A Diamond's Cut
Cut actually refers to two aspects of a diamond. The first is its shape (round, marquise, etc) the second is how well the cutting has been executed.
A diamond's cut will most certainly influence its fire (the lovely rainbow colors that flash from within) and brilliance (the liveliness and sparkle), as well as its perceived size and even, to some degree its apparent color. Different cuts reflect light in different angles. A diamond must be cut in a geometrically precise manner to maximize its brilliance.