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Folding tube maps

Back in 2012, I posted instructions for folding a tetrahedron from tube maps. When tube maps are used, the sides of the tetrahedron are not quite equal. What ratio would the rectangular maps need to be in to give a regular tetrahedron?

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If you enjoyed this puzzle, check out Sunday Afternoon Maths V,
puzzles about folding tube maps, or a random puzzle.

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