I was asked a question on the radio today that got me thinking; I wasn't totally sure so had to check a maths textbook during the news break!

The question - from Julian, thanks - was:

"If you took a solid metal cube and drilled circular holes into the faces so that the holes united at the centre, what shape would be formed at the point in the cube's centre where all the drill holes met?"

I suggested that this could be thought of, analogously, as the shape at the intersection of 3 cylinders in the x, y and z axes. Initially I thought the product would be a sphere, but a book I found says the result is a curved rhombic dodecahedron, volume given by 8(2-√2)r³, which was the final answer I gave.

Have I got this right?

Chris