Looking for the way to read a sentence containing a conjunction and a plural

Question

How does grammar tell me to parse this sentence:

Visualize the relation between two-dimensional and three-dimensional objects.

Are we being asked to visualize the relation between two-dimensional objects and also visualize the relation between three-dimensional objects (each dimension on its own)?

Or, are we being asked to visualize the relation between an object in the two-dimensional group and one in the three-dimensional group?

I think what's confusing me is the interaction between the plural objects and and. So, my question essentially is how to understand this sentence and similar ones having the same construct. Is there a grammatical rule?

Answer 1

There is indeed some ambiguity here, as you point out.

The most common and likely interpretation would be that the relation concerns the 2-d and 3-d objects mentioned in that sentence, and not a 3rd object - the context would probably help clarify though.

The other valid interpretation, which you proposed (involving a 3rd unmentioned object) would ideally be written by the author in a clearer way, such as:

Visualize the relation between two-dimensional and between three-dimensional objects.

(i.e. two uses of between.)

Answer 2

Visualize the relation between two-dimensional and three-dimensional objects.

The phrasing is ambiguous, but I would say you are being asked to compare class characteristics of a two-dimensional object versus those of a three-dimensional object.

Answer 3

I read that sentence as:

Visualize the global set of objects that are 2-d with the global set of objects that are 3-d.

Compare the sets themselves to eachother, not the specific objects within the sets with other specific objects.