title: Nets with collisions (unstable nets) and crystal chemistry.
abstract: Nets in which different vertices have identical barycentric coordinates (i.e. have collisions) are called unstable. Some such nets have automorphisms that do not correspond to crystallographic symmetries and are called non-crystallographic. Examples are given of nets taken from real crystal structures which have embeddings with crystallographic symmetry in which colliding nodes either are, or are not, topological neighbors (linked) and in which some links coincide. An example is also given of a crystallographic net of exceptional girth (16), which has collisions in barycentric coordinates but which also has embeddings without collisions with the same symmetry. In this last case the collisions are termed unforced.
authors.affiliation: Department of Applied Mathematics, Research School of Physics, Australian National University, Canberra, ACT 0200, Australia.
authors.forename: Olaf
authors.initials: O
authors.lastname: Delgado-Friedrichs
authors.forename: Stephen T
authors.initials: ST
authors.lastname: Hyde
authors.forename: Shin Won
authors.initials: SW
authors.lastname: Mun
authors.forename: Michael
authors.initials: M
authors.lastname: O'Keeffe
authors.forename: Davide M
authors.initials: DM
authors.lastname: Proserpio
keywords: crystal nets; unstable nets