Heinz Strobl invented a technique called “snapology” or “knotology”, to fold paper strips into all kind of shapes you can imagine. The idea is illustrated here, for instance.
In the image above, you can imagine hexagons (in orange) and pentagons (in purple) surrounding the vertices. A curious mathematical fact is that you can vary the number of hexagons quite freely, but not the number of pentagons: there must always be 12 pentagons to fit into a perfect shape. To prove this, you need to play around with Euler’s polyhedral formula.
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