beauty, as i imagine it, is not a spatial dimension. u could of course logically divide reality into dimensions of beauty/ugliness. then space would be part of both those dimensions, and directions would not be the separators of dimensions.
can u for example take a 3d lamp, and remove its beauty, without changing any of the 3 space dimensions it has? or, can you take away the 3d object and still preserve the (space?) dimension of beauty? u could say yes, but then beauty would not be part of the scientific, rational view of 3d reality.
u could change the colour of a 3d lamp, and call colours the dimension of beauty, but that doesn't work, scientifically, rationally speaking. because isn't light explained as 3 dimensional vibration? u could call heat beauty, but heat is moving 3d particles. so heat and colours are "properties" of 4D spacetime.
then of course, as we percieve the world, both heat and colours are separate from 3d forms. but our subjective opinions (such as for example beauty), or even our whole perception, are not existing in spacetime, they are merely electrical impulses in our brain. it always makes me wonder, what is science based on if not rationalizing our perception, non-existing in the rationalization...
DD