An Exploration of a Discrete Rhombohedral Lattice; of Possible Engineering or Physical Relevance (Revised Version)
Abstract
Description
A particular discrete rhombohedral lattice consisting of four symmetrically interlaced cuboctahedral point lattices is described that is interesting because of the high degree of symmetry it exhibits. The four constituent cuboctahedral lattices are denoted by four colours and the composite lattice is referred to as a 4-colour rhombohedral lattice. Each point of the 4-colour lattice can be referenced by an integer 4-tuple containing only the positive non-zero integers (the counting numbers). The relationship between the discrete rhombohedral lattice and a discrete Cartesian lattice is explained. Some interesting aspects of the lattice and of the counting-number 4-tuple coordinate system are pointed out.
Revised (as presented) version of a paper included in the electronic proceedings of the International Mathematica Symposium, Maastricht, The Netherlands, June 20-24th 2008, containing some significant changes
Revised (as presented) version of a paper included in the electronic proceedings of the International Mathematica Symposium, Maastricht, The Netherlands, June 20-24th 2008, containing some significant changes