Polyhedral truncations as eutactic transformations.

An eutactic star is a set of N vectors in {\bb R}^n (N\,\gt\, n) that are projections of N orthogonal vectors in {\bb R}^N. First introduced in the context of regular polytopes, eutactic stars are particularly useful in the field of quasicrystals where a method to generate quasiperiodic tilings is by projecting higher-dimensional lattices. Here are defined the concepts of eutactic transformations (as mappings that preserve eutacticity) and of vector radiations (vectors that stem from the vectors of an eutactic star), which are used to describe and parameterize polyhedral truncations. The polyhedral truncations preserve eutacticity, a result of relevance to the faceting and habit-forming characteristics of quasicrystals.