Part of the "Megastructures: The Visual Encyclopedia" book project, on sale now at https://www.kickstarter.com/projects/artofsoulburn/megastructures-the-visual-encyclopedia-book-project
A Topopolis would be a tube-shaped space habitat that would loop into a ring with a star at its centroid, or could be looped several times around the star to create a “Torus Knot.” Inhabitants would live on the inside of the structure, with gravity provided by the tube rotating along its radius, instead of rotating around its centroid like in a Ringworld. Another way to imagine a Topopolis is as a set of thousands of O’Neill Cylinders formed into a chain. Bend the chain to form a circle around the star, and the individual cylinders would rotate the same way a standard O’Neill Cylinder would to create gravity.
If the Topopolis’ inhabitants looked along the axis of revolution, they would see what appeared to be a cylinder going off into infinity. In fact, the cylinder would gently curve as it traveled farther from the viewer, but the size would be so massive that you wouldn’t be able to notice the curve. A train traveling in a full hundred-million-kilometer circle could be set into the middle of the land.