title: Non-crystallographic nets with freely acting, non-abelian local automorphism groups.
abstract: 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.
authors.affiliation: Instituto de Ciências Exatas, Matemática Pura, Universidade Federal Rural do Rio de Janeiro, Rio de Janeiro, Brazil.
authors.forename: Montauban Moreira
authors.initials: MM
authors.lastname: de Oliveira
authors.forename: Jean Guillaume
authors.initials: JG
authors.lastname: Eon