Algorithm notation. The 3x3x4 follows Rubik's Cube notation over its four horizontal layers: U and D are the top and bottom, 2U and 2D the two inner layers, and Uw or lowercase u turns U and 2U together; they all turn a quarter turn, with ' for counter-clockwise and 2 for a half turn. The side layers R L F B and the slices M and S only turn 180 degrees, written R2, M2 and so on, and a 90-degree side move is rejected. y spins the puzzle and x2 or z2 rolls it over. Brackets repeat or invert a group: (U R2 2U' F2)x3 or (U R2 2U' F2)3 and (U R2)'. The second input loads an algorithm into the player under the cube, played on the cube as it stands (set up a scramble with the first input): step through it with the buttons, press play, or click a move to jump there.

3x3x4 Cube simulator: solved on the left, scrambled on the right

Online 3x3x4 Cube Simulator

Free 3x3x4 cube simulator: turn a 3D four-layer cuboid online with real half-turn sides, scramble, time your solves and step through algorithms to solve it.

3x3x4 cube simulator: a Rubik's Cube one layer taller

The 3x3x4 cuboid looks like a Rubik's Cube with an extra layer: 3x3 faces on top and bottom and four 3x4 sides. Inside, the physical puzzle uses the classic 3x3x3 core mechanism. You can also think of it as two Rubik's Dominoes stacked on top of each other. The top and bottom faces and the two inner layers turn by quarter or half turns, but the four tall sides only make half turns, because a quarter turn would lay them across the puzzle. Jaap Scherphuis counts 41,295,442,083,840,000 positions, about a thousandth of a 3x3, but the half-turn restriction makes the familiar 3x3 algorithms mostly useless.

3x3x4 cuboid puzzle with its layers slightly turned

Using the 3x3x4 simulator

  • Turning: drag a sticker to turn its layer, drag the background to orbit. Horizontal layers snap to quarter turns, the sides to half turns, as on the real puzzle.
  • Keyboard: U and D turn the top and bottom, J and K the two inner layers, Shift reverses those; R L F B and the slices M and S always make the half turn, and Y spins the puzzle.
  • Notation: 2U and 2D are the inner layers, Uw or u turns U and 2U together (as in the notation for bigger cubes), side moves are written R2, M2 and so on. A 90-degree side move is rejected.
  • Algorithms: Apply plays a sequence on the puzzle; the player below steps through an algorithm move by move, forwards or back, so you can see exactly which pieces swap.
  • Practice tools: Scramble, Undo, Reset, a move counter and a timer that Scramble zeroes without starting; Space starts and stops it. The link and embed boxes share your scramble and algorithm.

How to solve the 3x3x4

As on the Domino, the half-turn sides keep every top and bottom sticker on the top or bottom, so the main job is putting pieces in the right place. One approach, used in the Ruwix 3x3x4 solution, works from the inside out:

  1. Middle edges: solve the edges of the two inner layers, first the upper one, then the lower one.
  2. Middle centres: move the centre pieces of the inner layers to their layers, then swap them into place.
  3. Corners: bring the corners to their layers and solve the bottom corners, then flip the puzzle and solve the top ones with the same sequence.
  4. Top and bottom edges: move them into their layers and solve them, then repair the middle edges the algorithms disturb.
Numbered diagram of a 3x3x4 showing the order in which the inner edges, centres, corners and outer edges are solved
The solving order from the Ruwix guide, step by step.

The Ruwix guide writes U and D for turns of two layers until the corner step, and it includes a fix for a parity case in which two marked middle edges end up swapped. Its letters do not match the standard notation used here one to one, so translate before you paste an algorithm into the player: its plain R, L, F, B are half turns (R2 here), its two-layer U is Uw here, and its lowercase u, a single inner layer, is 2U here.

Tips

  • Practise the inner-layer steps on their own: scramble, solve just the middle edges, Reset, repeat. The rest of the solve depends on them.
  • Turn the inner layers with J and K to line up pieces before you start an algorithm.
  • Use the step-by-step player on any swap you learn; on this puzzle, seeing where the inner layers go is the hard part.

Can I use 3x3 algorithms on the 3x3x4?

Only a few. Most 3x3 algorithms rely on quarter turns of the sides, which the 3x3x4 does not allow. Sequences built from U, D and half turns, such as R2 U R2, are the building blocks here.

Is the 3x3x4 harder than the Domino?

Yes. It has the same corners and outer edges plus two inner layers with their own edges and centres, so there are more steps and more pieces to keep track of.