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From the FAQ:

4.9 Ring Worlds & Sphere Worlds
4.9.1 To Build a Ring worlds (or Sphere worlds) you need to:
4.9.1.1 Research Stellar Manipulation to level 5 for Ringworlds (level 8 for Sphereworlds) and Base Construction to level 3. (Quikngruvn)
4.9.1.2. build on a star.
4.9.1.3. create a Space yard ship (a ship that contains a shipyard component)
4.9.1.4. take the space yard ship to the star you want to build your world on.
4.9.1.5 start building STARBASES containing the components you need for the Ring/Sphere world.
4.9.1.6 once you have all necessary components, build go to the component activation icon to activate the construct - all the built star bases and components will disappear and you will have a ring/sphere world there instead.
4.9.2 NOTE: to speed construction (it takes awhile) you can construct bases housing more shipyards. (Taz-in-Space)
4.9.3 Ring- and sphereworlds count as both a star, and not a star. They count as not-a-star for purposes of planet building, solar panels, and star destroyers. They count as a star for purposes of building new stars (i.e.: you can't). (Suicide Junkie)
4.9.4 Ringworlds and sphereworlds are made using your default planet type and atmosphere. they are simply extra huge planets and must be colonized before you can use them.
4.9.5 To build a Ringworld you need 5 bases full with cables and 5 bases full with plating, and one placement base, ie 11 bases.
For a Sphereworld that is 10 plating bases and 10 cable bases and 1 placement base, i e 21 bases.