the top centre turns half a turn.

!A solved Windmill Cube with every centre facing the right way: this is how your cube should look after fixing the centres Photo: [Luis Alvaz / Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Cubo_Windmill_resuelto_02.jpg), CC BY-SA 4.0

Two centres each turned 90 degrees

The basic algorithm, from Jaap's Puzzle Page:

R L' F B' U D' R' U' D F' B R' L U

It turns the top centre a quarter turn clockwise and the right centre a quarter turn anticlockwise (looking straight at each face). Every corner and edge stays where it is. Do it three times in a row and the two centres turn the other way instead.

Hold the cube so the two turned centres are on the top and right faces, then check which way each one needs to turn:

• Top centre needs to turn clockwise, right centre anticlockwise: do the algorithm once.
• Top centre needs to turn anticlockwise, right centre clockwise: do the algorithm three times.
• Both centres need to turn the same way: do the algorithm once (if the top centre needs to turn clockwise) or three times (if anticlockwise). The top centre is now right, and the right centre is now 180 degrees off. Tilt the whole cube to the left so the right face comes to the top, then use the one-centre 180-degree algorithm above.

!A solved Windmill Cube from another angle, with all the side centres facing the right way Photo: [Luis Alvaz / Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Cubo_Windmill_resuelto_03.jpg), CC BY-SA 4.0

Two turned centres on opposite faces

The algorithm above only turns two centres that are next to each other, so you fix these by going through a side face, in this order:

1. First hold: one centre turned 90 degrees is on the top face, so the other turned centre is on the bottom face. Any face can be the right face.
2. Fix the top centre: do the two-centre algorithm once if the top centre needs to turn clockwise, three times if it needs to turn anticlockwise. The top centre is now right, but the right centre has just been turned 90 degrees.
3. Second hold: tilt the whole cube to the left so the right face comes to the top. The turned centre that was on the bottom face is now on the right face.
4. Fix the last two centres: the two turned centres are now on the top and right faces, next to each other. Follow the section on two centres each turned 90 degrees above.

The centre you need to fix isn't on top?

All three algorithms only need the right hold. Just turn the whole cube to bring the centre you need to fix to the top (and the second centre to the right), then do the algorithm. Don't turn a single face to "bring" the centre up, because centres can't move to a new place: you have to turn the whole cube.

Tips for choosing and practising shape mods

• Get smooth at solving a normal 3x3 first. Once you know the steps by heart, you can put all your attention on spotting the pieces.
• Start with the Windmill or Fisher. They keep the same colours as a normal 3x3 and only have four centres that need to face the right way. Save the Axis Cube and Mastermorphix for later.
• The Fisher Cube has one spot where people trip up on the last layer. The fix is in the section just below.
• Shape mods are not part of WCA competitions. Think of them as toys that challenge your eyes, not something for speed practice.

If you're still choosing your first cube, read which Rubik's Cube to buy as a beginner first.

Fisher Cube: an odd number of top-layer edges facing the right way

According to Ruwix, the four middle-layer edges of the Fisher Cube are only one colour, so you can't see which way they are facing. Because of that, in about half of your solves, after finishing the first two layers you'll find that the number of top-layer edges facing the right way is 1 or 3. On a normal 3x3, this never happens (Ruwix – Fisher Cube).

The fix: flip one middle-layer edge in place, then solve the top layer as usual.

1. Hold the cube as you would while solving: the two finished layers at the bottom. R, U and F here mean the faces the puzzle actually turns, not the flat faces you see on the outside.
2. Do the algorithm Ruwix gives: R U R' U2 R U2 R' U F' U' F
3. The middle-layer edge at the front right is flipped, and the two bottom layers stay as they were. The top layer gets mixed up again, but now the number of edges facing the right way is even, and you carry on solving like a normal 3x3.

The picture below is drawn on a normal 3x3: the front-right edge (coloured in) is flipped in the before picture and correct in the after picture, while the two bottom layers stay the same. The top layer in the picture also changes with the algorithm.

1. You start with (input)
3. After the formula

Sources

• Rubik's Cube Shape Mods – Ruwix
• The Fisher Cube – Ruwix
• Rubik's Cube 3x3x3 – Jaap's Puzzle Page
• WCA Regulations, Article 9b – World Cube Association