dimensionality

The state or characteristic of possessing dimensions.

The number of dimensions something has.

That is to say, it is the Analogue of Space, not in the sense in which we formerly regarded Space as the negation of Matter; but in the sense of Infinite Dimensionality, or of Dimensionality in all directions, as a vague generalization from the three spatial dimensions Length, Breadth, and Thickness.

This often happens, for example, when a two-dimensional solution is obtained for data whose appropriate dimensionality is higher.