Are hypercubes really visualisations of objects from higher dimensions? Wouldn't it make more sense enrich clouds of 3D points with new attributes that encode

Are hypercubes really visualisations of objects from higher dimensions? Wouldn't it make more sense enrich clouds of 3D points with new attributes that encode the value in the higher dimensions? e.g. 3 spatial dimensions, with the fourth dimension being color. A fifth dimension could then turn the dots into numbers. Then you have the information from 4 or 5 dimensions encoded into 3D space in a way humans can still understand to some degree.