Euler says:

\[v-e+f = 2\]If one tries to tessellate the sphere surface with solely hexagon. Let $x$ be the number of hexagon, then:

\[\begin{align} v &= 6x/3 \\ e &= 6x/2 \\ f &= x \\ v - e + f &= 2x-3x+x = 2 \end{align}\]This leads to contradiction.

To make tessellation possible, we have to add $y$ pentagons, so that:

\[\begin{align} v &= (6x+5y)/3 \\ e &= (6x+5y)/2 \\ f & = x+y \\ v-e+f &= y/6 = 2 \end{align}\]So we can solve and get $y = 12$.

So a sphere surface can be tesellated with 12 pentagons plus (many) hexagons.

See also: https://github.com/vraid/earthgen-old