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An Exploration of a Discrete Rhombohedral Lattice

Jim McGovern
Organization: Dublin Institute of Technology
Department: School of Mechanical and Transport Engineering
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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.

*Engineering > Chemical Engineering
*Engineering > Mechanical and Structural Engineering
*Mathematics > Geometry
*Science > Physics

discrete, 4-colour, 4-color, 4-tuple, rhombohedral lattice, cuboctahedral lattice, cartesian lattice, coordinate system, jim mcgovern, symmetry, engineering, physics, mathematics

EDRLJMcG+410+r01.nbp (763.3 KB) - Mathematica Player Notebook [for Mathematica 6.0]