For n,m≥ 2 this paper is devoted to the description of the sets of extreme and exposed points of the closed unit balls of and , where is the space of n-linear forms on with the supremum norm, and is the subspace of consisting of symmetric n-linear forms. First we classify the extreme points of the unit balls of and , respectively. We show that ext ⊂ ext , which answers the question in . We show that every extreme point of the unit balls of and is exposed, correspondingly. We also show that
We classify the extreme 2-homogeneous polynomials on
2 with the hexagonal norm of weight ½. As applications, using its extreme points with the Krein-Milman Theorem, we explicitly compute the polarization and unconditional constants of .