Hmmm. The Golden Ratio....
If you were to do this, you'd end up with a bat that looks like the following:
Handle length: 31.9 cm (29.2cm)
Blade length: 53.2 cm (55.9cm)
Middle distance from toe: 19.95cm
Spine height (using golden ratio of spine height to width): 6.75cm
What I think is quite interesting about these numbers is that they are not far from a normal bat. The normal numbers are in brackets next to these calcs.
Just looking at this, I'd suggest you'd end up with something similar to a Mongoose CoR3 with a mid-middle that would pick up reasonably well, look big and dependent on cleft and batmaker, could be quite heavy.