lets destroy the sun

[Kelb_Panthera]

Sorry, I thought I'd addressed that. The problem is precisely that they won't remain at all stable relative to each other. A geosynchronous polar orbit, for example, moves perpendicular to a geosynchronous equatorial some of the time, and parallel to it some of the time; the distance between them can vary drastically (if you're lucky, perhaps only by a few hundred miles). None of the other orbits will be fundamentally any better, and there is no way to fully synchronize them.

What you would in fact need is an orbit that doesn't exist: one that describes a circle around a center point that is nowhere near the Earth's center of mass. For example, the anchor point near the Pole would need a relatively small orbit that centers somewhere along Earth's axis, but not necessarily within the crust at all. This is because you're designing a spherical cover for a (rough) sphere and making it orbit as a whole; a given unified body can only have one orbit, not the numerous disparate orbits the anchors would need to remain aloft.

Come to think of it, this is basically the problem that governs certain choices in the Dyson sphere ideas — specifically, the decision to use solar wind/light pressure to support the structure, rather than orbiting as such. Which you could do, except that Earth-like planets don't radiate much at all.

I follow now, but at the same time, the choice of 6 anchor points was essentially arbitrary. You can get 2 anchors in geosynchronous or even geostationary orbit and have them stable to each other for the same net-effect. The whole wall is springing into existence in an instant in the basic version.

For the completist version start with the anchors in geostationary orbit, create a ring using the afformentioned mindless contingency carriers, and then build outward toward the poles with subsequent castings. In fact, you could build the ring up pretty massive before expanding outward to make it good and sturdy and to give it the momentum to resist gravity during the short periods that it might be a touch unstable.