Our space is (of) three dimensional

Question

I think I have seen both

1. Our space is three dimensional.
2. Our space is of three dimensional.

Are these both correct? If so what is the difference between them?

Answer 1

The first is grammatical; the second is not. "Three-dimensional" is an adjective phrase, and you can't use "of" with an adjective that way: "the house is of red" is just as bad. Instead, to use "of" in this sense of description, you need to use a noun (phrase). So the second would be rephrased this way:

Our space is of three dimensions.

This still sounds a bit weird, mostly because using "of" in this sense is a rather old-fashioned or overly-formal style. Simply replacing "is of" with "has" here works well, although it changes the descriptiveness slightly from the essence of the thing to the characteristics of it. (That is, saying space is of three dimensions implies that the three-dimensional nature is absolutely central to the nature of space; saying that it has three dimensions makes it a bit more incidental, as though, conceivably, space might have more or less dimensions if things were different.)