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Thanks for pointing that out!

You are quite correct, the text should have referred to figure 12 as representing a double torus. We've correct that mistake.

As someone who doesn't think visually myself, I agree that the concepts can be quite difficult to visualise. In the past I've ended up making some of the simpler shapes with material and a stapler which then helped me believe some of the more complicated constructions. (No paper and glue for me: material is more bendy than paper and glue... I have no patience with glue!) In particular I think I ended up attempting a double torus using stretchy material. I must admit it didn't really work but it did help me to visualise it in an ideal setting; that after sticking together two pairs of opposing edges, there were still two other pairs of edges to stick together to make two, joined, tori.

The other thing that might help is the Plus article Imaging maths – Inside the Klein bottle. The animations and cut-away views allow you to explore the surfaces which certainly helped me to visualise these shapes.

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