An orthogonal view of Globus Cassus.
The Invisibles refers to the Kardashev scale, a speculative system of measuring a civilization’s technological advancement based on the amount of energy and resources it can wield. Loosely, a type one civilization uses what’s available on its local planet, type two can take advantage of the local star, and so on. A civilization capable of building Globus Cassus might be the pinnacle of type one — unless it took more energy than the planet contains to retrofit it into a hollow sphere.
Picture it: the Earth is mined for the material making up the core. That material is piled up on the outside and arranged in various ways. The squashed sphere of Earth becomes more like a flattened egg. Some portions of the exterior become windows to let in light from the sun. Humanity lives on the portions of the interior where centrifugal force generates gravity, which provide more than ample living space. Low gravity and airless zones have specialized purposes: manufacturing, storage and so on.
Exerting that level of control over one’s environment must be a step on the road, probably an early one, to becoming peers with civilizations like the People or the Culture. How big — and ridiculously well-equipped — would an interstellar empire have to be to decide, “You know, there’s nothing happening in that star system. Let’s hollow out some planets to create habitable space”?
On the other end of the timescale, an excavated world would be a fascinating artifact of a bygone civilization to run across in the deep of space. It’s a bit like Ringworld, but I’m put more in mind of Terry Pratchett’s Strata, for some reason. Maybe it’s the psychological component of going down into the hollow world. The exterior hides its secrets. Explorers “descend” into the unknown. There could be anything down there: bug-eyed monsters, detrimental robots, anarcho-syndicalist communes scraping by, anything!
It’s gnarly and a bit more atypical than yer Dyson sphere or ringworld. I like it.
Wikipedia article via @AllenVarney.
 A flattened icosahedron, no less!
 Come to think of it, I am reminded of the Draconis campaign frame in GURPS Bio-Tech, only remodeling the planet instead of terraforming it.