This is an announcement for the paper "Orbits in symmetric spaces, II by N.J. Kalton, F.A. Sukochev, and D.V. Zanin. Abstract: Suppose $E$ is fully symmetric Banach function space on $(0,1)$ or $(0,\infty)$ or a fully symmetric Banach sequence space. We give necessary and sufficient conditions on $f\in E$ so that its orbit $\Omega(f)$ is the closed convex hull of its extreme points. We also give an application to symmetrically normed ideals of compact operators on a Hilbert space. Archive classification: math.FA Mathematics Subject Classification: 46E30, 46B70, 46B20 Submitted from: zani0005@csem.flinders.edu.au The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1003.1817 or http://arxiv.org/abs/1003.1817