Re: Two improvements
"One is making the batteries hexagonal, thus eliminating most of the wasted space between each battery element,"
Except you can't. Current LiIon tech is either "bag type" (which can have extremely high packaging densities but is vulnerable to damage) or in 18650s and friends is a rolled up 3 layer strip, like an electrolytic capacitor (in a can, for durability)
https://www.youtube.com/watch?v=AvzhmUPOmRc - for disassembly. Don't try this at home.