Soma Cube

A cube can be made from these seven coloured pieces.

Tasks
Can you work out the size of the cube?
Form a cube out of the seven coloured pieces.
Given a solution, how many different solutions can be obtained from rotating the cube? How many different solutions can be obtained from rotating pieces?
Maths

The Soma Cube is made from seven pieces. Each piece contains three or four units. In total the pieces have 27 units, which form a 3×3 cube.
There are 240 possible solutions (not including rotations). Each solution has 24 rotations of the cube. Each solution has 96 rotations of the pieces.
Every solution can be rotated so the T piece is in the bottom layer. If the T piece was in the centre layer, then it is impossible for the remaining pieces to fill all 8 corners of the cube.
History

The Soma cube was invented by Piet Hein in 1933 while listening to a lecture on quantum mechanics by famous physicist Werner Heisenberg. Hein was clearly distracted. It became a popular puzzle, and small wooden or plastic versions are still available to buy. Mathematician John Conway thoroughly analysed the puzzle in 1958.
People
Piet Hein 1905 – 1996
Piet Hein was a Danish mathematician, inventor, designer, author and poet. During World War II Piet was a member of the Danish Resistance. After the war Piet designed many puzzles including the famous Soma Cube.
John Conway 1937 – 2020
John Conway was an English mathematician currently working in Princeton University in the USA. Apart from his important work in mathematics, John is a fan of games and puzzles. He is most famous for his “Game of Life”.
Applications

Some puzzles don’t have a direct real-life application, but are good for practising mathematical thinking. When you investigate a puzzle like this, you are learning how to prove things, which are skills you can use to prove more important problems later on. The Soma Cube is a good example of a puzzle that helps you practice your mathematical thinking.
Maths at Home

You can make your own Soma Cube at home. You will need to make unit cubes, and attach them to make seven pieces like this:

You can even make the unit cubes with paper and origami. Here is a set of instructions and video.