Basic Information
A Topopolis is a hypothetical megastructure that could orbit a star. From the inside, it would look like a tube, and it's rotation would create gravity on the walls of the tube, so you could look "up" and see "across the world". The tube would extend into a large torus or doughnut shape, and when seen from outside, it would wrap around the local sun. It may not be as simple as a mere Torus however, as you'd be able to created more surface area for habitation by making it a complicated Torus Knot, like a 3D representation of celtic knotwork on an extremely large scale. The whole knot would be hundreds of millions of kilometers long, and each strand or tube would be at least several kilometers (a few miles) in diameter. A Topopolis with this knotted shape is sometimes called Cosmic Spaghetti.
As with most stellar-scale megastructures, a Topopolis would require a very high degree of technology and engineering, plus incredible resources to build and maintain. It provides a huge amount of dwelling and surface space, and could house trillions of beings.
A Topopolis is similar in construction to an O'Neill Cylinder space station, though much larger and wound around a star.
Sources
Wikipedia mentions that Topopoli appear in the novel Matter by Iain Banks and the article Bigger Than Worlds by Larry Niven. I haven't read either, but I imagine they could fill in the details this page is lacking. For example, I'm not really sure how day and night works in a Topopolis. They may have big transparent sections to let the light in, like the O'Neill Cylinder illustration on the Wikipedia page. Or, they may have an opaque surface with solar collectors, and then rely on artificial lighting within. You may want to do more research (or just make a decision) before using one in your game or story.
Game and Story Use
- If the Topopolis is knotted to the point of Cosmic Spaghetti, traveling the length of it could take centuries. If you really need to get to some other part in a hurry, it may be easier to leave the structure in a shuttle, and fly outside the spaghetti to a different part of it then re-enter. Two sections might be only a few score miles apart from each other in a straight line, but hundreds of millions of miles apart if you're limited to traveling only by routes inside the torus.
- The existence of a Topopolis suggests an extremely advanced and prosperous society. Let's say you find one that's empty (or has "gone wild" and is experiencing Post Apocalyptic Decay) - just exploring its inner curves, trying to find clues to the fate of its makers, could occupy an entire campaign (or several life-times in-character).
- Pockets of survivors may be separated from each other by millions of miles, and have developed divergent cultures in the absence of interaction. This sort of segregation could be caused by loss of life-support in some portions of the structure.
- Perhaps spikes in cosmic rays made three quarters of the structure unlivable for a time. They can now be re-inhabited, but everyone in the heavily-dosed sections died. Population density is then very thin, and people live in fear of a recurrence of the stellar phenomena that nearly wiped them all out.
- An aging Topopolis has sprung a leak - and pressure differences are draining it to the vacuum of space. However, it's so massive, the Topopolis has it's own gravity, and the venting gases aren't going very far. There's one region of it where the atmosphere is now to thin to support life, and the regions bordering it experience a multi-year hurricane as their atmosphere is ripped away. Over the next few centuries this may even out and kill everyone unless it's fixed. In the meantime, it effectively breaks circular travel throughout the structure. If some sort of decadent societal collapse has resulted in lost technology, there may be little hope for those who've inherited this place.
- Pockets of survivors may be separated from each other by millions of miles, and have developed divergent cultures in the absence of interaction. This sort of segregation could be caused by loss of life-support in some portions of the structure.