Is there any difference between "3-dimension space" and "3-dimensional space"? We should use "3-dimension space" or "3-dimensional space" to mean a space with three dimension? Why?
The answer is 3-dimensional space. There's no grammatical reason I can give you. It's just due to common usage. This is a really good question. There are others: 3-bedroom house or 3-bedroomed house 3-leg stool or 3-legged stool Sometimes the adjective wins and sometimes the noun (playing the role of of an adjective) wins. It's a usage question not a grammar question. Sorry for such a disappointing answer. More on compound adjectives
Thank you.