How to cover?
I suggest you start with this video showing a 1V geodesic dome cover
2:45: they add wood to reduce the gaps for the cover
3:45: they start to unfold the tarpaulin. First they staple it to the uprights, pulling it tight. The staples are only there for tension, it will later be fixed with lintels. They do the walls first
5:20: They add the lintels by nailing them to the studs (you can also screw them in)
Which material?
The materials will depend on what you want to achieve: whether you want to turn your geodesic dome into a chicken house, a greenhouse, a workshop or a garden shed
If you want to turn it into a greenhouse, then UV protection is essential. Just search for “greenhouse tarpaulin”. Here are some options
https://www.baches-direct.com/fr/pm/baches-serre-largeur-3m
In 150 micron LDPE (polyethylene)
https://www.serre-en-direct.fr/bache-pour-serre/68-bache-pour-serre-sur-mesure-polyane-pro-200.html
In 200 micron polyane at less than 2€ / m² with a 5-year guarantee
https://www.jardincouvert.com/films-baches-filets/baches-films-serre/
Which offers either “thermal” or “diffusing” tarpaulins
You can avoid a lot of cutting by realising that all you need for the base is a roll: as you go round, the tarpaulin will fit without needing to make any cuts
For the top, you need a hexagon where you’ve just cut out a triangle