Projection matrices for Niggli-reduced cells

Crystallographic unit cells can be characterized by vectors in Euclidean six-dimensional space, with components derived from the Niggli matrices. All non-triclinic Bravais-lattice types are represented by vectors from one-, two-, three- and four-dimensional specific linear subspaces. Projection matrices onto these subspaces were derived. The distance between an experimentally determined and reduced cell and the projection onto each subspace can be easily calculated and used to select the correct Bravais lattice. Presented results are numerically exact.