[cletus]

"Dyson sphere" is a misnomer in that at some point this was conflated to mean a shell than physically encompasses a star. That was never the original meaning or intent, which is why some people (including Isaac Arthur) prefer the term "Dyson swarm" as being true to the original idea and clear in intent.

A Dyson sphere/swarm is simple a sufficient cloud of habitats orbiting the star as to essentially block out the vast majority of its light, kind of like how droplets of water block light in a fog.

[semi-extrinsic]

This feels like it would violate the hairy ball theorem, no?

https://en.wikipedia.org/wiki/Hairy_ball_theorem

[MertsA]

No, for one you can only orbit in an ellipse around the center of mass. You can only "comb" in a direction that takes you around the middle of the ball. The major difference though, is that you can have overlapping orbits. There is no way to cover the entire surface without overlapping because of this, but you can still cover everything if you're willing to pay a price in efficiency by having portions of the constellation shade one another.

[semi-extrinsic]

Hmm, but it feels like a good tradeoff in marginal increase in total energy caught versus marginal decrease in efficiency would get you pretty far from 100% coverage.

[adrianN]

The satellites of the swarm don't have be at the same distance from the star and the orbits can overlap.