Abstract. The present paper continues work started by G. A. Muñoz-Fernández, Sz. Gy. Révész and J. B. Seoane-Sepúlveda [10] (degree 2 homogeneous polynomials, description of all extreme points) and L. Milev, N. Naidenov [8] (degree 2 algebraic polynomials, definite extreme points) by describing the indefinite extreme points of the unit ball of the space of degree 2 bivariate algebraic polynomials equipped with the maximum norm on the standard triangle of the plane. The main motivation for taking up this work is the hope that via the Krein--Milman theorem, this description will be useful in deriving the exact constants in certain inequalities, including the multivariate Bernstein inequality over general, non-symmetric convex bodies.

AMS Subject Classification (1991): 52A21, 26C05, 26B25

Keyword(s): convexity, extreme points, polynomials

Received January 8, 2010, and in final form May 18, 2010. (Registered under 3/2010.)