Dyson sphere

A Dyson sphere was a hollow sphere, with a sun at the centre, designed to completely enclose the star and collect all the energy that would otherwise escape into space. (PROSE: Lucifer Rising) They were the products of ultra-high-level civilisations, and could fit a couple quadrillion people. (PROSE: Down)

"Cramped Future Civilisations: take a solar system – actually take several, there isn't enough mass in one - build machines to build machines to build more machines to take the planets apart and rebuild them into a sphere with the nicest of the available suns at its centre. Live on the outside and plate the inside with solar-power collectors, or if you are technically advanced use gravity generators to live on the inside. Orbit a computer the size of a planet around the internal star and call it Cod and let it do all the difficult environmental stuff. This should solve all your overpopulation and space problems, except what to do with your increased leisure time. Take no calls from clones, or emulations of Freeman Dyson, his descendants or their lawyers."

- Mega-Hints For Type II Civilizations

The People lived in the inner shell of such a construct, known as the Worldsphere. (PROSE: The Also People, Walking to Babylon)

The Mistress and K9 also had an adventure in a Dyson Sphere. (AUDIO: The Search)

Prior to her travels with the Seventh Doctor, Bernice Summerfield was part of a team of archaeologists who excavated the remnants of a Dyson Sphere around a white dwarf in the Vartaq Veil. Tidal stresses had pulled it out of shape until it degenerated into disconnected fragments, slowly leaking the atmosphere. The builders became nomadic and migrated from fragment to fragment. (PROSE: Lucifer Rising)

The Helio-Sphere was a Dyson Sphere and was considered one of the least genteel places in its quadrant of the galaxy. (PROSE: Adorable Illusion)

The Infernal Sphere was a Dyson sphere notable for being built around a black hole instead of a star. As a result, it was dark and terrifying Hell, suitably satisfying the whims of its demonic inhabitants. (PROSE: T.memeticus: A Morphology)

Behind the scenes

 * The Dyson Sphere takes its name from the Earth physicist who first proposed it,.
 * Most fictional depictions of a Dyson Sphere, including those in Doctor Who, would more correctly be called a Dyson Shell, something generally considered to be an engineering impossibility. Closer to the original concept would be an arrangement of independent  structures, like living habitats and energy-collecting satellites around a star. In this case, the "sphere" is the shape of that swarm or bubble, not a solid object.