What is the ?
By "diameter" I assume you mean the longest measurement, corresponding to the long diagonal (the one that goes through the center, not along one side;top to bottom and front to back and left to right) of a 3D cube.
We look at the known cases and generalize:
Using regular figures of side s
Length of diagonal = sqare root of (s^2 + s^2) = root2 * s
Length of long diagonal = square root of (s^2 + s^2 + s^2) = root3 * s
Generalizing to n ...
Diameter of a 16 space hypercube is determined.