If you are doing points on a multi dimensional space, you can start using various shapes (Length, Width, Height) or Number of faces. Alternatively you can also do stars with spikes coming out (more spikes per higher value), I find this the easiest to visualize rather than shape sizes.
If you are going to play tricks using color, you may as well use flavors and odors for a sixth dimension visualization (and any other property you may think of for further extending dimensions).
I call bullshit.
This might give you an idea of what they can be used for: http://en.wikipedia.org/wiki/Level_set_method
What is the proof that there are only three spatial dimensions?
You say "three spatial dimensions and time." Is time a dimension just like the spatial ones but we perceive it differently? Or is time something other than a dimension? And when was this proved or demonstrated?
Time is a unidirectional so it's considered to be a different kind of dimension than the spacial (bidirectional) dimensions.