There is no shortage of geodesic dome theory available on the web, and probably this forum. I won’t even try to address that, and Bucky Fuller would be horrified by this shortcut, but if I wanted to approximate a dome, I would do this:
The pentagon in the Goldberg distribution is proportionally too small compared with the scale of the hexagons (assuming the pattern is mapped to a pure sphere) and doesn’t match up with the photos.
Maybe the dome is not a true sphere? Could it be a flatter dome shape?
A couple of years ago, while attempting to figure out the structure of covid we studied a bunch of these - one useful example we found was this one: geodesic2017_edit.gh (27.9 KB)
*It’s actually the link Joseph shared above! Nice - I didn’t have the bookmark anymore, just a tweaked file