What are exacly sphere world & ring World

Ringworlds and Sphereworlds (Dyson Spheres) are much larger than normal planets. A Ringworld is 4 times as large as a huge planet, and a Sphereworld is 8 times as large as a huge planet. Because they have so much storage space available, they are very, very powerful when nearly full of weapons platforms. The 100 and 200 facility spaces available on the respective planets also makes the best use of the different bonus facilities (such as Central Computer Complex).

This is why they are so expensive to build - you're making a truly massive planet out of nothing.

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They have 100 and 200 facility spaces and numerous cargo space, and the mineral, organic, and radioactive value begins at 150%. They literally take up an entire system and are worth 20 entire planets due to the ease at which they are defended using WPs and fighters, and also because of how well they produce any type of resource and get a MASSIVE bonus to construction and production once you get them even hlafway filled up with the 32 or 64 billion people they can hold.

they are ridicously large, they take up about 1/2 the solar system when built.

FYI - without going into the detail, which can probably be found in Wikipedia or such,
The idea of a Ringworld (also known as a Niven Ring) came from Larry Niven's Ringworld sci-fi novel. In short, it's a "ribbon" of land circling a star that spins to simulate gravity on its inner surface through centrifugal force (centripedal, whatever). A series of interspersed panels circle at a different rate nearer the star to give some simulation of days and nights. (The books are so-so, but the idea is intriguing).
In a Dyson Sphere, the sun is completely surrounded by a sphere, in hopes of capturing all of the sun's expelled energy for use. Again, people would typically live on the inner surface, but this type of design also seems to rely on the need for artificial gravity to stick people to the inner surface.

They pretty much take up half an entire system. You cannot have any colonies or ships inside that system (other than the ships that are building it) when you build it and any uncolonized planets will be turned into asteroids orbiting the creation. In fact, a Sphereworld looks almost EXACTLY like the death star from the Star Wars seris.

The idea of a ring/sphere world (from the construction standpoint) is that it takes all of the mass orbiting a star to make one, plus no free floating objects in the solar system means there's less chance of damage to the massive investment. In the later Ringworld books, Niven describes a system of stabilizers that prevent the ring from gaining velocity relative to the sun and brushing against the sun. This just gives an idea of what kind of problems designing such a world might have to deal with.

I think one gameplay mechanic that would make Ringworlds (and sphereworlds) more interesting is if they were so big only so many weapon platforms can reach any particular ship at any given time. That is, all of that big mass of weapon platforms and only 1% of them can fire at once. Likewise, the world also ought to be treated much much like several huge worlds rather than one single one.

Just because the south pole got invaded, it means nothing to me on the North pole? They are certianly big enought that it might take me a turn or two to move troops to be close enough to respond. I'd like to think that if aliens landed in China, the US would be concerned about that sort of behavior. We might not nuke'em, but some Carrier battle groups would certianly be making tracks to go have a word with the bad guys.

Not exactly! The general idea of the ring/sphereworlds is that they have a radius of ~1 AU (at least, when humans build one around a sol-like star). Which means there's a huge amount of distance between the north pole and the south pole. So huge that it would be like ships being able to battle with ships in other hexes. It would take some time to get troops from one area to another.

Distances on a star system's scale are so large as to be incomprehensible to most people.

Light travels at 186000 miles per second in a vacuum. It takes light about 8 minutes to reach us from the sun. Thats 480 times that 186000 number. If a Dyson Sphere is one AU in radius, then it is two AU's in diameter - and more than 3 AU's to go the circumference from one pole to the other. 89 and a quarter MILLION miles (1 AU if my math is right) is not something you can reasonably expect someone driving along at 90 mph or flying along at a couple hundred mph to travel in any realistic timeframe to counter an alien invasion at the opposite side of the planet.

A dyson sphere with a radius of 1 AU would have a surface area of around 600 million times of that of Earth.

But solid dyson spheres are not stable anyway...

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Well, there is no 'ceiling', so you can still use ships, just get
'above' the atmospheric layer and use an FTL drive.

With ships in SE V, getting forces from one side of a ring/sphere world to the other would be akin to moving a force from one side of Earth to the other via the oceans. It takes upwards of a month to move a lot of ships in the ocean from one part of the world to the other, and it takes about a month for a faster ship in SE V to cover the distance of a sphere/ring worlds diameter.

There is also a question of things like transport networks, such as tubes that can handle effective sub-luminal speeds (which I think existed in the Ring World by Niven), or even some sort of teleportation grid (also Niven's ring world, the 'mini ring worlds' from the Halo game setting, etc).

Overall, SE V treats them as being next to nothing. A Ring World alone, if 10,000 miles 'wide' (interior surface wise), would probably have millions of times the surface area of an Earth sized planet, while a Dyson Sphere will have yet more space.

Break it down into small segments seperated by 'walls' (mountain range sized ones), or segments of a Ringworld, and you could fit all of the SE races on a Ring or Sphere world and each could get trillions of people and they should still have plenty of space, with each section/segment capable of having its own atmosphere/environment type, while a Sphere World ould have even more space to spare.

For a rough example of their size...
1 AU is 93,000,000 miles or 150,000,000km.
For a Ring World with an almost 1,000,000 mile/1,600,000 km wide band such as Niven's Ringworld, you would have a surface area of...
600,000,000,000,000 square miles
1,600,000,000,000,000 square kilometers
Or about 3 million times more surface area than Earth.

Even if just 10,000 miles/16,000 km wide with a 1 AU diameter, it would have...
5,800,000,000,000 square miles
15,000,000,000,000 square km

for a 1 AU diameter Sphere world, it would have a surface area of...
108,686,000,000,000,000 square miles
282,743,000,000,000,000 square km
Although, without artificial gravity, only the area near the equator would be 'habitable', but even then, the rest of the space could be used for other stuff, including capturing solar energy.
Although that puts SE V as a waste of space at over 4 million square km per person with a population of 64 billion...

For Comparison, Earth

Radius = 6,371km
Circumferance = 40,041.47 km
Surface Area = 510,065,600 square km (149 million land, 361 million water)

On a side note, I like the idea of a 'hybrid' dyson sphere, apparently 'solid', but actually similar to Dyson's sphere inthat it is composed of many (perhaps millions or billions) of independent sections that are not 'fixed' together, using the star's own gravity and energy, plus assorted gravity based tech and 'flexible' connections to keep the whole thing in the proper shape and in a stable 'orbit' around the star.

Also got to love the idea of the type of weapons a ring or sphere world could handle when you got potential for billions or trillions of kilometers of solar energy collectors... Massive Mount Wave Motion Guns for 'point defense' comes to mind... don't need to worry about aiming at targets, even a 15m big fighter is easy to hit if you can toss out km wide beams or a pulse of energy that can wipe out anything in a several thousand km wide area...

Basically a ring world would look like the Halo ring from(Duuh) "Halo", and the Sphereworld would look like the Nomad planet from "Freelancer" (the last mission), if you google for them youll have an idea

They are of limited usefulness in a game anyway. I build it just for the cool-ness factor.

I find them great as supply sources for your battlefront. Almost limitless supply for populations too. If you have about 4 planets or asteroid belts to make planets and have space yards on them around the ring or sphere even better. Make large fleets, open warp point to enemy space, take it over and you are 1 jump point from a complete population of your new system as well as resupply your fleet. Rinse and repeat. No tedious messing around with long supply lines and trying to supply them with such limited planets supplies that have a tough time filling 1 ship. The only problem I have is taking so long to get the tech level that high that the game is often over first.