What kind of corners does a grain of sugar have ?
If you look at sugar closely it will resemble small cube-like grains. However, individual sugar grains are actually shaped like a hexagonal prism, or fallen column. That is, oblong with slanted sides. The image below shows sugar grains that have been magnified by a factor of 40.
The edges of these grains is also sharper when compared to other common crystals, like salt.
According to the Beet-sugar handbook (Asadi, 2007), sugar crystals actually have a monoclinic form
The monoclinic form is one of the seven crystal lattice structures. In layman's terms, this crystal form usually has sides with different length. This is why sugar has a prism form, rather than cube form.
Individual grains can be broken. In this case they lose their intrinsic prism shape and can take on sub-forms.
The reason for this intrinsic shape comes from the shape of the individual molecules, and the bonding process. Salt molecules are cubic, so it makes sense that a collection of salt molecules is also cubic. However, the form of sugar molecules is roughly hexagonal, so the resulting shape of the grain follows suit.