Weekly challenge

Designing a Soma Cube

This week’s puzzle is a simplification of the problem that Piet Hein devised and solved some 85 or so years ago*

The challenge is to see how many different solids we can create by adding a cube to a 3-cube L shape. A constraint is that the cube must connect at least one other cube. Given that the 3 cube L shape has 14 available faces on which to attach the cube, it suggests that there are 14 new solids that can be made. Some of those attachments, however, will either:

Use these 2 pieces to create other solids
  • be the same as other models
  • connect with more than 1 cube (face to face that is)

The challenge then becomes to sort how many pieces fit our constraints. You should get the solids that the Soma Cube is comprised of. The Wikipedia page on the Soma Cube shows all the pieces and how they are constructed. I’m not sure I agree with the description of the construction of piece 4 which makes the entry all the more valuable. I’d love to hear what you think.

Can you see how our constraints allow all of these solids? Are there any others that could be created? Are there any that don’t fit within our puzzle?

The Soma cube is one of the more popular challenges in our clubs and Maths Moves! programme. We will see it a few times in this term’s challenges.

Try drawing the models that you come up with. You can download isometric paper to help you. To help you get more life like models, try to figure out which lines will be covered up by other cubes. There are also a couple of really cool tools that can help you draw cubes and other cuboid based 3D shapes – IsoSketch and IsoCube

*There is some uncertainty in the date that Piet Hein actually conceived of this idea. The accepted story is that he was struck with the idea while attending, ironically, a lecture by Werner Heisenberg (who is known for Heisenberg’s Uncertainty Principle) in 1936. The uncertainty comes in because the patent for the Soma Cube was issued in 1934. For more on the mystery of the origin of the Soma cube, see the fam-bundgaard website.

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