An Exploration of a Discrete Rhombohedral Lattice; of Possible Engineering or Physical Relevance (Revised Version)

Details An Exploration of a Discrete Rhombohedral Lattice; of Possible Engineering or Physical Relevance (Revised Version) An Exploration of a Discrete Rhombohedral Lattice; of Possible Engineering or Physical Relevance (Revised Version)

2008-08-16

arxiv.org/abs/0808.2242v1

Physics

General Physics

Revised (as presented) version of a paper included in the electronic proceedings of the International Mathematica Symposium, M

Scientific paper

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.

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