The Honeycomb Hives system is designed to tackle bee colony losses by making hives which apparently keep pests out, get rid of condensation and which retain heat more efficiently – all problems which can be a bane to honey bees.
As you may have guessed, the hexagonal shape is the key. Take condensation, for example. The creators of Honeycomb Hives reckon flat-top hives will cause condensation to drip back down onto the bees, which can be lethal to them in winter (I'm no bee expert, but a spot of Googling seems to confirm that this is indeed a thing.) A hexagonal prism affords an angled roof, so the condensation runs down these and the side walls, causing less damage.