Math CentralQuandaries & Queries


Question from Angela, a student:

A sphere is made of 112 hexagons. Each side measures 10 cm. The width of the border between each hexagon is 5 cm. What is the radius of the sphere?

We have two responses for you

I would point out that it is not possible to have a spherical topology with all faces hexagons!
Euler's theorem applies here - the average size of a face must be under 6.



I doubt if one can make a sphere from hexagons. The angles don't fit together correctly. In addition to hexagons you need polygons with fewer vertices. For example, a soccer ball is made up of 20 hexagons and 12 pentagons. How did you come up with the problem? Can you modify what you desire so that you get something that is possible to construct?


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