E.M.S. Hitzer, C. Perwass
The hidden beauty of gold
Proceedings of the International Symposium on Advanced Mechanical and Power Engineering, between University of Fukui (Japan), Pukyong National University (Korea) and University of Shanghai for Science and Technology (China), 22-25 Nov. 2007, pp. 157-167 (2007).
Abstract: This paper first reviews the history, the economy, the material properties, and the applications of gold. Then the geometry of the fcc gold lattice is introduced. Based on the symmetric arrangement of atoms the gold lattice has a rich variety of symmetry transformations, that interchange the positions of atoms, but leave the lattice as a whole invariant. This begins with the point group symmetry of a single fcc lattice cell and is extended by combination with lattice translations to the full space group symmetry of the whole (practically infinite) lattice. We use the newly created interactive Space Group Visualizer (based on geometric algebra) in order to systematically picture all these symmetries. We can thus understand their origin and their relationships. In particular we give a full geometric explanation of the 192 screw symmetries passing through a single fcc cell of the gold lattice.