Soma Cube

The Soma cube is a solid dissection puzzle (which was invented by Piet Hein during a lecture on quantum mechanics in 1933). Over the years it has been sold by Parker Brothers and others. I remember playing with it as a child – and not appreciating it.

Lately I’m become reacquainted with the Soma Cube and found it to be beneficial.

Spatial ability, defined by a capacity for mentally generating, rotating, and transforming visual images, is one of the three specific cognitive abilities most important for developing expertise in learning and work settings. [The other two being quantitative and verbal ability’] Scientific American

The Soma Cube puzzle has 7 pieces. Six pieces are made of 4 cubes. One piece is made of 3 cubes. 6×4 + 1×3 = 27. The 7 pieces can be assembled into a 3x3x3 cube. It actually can be done in 240 ways.

What makes it interesting is all the things you can build with fewer than 7 pieces and all the all the other things you can build with all 7 pieces.


Soma cube pieces are (traditionally) made of wood, but can be made out of LEGO or played on tablet/iPad apps.

My Tips

  1. Become familiar with the pieces, and name them.7SomaPieces
    1. The names I use (in order from the diagram) are: V, L, T, Z, Corner, Weird A, Weird B.
    2. Notice one, the V, has (only) 3 cubes and the other six each have 4 cubes.
    3. Notice the first four (top row) all will lay flat. The other three are ‘3D.’
    4. Practice with the two ‘weird’ pieces (which are reflections of one another). They can be placed sitting on 1, 2, or 3 cubes on the bottom.
  2. When making a puzzle with fewer than all 7 pieces, count how many cubes you need to know if the V (with 3 cubes) is needed and to know how many pieces will be needed.
  3. (Personal opinion, I don’t always do this.) When building, I often save the V and the L for the end.


The  iOS app I used to used has disappeared from the app store.  I’m looking for one!  If you know of one, please let me know.
Android Soma Cubes app – I haven’t tried this one yet.


Soma Cube Animation

Webpages – yep, wikipedia overview. Includes a proof of where the T needs to go.

Soma Cube from WolframMathWorld

Thorleif’s SOMA page – very comprehensive

Mathematische-basteleien page – a little old, but interesting.

Eric Harshbarger’s LEGO Puzzles page – included is Soma Cubes made out of LEGO

Mathematrix page – shows some of the classic Soma Cube puzzles, such as the Bed, Tub, Swan, Well, …

Large Soma Puzzle made at MoMath – finished 3x3x3 cube more than 6′ tall.

On the benefits of spatial visualization – which can be learned!

A few articles that explain why spatial visualization is beneficial for students, and that spatial visualization abilities can be learned.

Scientific American

What is spatial ability? Why is spatial ability important? (has references)

Harvard Business Review

Journal of Educational Psychology

Characterizing and Improving Spatial Visualization Skills (has references)