Non-crystallographic nets with freely acting, non-abelian local automorphism groups

Non-crystallographic (NC) nets are defined as periodic nets whose automorphism groups are not isomorphic to any isometry group in Euclidean space. This work focuses on a simple class of NC nets, restricted to nets with non-abelian, freely acting local automorphism groups. A general method is presented to derive such NC nets from crystallographic nets and some non-trivial examples are explored. It is shown that the labelled quotient graph of these nets does not necessarily possess non-trivial automorphisms which exchange cycles having the same net voltage. However, barycentric representations of these nets systematically display vertex collisions.