We characterize generalized extreme points of compact convex sets. In particular, we show that if the polyconvex hull is convex in R m×n , min(m, n) ≤ 2, then it is constructed from polyconvex extreme points via sequential lamination. Further, we give theorems ensuring equality of the quasiconvex (polyconvex) and the rank-1 convex envelopes of a lower semicontinuous function without explicit convexity assumptions on the quasiconvex (polyconvex) envelope.