The blades aren't entirely flexible.
They have a tube that is inflated with low-pressure nitrogen to give them some sturdiness. In 1 g, this is not enough structure even to notice. But in 0 g it should be enough to hold the wedges' shape.
It is a wierd ungainly design. And I'll be pleasantly surprised if there aren't any design gotchas.
But it's a wierd problem they have to solve: how do you get the pressure of the sunlight to work when you want it, and not work when you don't want it. Very complicated proposition in LEO!