SOME OLD AND NEW ASPECTS ON THE CRYSTALLOGRAPHIC GROUPS

Abstract

The derivation of crystallographic groups in the Euclidean n-space S" (think of n = 2,3) will be illustrated by the space groups Pm, Pb and Bm, Bb belonging to the geometric crystal. class (point group) m. Some new directions of investigations will be indicated, e.g. the orbit for densest ball packing. minimally presenting fundamental polyhedron, data base and computer realization for each space group class amongst the 219 (230) ones. This paper is based on the lectures held several times by the author.