These applets simulate several constructions of Dyson spheres: swarms of satellites that capture all the light from a star yet do not collide. The Donuts are probably unstable -- orbital precession will cause the paths of satellites to eventually collide.
A donut (my definition) is constructed by placing a satellite in an elliptical orbit around a sun and spinning that orbit around some line that intersects the sun and is not in the plane of the ellipse. The whole surface of a donut can be covered with satellites with the same period, which do not collide, and where neighbors stay next to neighbors. Often a continuum of nested nonintersecting donuts can be constructed with these same properties.
Here's my old page on donuts. A simulation of a donut, as seen from an object on the donut, is shown below.