FTO simulator and solver

Play a virtual FTO in your browser, or enter the colors of your own FTO and get a solution. Also known as Face-Turning Octahedron.

Info

Pieces

Type	Count	Stickers	Positions	Orientation (physical)	Orientation (visual)
2	12	2	12	2	2
3	24	1	24	1	1
4	6	4	6	4	4

One row per orbit. Orientation counts are per position; multiple values mean positions differ.

Stickers

Axes

48 cut planes across them

Solver

Available

Distinct-piece states

≈ 1.32 × 10²⁸316,521,620,122,978,725,396,480,000,000 arrangements of the stickers the moves reach (Schreier–Sims)÷ 24 turns of the whole puzzle= 13,188,400,838,457,446,891,520,000,000Tracks individual sticker identities, even on identical-looking pieces; whole-puzzle rotations are identified. Invisible rotations of a piece and internal pieces are not counted.

Indistinguishable arrangements

1,679,6163! × 3! × 3! × 3! × 3! × 3! × 3! × 3! = 1,679,6168 groups of visually interchangeable pieces within their movement orbits, using the original stickers.Counts all permutations within these groups, without checking which combinations are reachable. Internal pieces are excluded because the state count tracks stickers only.

Visually distinct states

Not computedVisually distinct states = distinct-piece states ÷ reachable indistinguishable arrangements.Reachable indistinguishable arrangements = 1,679,616 × reachable fraction.The reachable fraction accounts for restrictions such as permutation parity. Computing the correct fraction and the final visual state count is not yet implemented.

Put together at random

1 in 11,342,052,327,424 reaches the original sticker identities6!·4⁶ · 24!·1²⁴ · 12!·2¹² = 3,590,004,778,195,846,045,486,782,961,177,067,520,000,000 ways to put the pieces in: per type of piece, its pieces in any order and each in any orientation that looks different÷ 316,521,620,122,978,725,396,480,000,000 arrangements the moves reach = 11,342,052,327,424This uses distinct piece identities; the chance of reaching a visually solved state may be higher.

Moves

Face turns

Whole-puzzle rotations

FTO beginner method

Solve the edges, then the six vertices, then the centers. Every phase can be read from any position.

The reference upper edge fixes the hold. Algorithms use this app's face labels; regrips and setups are shown explicitly.

First three edges

Make one triangle of correctly ordered edges.

Match the edge colors to the color arrangement on the vertices.
The tutorial fixes one upper edge as its reference; place the other two around it.

U face turn

Place an upper edge without losing those already placed.

Middle edges

Insert six edges while preserving the upper triangle.

Align a bottom edge under its slot.
Insert it left or right. Extract a misplaced middle edge with the same insertion.

Before this phase: First three edges.

Insert a middle edge to the right

BR' D BR

Insert from the bottom triangle; use an insertion to extract a misplaced middle edge first. Upper edges stay fixed.

Insert a middle edge to the left

F D' F'

Insert from the bottom triangle; use an insertion to extract a misplaced middle edge first. Upper edges stay fixed.

Last three edges

Align the remaining bottom edges.

Once the other nine edges are solved, a bottom turn completes the edge stage.

Before this phase: First three edges, Middle edges.

Align bottom edges

Turn the bottom triangle into alignment.

Align bottom edges in reverse

D'

Turn the bottom triangle into alignment.

Vertex positions

Put six vertices in their slots, ignoring their flips.

Use three-cycles in the suggested hold; keep all edges solved.

Before this phase: First three edges, Middle edges, Last three edges.

Cycle three vertices

[BR, U']

Place vertices without changing the solved edges. Centers may move.

Cycle three vertices

[BR, U]

Place vertices without changing the solved edges. Centers may move.

Vertex orientation

Correct flipped vertices in pairs.

Apply the suggested pair flips. The vertex positions and solved edges are preserved.

Before this phase: First three edges, Middle edges, Last three edges, Vertex positions.

Flip two adjacent vertices

BR' U F' U' F U' BR U

Flip a pair while preserving all edges and vertex positions.

Centers

Complete each face's three center triangles.

Choose a face with a missing center and a donor carrying that color.
Set up, cycle, and undo the setup. Repeat for the remaining colors.

Before this phase: First three edges, Middle edges, Last three edges, Vertex positions, Vertex orientation.

Cycle three centers

[2BR, U]5

Set up the receiving face and the donor face, cycle three centers, then undo the setup. All edges and vertices return to their previous positions.

Well known algorithms and patterns

Beginner — Jaap's method

Middle edge insertion — right

BR' D BR

Source phase 1: preserve the three solved upper edges while inserting a middle edge. Published expression: R' D R Jaap holds an edge of U toward the viewer; this app holds a corner toward the viewer. Physical bindings: source U/D/F/L/R → app U/D/R/F/BR; source inner r → app 2BR. The source's r is a slice, not a wide turn.

Middle edge insertion — left

F D' F'

Source phase 1: preserve the three solved upper edges while inserting a middle edge. Published expression: L D' L' Jaap holds an edge of U toward the viewer; this app holds a corner toward the viewer. Physical bindings: source U/D/F/L/R → app U/D/R/F/BR; source inner r → app 2BR. The source's r is a slice, not a wide turn.

Vertices — three-cycle

[BR, U']

Source phase 2: cycle three vertices while preserving every edge; centers may move. Published expression: R U' R' U Jaap holds an edge of U toward the viewer; this app holds a corner toward the viewer. Physical bindings: source U/D/F/L/R → app U/D/R/F/BR; source inner r → app 2BR. The source's r is a slice, not a wide turn.

Vertices — alternate three-cycle

[BR, U]

Source phase 2: cycle UR → UB → LR under the source's hold, preserving every edge; centers may move. The arrow printed beside this sequence in the source runs the other way. Published expression: R U R' U' Jaap holds an edge of U toward the viewer; this app holds a corner toward the viewer. Physical bindings: source U/D/F/L/R → app U/D/R/F/BR; source inner r → app 2BR. The source's r is a slice, not a wide turn.

Vertices — flip two

BR' U F' U' F U' BR U

Source phase 2: flip two vertices in place; preserve all edges; centers may move. Published expression: R' U L' U' L U' R U Jaap holds an edge of U toward the viewer; this app holds a corner toward the viewer. Physical bindings: source U/D/F/L/R → app U/D/R/F/BR; source inner r → app 2BR. The source's r is a slice, not a wide turn.

Centers — three-cycle

[2BR, U]5

Source phase 3: cycle three centers while preserving all edges and vertices. Published expression: (r U r' U')5 Jaap holds an edge of U toward the viewer; this app holds a corner toward the viewer. Physical bindings: source U/D/F/L/R → app U/D/R/F/BR; source inner r → app 2BR. The source's r is a slice, not a wide turn.