Black-and-White Symmetry, Magnetic Symmetry, Self-Duality and Antiprismatic Symmetry: The Common Mathematical Background

Gábor Gévay

Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary
E-mail: gevay@math.u-szeged.hu

(Received December 15, 1999; Accepted March 8, 2000)

Keywords: Magnetic Crystal, 2-Coloured Pattern, Self-Dual Polyhedron, Symmetry Group, Group Extension

Abstract. Seemingly distant areas of symmetry, such as mentioned in the title, are closely related to each other on an abstract level. The unified treatment is made possible by some common features of the symmetry groups used in the mathematical description of these types of symmetries. The key property is the way as a two-element group generated by an involutory transformation can extend a geometric symmetry group.