This is kind of old but I have been investigating how to do this myself and I wanted to share what I have found so far.
TL;DR: It is not possible to wrap a flat sheet around a spherical (or semi-spherical) shape without having some amount of "excess". If you don't manage it somehow it will just "flap around" looking ugly and noisy with the wind.
Option one: use a double layer cover and blow air between both layers with an air blower. The extra layer of air between layers will act as thermal insulation, and the outer layer will be mostly flat. The downside is of course some continuous energy use, and noise.
Option two: put the excess in the hubs. This is what the Zip Tie Domes guys propose. Their hubs are big enough so that you can attach a sheet to them via some zip ties, and leave excess plastic in the center hub. It is described in detail here:
I am reproducing the most relevant part here in case it falls off internet:
You would get a "virus-like" appearance, with flappy bits of cover on hubs, but otherwise the faces would be fairly flat, provided that you managed to make the plastic tight enough. I would suggest starting with the loose zipties and gradually tightening everything up. Don't try on a windy day!
You can use this approach even if you are not using Zip Tie Hubs - you could add bits of tube protruding bolts from your nodes - just need something for the zip ties to attach to.
Option three: give up on using a flat sheet, and cut it in pieces. If you are willing to go this route, then the game becomes minimizing the amount of cuts and seams.
Here's a video from Paul Robinson in which he details several ways to approach this.
Paul Robinson - Covering WangerFlange structures
Here's a screenshot that should give you a general idea about how this is done:
Notice that the dome he covers on that video is not a "standard" one! Apparently he deformed some of the triangles in order to allow for easier cuts. Please watch the video for more details.
EDIT: Here's an extra video where he explains how he wraps the sheets around the parts. Key takeaways:
- Use multiple, thick staples. But wrap the plastic around the borders and staple on the "internal" side of the structures. Don't have any visible staples on the interior.
- Plastic expands with heat! Wrap it on a heated room. When you take it out to the cold outside the plastic will naturally shrink and make everything terser. Conversely, if you wrap it in the cold the plastic might get flappy when the temperature increases.
Option four: consider other materials besides poly sheets. In particular, I am a huge fan of what Atelier Kristoffer Tejlgaard did with their Dome of Visions series.
They used 6mm transparent polycarbonate, which comes in flat sheets, but allows for certain curvature. They used rhomboids to maximize the amount of material they used, while keeping seems to a minimum. The rhomboids overlap on their borders as fish scales, so that water would naturally flow out. And the cover is separated from the wooden structure so that if water somehow gets in, it can flow out. It also uses curved struts and custom hubs, which are probably out of most people's budgets.
A similar structure could be done with thinner polycarbonate, which would allow for more curvature. Something more similar to The Troplet, by the same studio https://www.behance.net/gallery/59391165/The-Droplet, which is gorgeous and self-sustaining.
But coming back to earth, one could envision a cover done with more common and cheaper twinwall polycarbonate which takes some of the lessons from Dome of Visions using rhomboid fishscales and some separation between structure and cover.