Origin and application of the Lorentz factor in X-ray diffraction

This review treats the role of the Lorentz factor in quantitative analysis of X-ray diffraction data. The origin of the Lorentz factor, its derivation and practical implementations for a variety of modern X-ray diffraction methods are discussed.

Symmetric vertex- and edge-transitive 3-periodic nets

We show that most crystal structures found in nature correspond to symmetric or supersymmetric nets, which are tolerable (tessellate). Remarkably, we find only one reported structure based on a symmetric net that is decussate (untileable).

Tiles from projections of the root and weight lattices of A_n

The 2D faces of the Voronoi cell of the lattice A₄* are of two types: regular hexagons and squares in 4D, but project into two types of hexagons and two types of rhombuses with edges of two lengths in proportion to the golden ratio.