Objects of Constant Width
What the large Lego man is demonstrating here is that the shapes of constant width seen above (with the little Lego man) become objects of constant width when modelled in 3D. This means they can be used as ball bearings* and allow you to move smoothly over them without a change in your position.
Other examples of the shapes are 20p and 50p coins - so the vending machines can recognise the coins as you try to buy a can of Irn Bru and a KitKat. Blowing your mind yet? Try this clip (the commentary is blockbuster stuff, ahem, but the display is well worth a look).
To sum up, great evening out at The Festival of the Spoken Nerd.
* inefficient ball bearings right enough, but ball bearings none the less
- Apple iPhone