In the case of the "course ball" I have from Srixon (no number on it) it doesn't follow this rule. It is a clear mix of pentagon and hexagon patterns each with a surround of dimples. on axis, it is penta; 5x squished hex with tetra interleave; 5x penta interleaved with 5x hex; and finally, at the seam, 10x hex.
The seam is what makes it a hemispherical division. In this case, the hemisphere pattern is not mirrored, it is 180 degrees out of phase on the other side.
I will see if I can do a rough division sometime soon.
