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A Tide World is a habitable megastructure (like a Ringworld, Dyson Sphere, or Annular Planet) which gets its gravity from the tides of whatever it is orbiting. As far as I know, the only example of something like this in extant sci-fi is an Integral Tree.

If the object which a Tide World is orbiting is not its light source, day and night cycles will be created as each end swings to face the light source. This is the case for Integral Trees. If the Tide World orbits its own light source, however, a bit of extra engineering is in order if one wants day/night cycles.

Larry Niven's Integral Trees orbited a neutron star, whose extremely high gravity and therefore extreme tide allowed the trees to be relatively small. Because of their small size, they could be solid all the way through. Something that would orbit the Sun, however, would have to be extremely large, and there is really no sense in filling in the entire structure when only the ends would have the level of gravity you want. Thus, the best design seems to be a set of two large flat* living surfaces facing in opposite directions and connected by cables:

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The sunward side would be in constant darkness, and the outward side would be in constant light, save for the bit on the middle that falls in the sunward side's shadow. If we make the structure wobble up and down as it orbits, the shadow will travel back and forth across the lightside, simulating day/night cycles with the eclipse if the inward platform is large/close enough. Mirrors could be used to light the sunward darkside.

One particularly interesting property of Tide Worlds is that they can be used to more easily construct Ringworlds. Typically, a Ringworld is uninhabitable until it is completely finished. Until then, there is no gravity to hold in the atmosphere. Also, a nearly-finished Ringworld must be spun up, which requires obscenely large amounts of energy. Now imagine that the flat surfaces of a Tide World are not just isolated chunks, but sections of a ring. A Ringworld could be constructed by tacking together a long string of Tide Worlds, until the collection is large enough to circle the entire star (or whatever other body you happen to be using). Unlike a normal Ringworld, the Tide World version can be built in stages, so a sudden worker strike or shortage of energy or resources won't spell doom for the whole project, and will be inhabitable at every step along the way, so it won't be a waste if the project has to be abandoned or put on hold indefinitely. Additionally, the material used in the construction of the rings does not need to be quite so ludicrously strong as scrith, as much of the stress will now be born by the cables connecting them together; this is sort of cheating, though as it's really just shifting the stress somewhere else rather than eliminating it, and it is now the cables which have to be ludicrously strong.

The smallest Tide World that could be constructed around the Sun and have Earth-normal gravity (~9.8 meters per second squared) would be 33700 kilometers long and orbit at a distance of approximately 770000 kilometers**. This is, however, only 75000 kilometers above the Sun's surface, so things would get a bit hot. The size of the Tide World necessary to maintain the same gravity increases as its orbital radius increases.

Not entirely flat, actually. More likely a shallow catenary shape so as to be stronger and also provide a rise at the edges to hold in the atmosphere.
**Assuming it acted like a point-mass, which it doesn't. In actuality, it would orbit with its center of mass slightly father out, as significantly lengthy objects orbit slightly faster than point-masses at the same altitude due to the fact that gravity obeys and inverse-square rather than a linear force law, and thus the increased gravitational attraction at the inward extremity is not exactly balanced by the decreased attraction at the outward extremity.