How to Solve the FTO - Step-by-Step Course

Before you start

Grab an FTO - the best way to learn is to repeat the moves on the real puzzle. You can rotate the animations in this course: drag the puzzle with your finger or mouse. The course is for beginners, but knowing the 3x3 cube will help - if you cannot solve it yet, start with the Rubik's Cube course.

What the FTO is

FTO stands for Face-Turning Octahedron, an octahedron that turns by its faces. It has 8 triangular faces in eight colours, and each of them can be turned by a third of a turn. From 2 January 2027 the FTO is an official WCA competition event (the result is an average of five solves) - the first new event since the Skewb in 2014.

It has three kinds of pieces:

• 6 corners - at the vertices of the octahedron, each with four colours.
• 12 edges - in the middle of each border, with two colours.
• 24 triangles (centres) - three on each face, with one colour. The FTO has no single face centre that stays in place - the triangles move around, so the colour of a face is only defined by the edges.

The FTO has about 31 sextillion positions - over 700 times more than the 3x3 cube. Even so, it is solved with a few short algorithms, and two of its features help a lot:

• Edges cannot be flipped. An edge that is in its place is always oriented correctly - you only have to get it there.
• The triangles come in two groups that never mix: the triangles of the white, green, grey and orange faces travel only around those four faces, and the triangles of the red, purple, blue and yellow faces - only around theirs.

How to hold it

The FTO is held with a vertex towards you. You then see a square made of four faces: U at the top, R on the right, F at the bottom, L on the left. The four faces at the back are hidden. This is also how the FTO looks in the scramble images at competitions and in every animation of this course.

Colours of opposite faces: white - yellow, green - blue, red - orange, purple - grey. This is the scheme used in WCA scrambles; most FTOs in shops have exactly these colours.

The solving plan

We solve in this order: edges, corners, triangles. Each part only uses moves that do not break the previous one:

1. White edges - the three edges of the white face, no algorithms.
2. Remaining edges - 6 middle edges, inserted with R U R', and the last 3 with a single turn.
3. Permuting the corners - two algorithms of 4-5 moves.
4. Orienting the corners - one algorithm of 8 moves.
5. Triangles - one algorithm of 11 moves, repeated with different setups.

In the first three stages do not look at the triangles - they will get mixed up, and that is normal. That is why the triangles are grey in the animations of those stages.

1Move notation

Moves are written with face letters, just like on the 3x3 cube. With the FTO held vertex towards you, at the front there are:

• U - the top face, R - right, F - bottom, L - left;
• at the back: B - back top (opposite F), BR - back right (opposite L), BL - back left (opposite R), D - back bottom (opposite U).

A letter, e.g. R, means turning that face by one third of a turn clockwise, when you look straight at that face. An apostrophe (R', read “R prime”) is a turn the other way. The face turns together with the whole layer under it: with the corners and parts of the three neighbouring faces. This is how moves are written in official WCA scrambles. Click a move below to see it on the puzzle:

You do the back face moves with your fingers from behind - in this course you rarely need them. Watch the direction: “clockwise” is judged looking at the given face, so for back faces - looking from the back.

Three symbols are rotations of the whole puzzle in your hands (no face moves):

• T - a quarter turn around the front vertex, clockwise: face U goes to where R was, R to F, F to L, L to U. The front and back vertices stay in place.
• Uv - a rotation around face U, like the U move but with the whole puzzle. Face U stays in its place.
• x2 - flipping over: the front vertex goes to the back, face U to where D was, F to B, R to BR, L to BL.

The most important sequence of the course is U F U' F' - faces U and F only touch at the front vertex. Repeat it a few times on the real puzzle: after three repetitions the FTO returns to its starting state.

2White edges

Goal: three white edges on face U, each matching the neighbouring face with its second colour. You do not look at the corners or the triangles.

The white face U has three edges: U-R (the diagonal from the centre to the top right corner of the square), U-L (to the top left corner) and U-B (the top side of the square, next to the back face B). The colours must lie as on a solved FTO: white-red next to R, white-purple next to L, white-blue next to B. You can insert the first edge anywhere - it determines where the red face is.

One rule

Faces F, BR, BL and D do not touch any edge of face U. You can turn them freely - the white edges you have inserted will not move. That is why you insert every edge the same way:

1. Rotate the whole FTO around the white face (Uv) so that the edge's slot is on the right (U-R).
2. Using faces F, BR, BL and D, bring the edge to face R: onto the diagonal in the bottom right corner (R-F) or onto the right side of the square (R-BR).
3. Turn R or R' - so that the edge goes up to the top.

If the edge is on the back faces (BL, D), first turn them to move it onto face F or BR - those are “free” faces too, so you will not break anything. If a white edge is on top but in the wrong place, turn the face under it (L or B) so that it comes down, and insert it like any other.

Finally, check: three white edges on face U, and their second colours - red, purple, blue - next to faces R, L and B. Looking at the white face from above, clockwise: blue, red, purple.

3Remaining edges

Goal: all 12 edges in their places.

Flip the FTO over (x2): the white face goes to the back bottom (D), and the yellow one comes to the top. The white edges are now next to faces F, BR and BL - these are the “bottom” faces, neighbouring the white one. Between them and faces R, L and B there are 6 middle edges. You can see two of them from the front: F-R (the right lower diagonal) and F-L (the left lower diagonal).

Where an edge belongs

A middle edge has the colour of one bottom face and one top face. You already know the bottom face colour - it is the second colour of the white edge next to that face. You can read the top face colour from a corner: find the corner that has white and the colours of two bottom faces next to each other - its fourth colour belongs to the top face between them. With the WCA scheme it is simpler: a top face has the colour opposite to the bottom face across from it (R opposite BL, L opposite BR, B opposite F).

Inserting

Rotate the whole puzzle (Uv) so that the bottom face in the edge's colour is at the front (F). The edge has to go to the right diagonal (F-R) or the left one (F-L). Turn U until the edge is on the top side of the square (U-B), and perform:

The moves R U R' and L' U' L do not touch the white edges or the other middle edges. They insert the edge from U-B and kick out whatever was in the slot to the top.

A middle edge in the wrong slot? Put that slot at the front and insert any edge from the top into it - the wrong one will pop out to the top, and then you insert it normally.

The last three edges

When 9 edges are in their places, the last three are on the yellow face U. No algorithm is needed: turn U (once, one way or the other), and all three drop into place. On the FTO you cannot swap just two edges, so a single turn is always enough.

4Permuting the corners

Goal: every corner at its own vertex. It may be twisted - you will deal with that in stage 5.

The edges now define the colour of every face. A corner is in its place when it has the same four colours as the faces around its vertex - even if they are on the wrong sides. From now on you can rotate the FTO in your hands however you like; the algorithms of this stage do not touch the edges.

Step 1: the front and back corners

The algorithm U F U' F' moves the corner from the top right corner to the front (to the front vertex). At the same time the front corner goes to the bottom left corner, and that one - to the top right. It does not touch the back vertex.

1. Find a corner that is already in its place, and rotate the FTO so that it is at the back (at the back vertex). If none is in place, skip this step.
2. Find the corner that belongs at the front vertex. Rotate the whole puzzle with T (the front and back stay in place) until that corner is in the top right corner, and perform U F U' F'.
3. If the front and back are not both correct yet, repeat from point 1 - at most two algorithms are enough.

If no corner was in place, choose the orientation so that the corner belonging at the front is not sitting at the back - then you can always rotate it to the top right corner.

Step 2: the four corners of the square

The front and back are correct. Four corners are left at the corners of the square. Count how many of them are in their places - there can be four (done), one or none.

• One correct - rotate the whole puzzle with T until the correct corner is in the top left corner, and perform F U F U' F. The other three cycle around; if they are still wrong, perform the algorithm once more.
• None - perform F U F U' F once from any orientation. Now one corner will be correct - proceed as above.

5Orienting the corners

Goal: all corners solved - the FTO is done apart from the triangles.

An FTO corner can sit in its place in two ways: correctly or twisted by half a turn - then each of its colours is on the wrong side. There is always an even number of twisted corners: two, four or six.

The algorithm U F U' F' L' R' L R twists two corners: the front one and the top right one. It is made of two moves you already know: U F U' F' and a similar four-move sequence on faces L and R.

1. Rotate the FTO so that a twisted corner is at the front.
2. Rotate the whole puzzle with T until the second twisted corner is in the top right corner, and perform the algorithm.
3. Repeat until all corners are correct.

If two twisted corners are left opposite each other (front and back), the T rotation will not bring the back one to the top right corner. Then perform the algorithm with a correct corner in the top right corner - the front one will become correct, and the top right one will end up twisted. That one and the back one already share an edge, so one more algorithm is enough.

6Triangles

Goal: three triangles of its own colour on every face - the FTO is solved.

The edges and corners are done. One algorithm is left, which moves one triangle and does not touch anything apart from three triangles:

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

It is easy to remember: R, the four moves F' L F L', R, the four moves U L' U' L, R. It works on the triangles of faces U and F:

• the triangle from the right corner of face F (next to the bottom right corner of the square) goes to the right corner of face U (next to the top right corner),
• the triangle from the right corner of U goes to the left corner of F, and that one - to the right corner of F.

Two faces from the same group

A triangle can only move to a face from its own group (white, green, grey, orange or red, purple, blue, yellow). Two faces of the same group always touch at a single vertex, like U and F at the front vertex. That is why every pair of faces from a group can be set up just like U and F in the algorithm.

How to solve them

Choose a face to solve - white to start with. For each wrong triangle on it:

1. On another, unsolved face of the same group, find a triangle in the colour of the face you are solving.
2. Rotate the FTO so that the shared vertex of these two faces is at the front, the face being solved on top (U), and the face with the triangle at the bottom (F).
3. Turn U so that the wrong triangle is in the right corner of U.
4. Turn F so that the triangle you need is in the right corner of F.
5. Perform the algorithm, then undo the F turn from step 4 and the U turn from step 3 (in that order).

The U and F turns in steps 3-4 break the edges and corners for a moment, but undoing them in step 5 restores everything. Do not skip the undo!

When a face is done, take the next one from the same group. The last face of a group solves itself - only its own triangles will be left on it. Then the second group in the same way. You will usually perform the algorithm 9-14 times; at first this is the longest part of the solve, but also the most repetitive.

Cheat sheet: all algorithms

Six algorithms for the whole FTO. Always held vertex towards you: U top, R right, F bottom, L left.

Printable cheat sheet (A4 / PDF)

1. White edges - white face on top, slot on the right (Uv). Faces F, BR, BL, D are free: use them to bring the edge onto face R, then R or R'.
2. Middle edges - x2 (white at the back bottom), the edge's bottom face at the front, edge on the top side (U-B): slot on the right R U R', on the left L' U' L. Last three: turn U.
3. Corners: front and back - correct corner at the back, the corner belonging at the front in the top right corner (T): U F U' F'.
4. Corners of the square - correct one in the top left corner (T): F U F U' F, once more if needed; none correct - once and start over.
5. Orienting the corners - twisted ones at the front and in the top right corner: U F U' F' L' R' L R.
6. Triangles - face being solved on top, face with the triangle you need at the bottom; U: wrong triangle to the right corner of U, F: the needed one to the right corner of F; R F' L F L' R U L' U' L R, undo F, undo U.

Solve it yourself

A simulator for practice. You can scramble the whole FTO or pick a single stage - then the earlier stages are already solved, and the goal checks only that one. Whole-puzzle rotations (T, Uv, x2) do not count as moves. The buttons cover all 8 faces; dragging on a sticker turns a face along the edge of the triangle.

Common problems

I did an algorithm and it is worse than before

Most often the grip is to blame: the FTO must be held vertex towards you, and face U is the one at the top of the square - not the top edge. The second cause is the direction of a back or side face move: “clockwise” is always judged looking straight at that face. Perform the algorithm slowly, move by move along with the animation.

The edges fell apart during the triangle stage

The U and F setup turns (steps 3-4) were not undone, or were undone in the wrong order. Undo F first, then U. If something fell apart, go back to stage 2 - you will solve the edges and corners quickly, and the solved triangle faces will need fixing anyway.

I do not know what colour a face is

The triangles move around, so do not look at them until you get to stage 6. The colour of a face is defined by the edges (after stage 3 all three edges of a face have its colour), and before that - by the corners: each corner has the four colours of the faces around its vertex.

Two edges are left swapped

After a completed stage 3 that is impossible - the FTO always has three last edges that a single U turn puts in place. If you see two swapped, one of the earlier edges is in the wrong place (most often the side got mixed up: F-R with F-L). Check the colours of all middle edges.

One twisted corner is left

A solved FTO cannot have a single twisted corner - the corner was twisted in place (e.g. when the puzzle was dropped). Carefully twist it with your fingers by half a turn, without forcing it, so that you do not damage the mechanism.

The faces catch

The FTO only turns when all faces are fully aligned - otherwise the triangles catch on each other. Finish every move completely. Modern models have magnets that align the faces on their own. See FTO puzzles.

How long does it take to learn?

Your first solve with the course will take one or two evenings. The method needs about 200 moves (about 150 of them on the triangles), which at first means 10-15 minutes, and after a few weeks 3-5 minutes.

What next?

Once you can solve the FTO a few times without looking at the course, start shortening the path. You will gain the most on the triangles: instead of moving them one at a time, learn to solve them together with the edges and corners in blocks. This is the basis of the Bencisco method, used by most fast solvers - first a block around one face, then further blocks and short algorithms for the last layer. The best solvers do the FTO in a dozen or so seconds.

If you like octahedra, also try the CTO (Corner-Turning Octahedron, turned by its vertices). And if you enjoy puzzles with moving centres, have a look at the Skewb or Megaminx course.