Description of the f.c.c. lattice geometry through a four-dimensional hypercube
I. Her · Acta Crystallographica Section A Foundations of Crystallography · 1995
In an n-dimensional space, generally, n coordinates are used in a coordinate system. Using more than n coordinates, however, is sometimes more efficient in representing discrete spaces. This paper illustrates the application of using four coordinates to describe a three-dimensional face-centered cubic (f.c.c.) lattice. By the proposed method of description, all points in a f.c.c. lattice can be conveniently addressed by integer numbers. Many geometric computations in this discrete space are also much simplified in the new coordinate system.