
Journal of Convex Analysis 26 (2019), No. 4, 11131123 Copyright Heldermann Verlag 2019 A Geometric Characterization of Polygonal Radon Planes Kalidas Mandal Department of Mathematics, Jadavpur University, Kolkata 700032, India kalidas.mandal14@gmail.com Debmalya Sain Indian Institute of Science, Bengaluru 560012, Karnataka, India saindebmalya@gmail.com Kallol Paul Department of Mathematics, Jadavpur University, Kolkata 700032, India kalloldada@gmail.com We study unit circles of polygonal Radon planes from a geometric point of view. In particular, we prove that a twodimensional real polygonal Banach space X cannot be a Radon plane if the number of vertices of its unit circle is 4n, for some natural number n. Also we obtain a complete characterization of polygonal Radon planes in terms of a tractable geometric concept introduced in this article. It follows from our characterization that every regular polygon with 4n+2 vertices, where n is a natural number, is the unit circle of a Radon plane. Furthermore, we describe types of Radon planes for which the unit circles are hexagons, but not regular ones. Keywords: Radon plane, BirkhoffJames orthogonality, polygonal Banach space. MSC: 46B20; 52A21 [ Fulltextpdf (6713 KB)] for subscribers only. 