[PLUG-TALK] Geometry Question

Richard C. Steffens rsteff at comcast.net
Wed Dec 3 22:54:15 UTC 2008


My niece is very much into soccer. For Christmas, I want to make her a 
wooden soccer ball. I am not into soccer, but having Googled for it, I 
have found that a soccer ball is (I think) a truncated icosahedron, 
having 32 faces, 20 of which are hexagons, and 12 of which are 
pentagons. See:

http://en.wikipedia.org/wiki/Soccer_ball

I can figure out how to cut the hexagons and pentagons out of wood. What 
I don't know is how to determine the angle of the edges based on the 
thickness of the wood. I think I'll use 1/2" thick lumber. If I were 
working with paper I'd just fold them and the angles would be whatever 
they felt like. Wood, at that size, doesn't bend so well. So, I'm trying 
to glue together these tiles, and it would be nice if the faces that get 
the glue were actually in the same plane.

Any geometry wizards out there who know the formula, or can point me to 
a reference?

As I'm thinking about this I realize that I need to decide on the 
"diameter" of the ball. (I know, it's not a sphere, so it isn't a 
diameter, but you get the idea.) So, I need to determine the size of the 
edges of the tiles for a given "diameter" and then I'll have the three 
sides of a triangle. Now, where did I put that book of trig tables...?

Does that sound right, or was high school too long ago?

TIA.

-- 
Regards,

Dick Steffens
 




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