Dear Uncle Colin,
I’m trying to sew a traditional football in the form of a truncated icosahedron. If I want a radius of 15cm, how big do the polygons need to be?
— Plugging In Euler Characteristic’s Excessive
Hello, PIECE, and thank you for your message!
Getting an exact answer to that is a little tricky, but we can come up with a pretty good approximation: if we assume the ball’s surface area is the same as that of a sphere, we can work it out.
The truncated icosahedron
Now, a truncated icosahedron is made of 12 regular pentagons and 20 regular hexagons, all of the same side…
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