  Three-dimensional lattices are fundamental to solid-state physics. The
description of a lattice with an atomic basis constitutes the necessary
information to predict solid phase properties and evolution. Here, we present a
new algorithm for systematically exploring crystallographic phase space.
Coupled with ab-initio techniques, such as density functional theory, this
algorithm offers a new approach for exploring and tuning materials behavior,
with a broad range of potential applications: polar and magnetic transitions,
martensitic phase transformations, and generally materials stability.
