Unsure of the Hexagon, but you can use the shapes to mark your pokemon from the PC. maybe if you're marking them as Bred or whatever, so you can filter by shape (presumably) or tell them apart at a glance.
RSN: Plucky9, Total: 2444. KoL: Plucky, currently a Pastamancer ACNL/3DS FC: 4897-5920-6758 Ricky of Farm
The circle, triangle, square, heart, star, and diamond are markings you can add to tell them apart. I don't think people have worked out what the hexagon is for yet but personally I think It means they were caught in Kalos