An engine for multiple dimensions?

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H&K

If you are flying around in your 3d Elite Clone, and you fly ahead without turning (With a "when you get to the edge of the map" it moves you to the other edge, like CIV, implementation), then you will eventualy get back to the spacestation
Then the game space is a 3d model of a 4d space. (Just like real space is)

True, but your ship and view is still restricted to your local 3D world. There is no way to travel "sideways" into the 4th dimension.

Incorrect, you ARE traveling in the Forth dimention, simply because of the nature of the spaceshape. If you defined your elite game without this wraparround, then you are not traveling in this specific forth Dimention. But if you defined is as stated you are. Its not a question of noticing.

A snake on the surface of the planet cannot know if the world is a 3d space, until it repeats a full circuit.

The original question was: can this be done all under the same code? It's probably possible, I just don't understand why you would waste time on dimensions which cannot be seen.

Mass.
Again, the original question didnt specify that it was spacial dimentions that was in question. If it is, (Which I now belive), then yes your right, (apart form as I said the shape of the 3dspace may be 4d), if on the other hand we just mean, any other scalar undefinable in the dimentions that we have, then no you are not right.