Alderson disk
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An Alderson disk (named after Dan Alderson, its originator) is an artificial astronomical megastructure, like Niven's Ringworld or a Dyson sphere. The disk is a giant platter, like a CD or phonograph record. The sun rests in the hole at the center of the disk. The radius of an Alderson disk would be roughly equivalent to the orbit of Mars or Jupiter, with a thickness of several thousand miles. According to the proposal, a sufficiently massive disk would have greater gravity than its sun (though the fact that the pull of the disk as a whole would still be toward its center causes problems with this idea).
Assuming the gravitational issues were overcome, however, life could exist on either side of the disc, although the closer to the sun one would get, the hotter it would get until life was impossible. Conversely, the further away, the colder it would become, until living beings would freeze.
One drawback to a disc is that the sun remains in the same place. There is no day/night cycle, only a perpetual twilight. This could be solved by forcing the sun to bob up and down within the disc, lighting first one side then another. (As the disc far outmasses the sun, this is a plausible option.)
An Alderson disk (the Godwheel) was a prominent feature of Malibu Comics' Ultraverse. The Godwheel was split between two societies, one which used technology and one which used magic (each occupied separate sides of the disc). Author Larry Niven designed the Godwheel and wrote stories surrounding certain events on it.
A disk-shaped planet similar to an Alderson disk (though far smaller) served as the home world of the fantasy "Aysle" setting (or "cosm") of West End Games' Torg roleplaying game. The "diskworld" of Aysle had a bobbing sun and multiple inner layers. Both sides of the disk were inhabited, as were the internal layers.
The Alderson disk is discussed in Larry Niven's "Bigger than Worlds" essay, 1974, which can be found in his "Playgrounds of the Mind" anthology.