Wyrme, Ouroborous and Spaghetti, topopoli in the Cableville system
A long, thin, rotating habitat in orbit around a star or planet, so that the long axis of the habitat passes completely around the orbit at least once. An alternate name is 'macaroni world'. If the short radius of loop is very much smaller than the long radius, then the difference between the inside and the outside radius of the loop is negligible, and the loop can rotate without noticeable internal distortion.
A topopolis (particularly if it only loops around a star once) is similar in long radius and shape to a ringworld, but most topopoli have less surface area than equivalent ringworlds. This is because topopoli typically spin to provide an internal gravity of 1 g, which (due to limits of material strength) limits the short radius to approximately 1,000 km. Using magmatter or active support can bypass this limit, but this removes one of the main advantages of topopoli over ringworlds. An alternative solution is to reduce the rotation rate (the same principle used in ribbonworlds) to allow a higher radius while still using conventional materials. Low-spin, low-gravity topopoli can have short radii of 100,000 km or more.
Due to its size, travel between distant parts of a topopolis can take a long time. While short-distance travel may be done using vac trains (running along the outside surface of the topopolis), long-distance travel requires the same kinds of spacecraft used for interplanetary travel.
There can be multiple topopoli around the same star at once, at different orbital distances. An example of this is Cableville, which has the three topopoli of Spaghetti, Ouroboros and Wyrme. The shading effect of inner topopoli on outer ones is negligible unless the topopoli are uncommonly wide and/or close together. Even in these rare cases, simply inclining each topopolis at a slight angle to the others will make the shading negligible again except at particular times of the year, during which the outer topopoli experience eclipses.
Alternatively, a single topopolis can be looped around its central star multiple times, resulting in a torus knot shape. At the extreme, such a topopolis can intercept a significant portion of a star's light, becoming a type of Dyson sphere. However, such topopoli are rare.