Soccer balls are usually covered with a design based on regular pentagons and hexagons.
How many pentagons/hexagons MUST there be, and why?
As mentioned earlier in these comments, one can "cover the sphere" with
regular pentagons and
regular hexagons by using 12 identical pentagons and either 0 or 20 hexagons.
It has also been mentioned that there can be other numbers of hexagons.
I've asked if the number of hexagons is "quantized" according to some pattern/formula.
But let me also ask... can we have a DIFFERENT number (not 0 or 20) of
hexagons and still "cover the sphere" using regular hexagons. Or
do we find that if we have a different number of hexagons, that the
hexagons are no longer regular?
A related question...
