32 and Truncated Icosahedron - Numberphile

Uploaded by numberphile on 05.06.2012


OK, so we're here at the Nottingham Forest Football
Stadium, and we wanted to find some
excuse to use the stadium.
So I thought, why not talk about the football itself?
Now, it's a very special shape, but I tell you what.
For the purpose of this video, I'm going to use this little
toy version.
This is a bit clearer to see.

Now, this is actually a special mathematical shape.
It's called a truncated icosahedron.
But what is an icosahedron?
Let's start with that.
So this prop, slightly less glamorous, I'm afraid.
It's a home-made prop.
I made it out of cardboard myself.
But this is the icosahedron.
It has 20 triangular faces, and it looks like this.
So now, if I cut off the corners of this shape--
we have 12 corners.
If I cut them off, I will now make my football shape, the
truncated icosahedron.
So the truncated icosahedron has 12 pentagon faces.
Here they are in black.
And 20 hexagon faces.
There they are in white, and they fit together.
And this is your traditional football.
This was used in professional games since the 1970s, and has
been more recently replaced with a modern ball, which
actually uses fewer panels.
Now, there is an advantage, though, to using the
old-fashioned ball.
Because although it's slightly counter-intuitive, the
stitching around the ball makes it a bit more rough.
It makes the surface a bit more rough, and it actually
makes it more aerodynamic.
What they find within modern balls, because they're
smoother and are less rough, they are actually less

So they have to artificially add dimples, and artificial
grooves, and stitching, so that it will have the same
sort of flight as the old-fashioned balls did.
Yeah, so this shape was also used by an American architect
called Bookie Fuller.
He used to build domes in this shape.
And it's him that they named the Bookie Ball after.
The Bookie Ball is this shape.
Yeah, you may have heard of the Bookie Ball.
It's also used in chemistry because it's a molecule of 60
carbon atoms, again, forming this shape, the truncated
So in a Bookie Ball, we have these 60 atoms, which are the
corners of this truncated icosahedron shape, making the
same shape as this football makes.