What is the optimum net for approximating towards the surface of a sphere?

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RAHoratia

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I'm a trainee teacher and one of the pupils asked about this. I thought that there ought to be a perfect/optimum configuration, depending on the size of the sphere and the number of faces. If there is no limit on the smallness of the faces, then I suppose the perfect net would be a tessellating pattern, such as hexagons? But then how would we get it to curve round rather than go on for ever as a flat surface?
 
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