The only logical place to build a Dyson sphere would be a red dwarf star, for several reasons...
1. MUCH smaller habitable zone, so much less material needed.
2. Much longer usability. A star like the sun will be too hot in one or two billion years at most. A red dwarf could remain habitable for a couple trillion.
Also, you'd probably be building rings and cages before you could graduate to a sphere. Even a ring world around a red dwarf would probably have a few hundred class M planets worth of space on it, and could have remained usable for all 13.7 billion years of the universe's current history, and 500 billion more afterward.
In this scenario, there's no need to build another Dyson Sphere.
There's already one built, and it's the Dyson Sphere that the Jenolan crashed onto.
Since the Federation found it, it's basically the "Greatest Find" of the 24th century next to the Bajoran Worm Hole.
I'm sure the UFP scientists are studying it, learning the secrets of how to make our own Neutronium since the Dyson Sphere shell is made of Neutronium.
Figuring out how to Renovate the Dyson Sphere would be a important step,
I have an entire thread on this in Trek Tech.
Think of all those Home Garden Network TV shows about "Renovating This Old House".
Think about expanding that to "Renovating This Old Dyson Sphere".
=D
You can literally spend a century or slightly longer to renovate the Dyson Sphere via mass produced automatons.
Fix up the local Star to be stable and cure it of whatever issues it might have via advanced Star Manipulation Tech.
Imagine having a Babylon 5 or DS9 like show, but set on the Dyson Sphere.
Have every Federation Member create a local Biome in their section of the Dyson Sphere with each section representing each Biome type.
I did some basic #'s.
The Dyson Sphere has a diameter of ~200 million km on the inside
- Internal Surface Area ~125,714,285,714,285,715 km² ~= 125.7142 Quadrillion km² to work with.
- External Surface Area ~125,714,290,742,857,193 km² with a 2062 m thick crust ±2 meters variability.
One of my basic Modifications would be to split each Biome section into Standard Internal Equilateral Hexagonal Regions with walls that are Mt. Everest in height used to isolate each Biome region from each other.
Obviously, the Mountain walls would be largely hollow and be made of similar material as the Dyson Sphere Shell. The wall would also house a Dyson Sphere wide network corridor for travel between and around each standardized Hexagonal region.
This way each Hexagonal region would have a large land area to work with for artificial Biome creation.
Given the way a Hexagons naturally tessellate on a Sphere, there will always be 12x Pentagons in your Sphere of tesselated Hexagons. That's just a property of the Geometry of Hexagons on a Sphere.
I would use those 12x Pentagons and create 12x standardized entrance gateways within the Pentagons and use those as standard Gateways to manage traffic In/Out of the Dyson Sphere.
I'd have a smaller Hexagonal regions on the outside of the Dyson Sphere since you can probably park standardized Arcology type modular Planetary Bases from each UFP Member Species.
Imagine the kind of Intergalactic UFP you can make by colonizing the Dyson Sphere.
The Internal Hexagons would have a wall length of 1,000 km per side.
For reference:
- Earth has a ~Surface Area of 510,065,623 km²
- The British Isles have a Land Surface Area ~= 315,159 km².
This would lead to each Hexagonal Zone have a Land Area to work with of ~= 2,598,076.211 km²
-> That’s equivalent to ~0.5094% surface area of Earth
This creates an estimated amount of (48,387,451,130) standardized 1,000 km per side long Large internal Hexagonal Habitat Zones.
That should be plenty of area to play with for each Biome that you would want to recreate.
That's not counting the outside smaller Hexagonal Zones used for Surface mounted Arcology bases.