Bravais lattice invariants

Invariants are those properties by which objects (in chemistry, physics, mathematics etc.) are commonly identified. They remove sensitivity to presentation and allow the intrinsic properties of the object to be seen. Invariants used for unit-cell comparison and for Bravais-lattice identification are reviewed, and proposals are made for possible directions of future research. The results of an exhaustive search for polynomial invariants of the components of the metric tensor through degree 12 are that polynomials in the volume squared are the only non-trivial such invariants.