I'm not a physicist just a curious mind, so please go easy!
I was just watching a BBC Horizon Documentary that featured a piece on the recently discovered material Graphene. One of the facts mentioned on the documentary was that a sheet of graphene, despite being a lattice of carbon atoms just one atom thick, could hold the weight of a household cat without breaking.
They showed an illustration of graphene's hexagonal structure and how a crude form of graphene could be created using Sellotape and piece of graphite.
OK so here's my question.. From what I can remember from Chemistry lessons in school, carbon has a valency of 4, so it can bind to 4 more carbon atoms. Surely (in theory at least) a sheet of carbon could exist that adopts a square grid lattice, as oppose to graphene's hexagonal structure. If so wouldn't such a material be stronger than graphene? Also would such a lattice naturally form under any circumstance or does carbon always assume a hexagonal structure when reduced to layers?