3x3x2 simulator and solver

Play a virtual 3x3x2 in your browser, or enter the colors of your own 3x3x2 and get a solution. Also known as Domino.

Info

Pieces

Type	Count	Stickers	Positions	Orientation (physical)	Orientation (visual)
1	2	1	2	4	1
2	8	2	8	1	1
3	8	3	8	1	1

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

Stickers

Axes

35 cut planes across them

Solver

Available

Distinct-piece states

≈ 4.06 × 10⁸3,251,404,800 arrangements of the stickers the moves reach (Schreier–Sims)÷ 8 turns of the whole puzzle= 406,425,600Tracks individual sticker identities, even on identical-looking pieces; whole-puzzle rotations are identified. Invisible rotations of a piece and internal pieces are not counted.

Visually distinct states

Not computedVisually distinct states = distinct-piece states ÷ reachable indistinguishable arrangements.Reachable indistinguishable arrangements = 1 × reachable fraction.No visually interchangeable sticker-bearing pieces were found.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 1 reaches the original sticker identities8!·1⁸ · 8!·1⁸ · 2!·1² = 3,251,404,800 ways to put the pieces in: per type of piece, its pieces in any order and each in any orientation that looks different÷ 3,251,404,800 arrangements the moves reach = 1This uses distinct piece identities; the chance of reaching a visually solved state may be higher.

Moves

Face turns

3×3×2 Domino beginner method

Solve both sets of corners, sort the edges into their layers, then permute the lower and upper edges.

Keep the short axis vertical and the 3×3 faces above and below. U/D are quarter-turns; R/L/F/B each mean one 180° side turn. Setups and their inverses restore the corners.

Top-layer corners

Solve the four corners around the upper square face.

Place the first three upper corners using short side turns and U/D alignment.
Use the final-corner insertion for the fourth, restoring the corners already placed.

Insert the final top corner

B D B D' B

Bring the last corner beneath its target, insert it, and restore the other three top corners.

Bottom-layer corners

Put the lower corners into their matching positions.

Align D, then identify an adjacent or diagonal corner swap.
The complete swap preserves all top corners.

Before this phase: Top-layer corners.

Bottom corners — adjacent swap

R F (D' F D R)2 D'

Swap the indicated bottom corners while leaving all top corners solved.

Bottom corners — diagonal swap

(F D2 R D)2 R D2 F D'

Swap the indicated bottom corners while leaving all top corners solved.

Edges in the correct layer

Move upper-color edges above and lower-color edges below, without disturbing the corners.

Find edges that belong in the other layer.
Align those edges, exchange one or two pairs, then undo the alignment.
Their exact side positions are handled in the next two phases.

Before this phase: Top-layer corners, Bottom-layer corners.

Edges — exchange layers

R (D2 F)3 R

Align the selected edges, exchange their layers, and undo the alignment so all corners return to their solved positions.

Edges — two neighboring layer exchanges

(F R)3

Align the selected edges, exchange their layers, and undo the alignment so all corners return to their solved positions.

Edges — two opposite layer exchanges

F R L B R L

Align the selected edges, exchange their layers, and undo the alignment so all corners return to their solved positions.

Bottom-layer edges

Permute the four lower edges into their matching slots.

Identify a swap, double swap, three-cycle, or four-cycle.
Use the suggested hold. All eight corners and all upper edges stay fixed.

Before this phase: Top-layer corners, Bottom-layer corners, Edges in the correct layer.

Bottom edges — adjacent swap

F U' F U2 R F U2 F R U' F

Permute the bottom edges while preserving every corner and every top edge.

Bottom edges — three-cycle

F D' (F R D2 R)2 D F

Permute the bottom edges while preserving every corner and every top edge.

Top-layer edges

Finish by permuting the upper edges while preserving the completed lower layer.

Prepare the turned-over hold and use the same edge algorithms.
The whole Domino is solved when these edges match; returning to the original hold is unnecessary.

Before this phase: Top-layer corners, Bottom-layer corners, Edges in the correct layer, Bottom-layer edges.

Top edges — adjacent swap

[x: F U' F U2 R F U2 F R U' F]

Prepare the turned-over hold, then use the bottom-edge sequence. All corners and previously completed edges stay solved.

Top edges — three-cycle

[x: F D' (F R D2 R)2 D F]

Prepare the turned-over hold, then use the bottom-edge sequence. All corners and previously completed edges stay solved.

Well known algorithms and patterns

Beginner — Domino

Insert final top corner

B D B D' B

Source solution 1, phase 1: final corner at DBL, targeting UBL. U/D are quarter turns; all four side letters are half turns.

Bottom corners — adjacent swap

R F (D' F D R)2 D'

Swap DBL and DBR; preserve the solved top corners.

Bottom corners — diagonal swap

(F D2 R D)2 R D2 F D'

Swap DFL and DBR; preserve the solved top corners.

Edges — exchange layers

R (D2 F)3 R

Swap DL and UR. Align U/D first to choose the edges that belong in the other layer.

Edges — two neighboring layer exchanges

(F R)3

Swap UF with DF, and UR with DR.

Edges — two opposite layer exchanges

F R L B R L

Swap UF with DF, and UB with DB.

Bottom edges — adjacent swap

F U' F U2 R F U2 F R U' F

Swap DF and DR with all corners solved.

Bottom edges — opposite swap

(R D2)3

Swap DF and DB with all corners solved.

Bottom edges — opposite double swap

F R L B U F R L B D'

Swap DF/DB and DL/DR.

Bottom edges — adjacent double swap

[D: F B D F R L B R L D' B F]

Swap DF/DR and DL/DB. The D setup and undo align the published sequence with those named pairs; without this setup it swaps DF/DL and DB/DR. Published expression: F B D F R L B R L D' B F

Bottom edges — three-cycle

F D' (F R D2 R)2 D F

Cycle DL → DF → DR → DL. Turn the whole puzzle over to use bottom-edge algorithms for the top edges.

Bottom edges — four-cycle

R L D F B U F R L B L D2 R D2 R

Cycle DL → DB → DR → DF → DL.

Bottom edges — alternate four-cycle

R D F B D F D' F B D' R D2

Cycle DL → DF → DB → DR → DL.