Soma cube solution step by step

Pick "Cube" in "Pick a figure" to see solution 1. Each press of "Next" shows which piece goes on which layer, starting from the floor.

What are the Soma cube pieces called

V, L, T, Z, A, B and P. V has three cubes and the others four, 27 in total; A and B are mirror images of each other.

The figure from my Soma booklet is not in the list

Draw it layer by layer in "Build your own". Shapes up to 5×5×5 fit, and "Solve this shape" works once the shape has 27 cubes.

Pieces fall over while building the solution

Read the sentence under the buttons. If a solution has a step where a piece floats, that step tells you to hold the piece by hand. "Another solution" may give one that is easier to stack.

Does the Soma cube really have 240 solutions

Yes. Counting turned and mirrored copies as one there are 240; counting them separately there are 11,520. "Count solutions" checks it.

Soma Cube Solver (3D step by step)

Shows how the 7 Soma pieces build the 3×3×3 cube and dozens of figures, one piece at a time in 3D; enter any shape and it finds a solution

Loading the tool…

When a child brings you a Soma cube (seven wooden pieces) and cannot build the cube or a figure from the booklet, pick the figure here and see the pieces placed one at a time, in 3D and as layer plans. There are 39 built-in figures, and you can draw any other shape on layer grids and solve it.

How to use

Choose a figure in the "Pick a figure" tab or from the "Figure" list at the top. The first solution appears at once.
Each press of "Next" places one piece. The sentence under the buttons names the piece and its layer, and in the "Layer plans" a thick border marks the piece just placed.
Drag the 3D view to turn it and use the wheel or two fingers to zoom. "View from the back" shows the other side.
Press "Another solution" for a different way to build it, or "Count solutions" to find out how many there are.
For a figure from a book or box, open "Build your own", set "Width", "Depth" and "Height (layers)", tap squares to fill them and press "Solve this shape". Turn pieces off under "Pieces to use" to solve shapes made with fewer pieces.

How it works

The solver is an exact-cover search: it tries every turned position of each piece (V 12, L 24, T, Z, A and B 12 each, P 8) and always fills the square with the fewest pieces that fit first. It runs in your browser.
"Another solution" skips solutions that match one already shown after turning or mirroring the whole figure.
The building order is chosen so each piece rests on the floor or on pieces already placed and can be lowered from above. When a solution has no such order (the mushroom, for example), the step where you must hold a piece is marked.
"Show piece letters (colour-blind mode)" puts the piece letters on the 3D cubes as well. Your own shape and settings are kept only in this browser.

How to solve the Soma cube: which piece to place first

For the 3×3×3 cube it is usually easier to lay the larger pieces on the floor first and fit the small V piece and the twisted A and B pieces into the gaps last. The order shown here also fills the bottom layer first, so you can copy it with the pieces in your hand.

A common mistake is swapping A and B. They are mirror images, so no turn makes one into the other. Match the colours and letters on screen with the real pieces, and check the drawings in "The 7 pieces" tab when in doubt.

How many Soma cube solutions are there

The 3×3×3 cube has 240 solutions when solutions that match after turning or mirroring the cube count as one. Counting every position separately gives 11,520, because the cube can be turned and mirrored in 48 ways: 11,520 ÷ 48 = 240. "Count solutions" counts them here and shows both numbers.

Other figures have very different counts. Some have only a few solutions, and some, like a 1×1×27 rod, have none. If a shape you draw cannot be built, the tool says so.

Questions and answers

Soma cube solution step by step: Pick "Cube" in "Pick a figure" to see solution 1. Each press of "Next" shows which piece goes on which layer, starting from the floor.
What are the Soma cube pieces called: V, L, T, Z, A, B and P. V has three cubes and the others four, 27 in total; A and B are mirror images of each other.
The figure from my Soma booklet is not in the list: Draw it layer by layer in "Build your own". Shapes up to 5×5×5 fit, and "Solve this shape" works once the shape has 27 cubes.
Pieces fall over while building the solution: Read the sentence under the buttons. If a solution has a step where a piece floats, that step tells you to hold the piece by hand. "Another solution" may give one that is easier to stack.
Does the Soma cube really have 240 solutions: Yes. Counting turned and mirrored copies as one there are 240; counting them separately there are 11,520. "Count solutions" checks it.