This is an announcement for the paper "Interaction of order and convexity" by S.S. Kutateladze. Abstract: This is an overview of merging the techniques of Riesz space theory and convex geometry. Archive classification: math.FA Mathematics Subject Classification: 46B42; 52A39 Remarks: Prepared for the Russian--German geometry meeting dedicated to the The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/ or http://arXiv.org/abs/ or by email in unzipped form by transmitting an empty message with subject line uget or in gzipped form by using subject line get to: math@arXiv.org.