Abstract
Some discoveries c. 1960 concerning the ordered structure of points, lines and planes in space known as space lattices appear to offer some interesting but as yet untried possibilities for the enhancement of the design of physical artifacts. Confirmation that Nature employs at least some of the properties to be discussed has come to light in the discovery of a new form for matter referred to as the quasicrystalline state.
This paper describes a method for generating a group of such lattices. The number of possible ‘genotypes' appears to be, at least in theory, uncountable though only a few members of this multitude seem to offer the possibility of significant practical application. At least two of the genotypes appear to offer the designer a seemingly endless variety of possible form variants. This variation is achieved with a relatively low number of kinds of component parts, because for each genotype one needs only two facially identical equilateral but otherwise different rhombohedra.
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