My second first Thursday maths night

Here’s a nice problem to test your spatial visualisation, posed to us by John Mason last night.

Draw a net of a cube (by “net of a cube” I mean a bunch of joined up squares that if you cut out and folded correctly would give you a cube).

Now turn this net into the net for a (non-square) rhombic parallelopiped. (By “rhombic parallelopiped” I mean — wait for it — a cube-like shape that has non-square rhombi as its faces. A rhombus has four equal sides, and if you imagine a tilted-over square you’ll be on the right track. Alternatively, you can imagine a rhombic parallelopiped by visualising a cube that that has been sheared or given a good shove in all three dimensions: it’s had its top pushed away a bit, it’s had one side pushed away a bit, and it’s had one end lifted up a bit. Or you could just look at the picture.)

Once you’ve designed the new net, cut it out, fold it up, and see if you are correct.