A new method for lattice reduction using directional and hyperplanar shearing

A new algorithm for lattice reduction based on a series of directional and hyperplanar shears and driven by the decrease of the basis rhombicity is proposed. It can be used to reduce unit cells in dimension 3 and higher.

Effects of Voigt diffraction peak profiles on the pair distribution function

General expressions for peak broadening in reciprocal and direct space are derived based on the Voigt function.

Chiral spiral cyclic twins

Two-dimensional point patterns for cyclic twins of six-, eight-, ten- and 12-fold symmetry are generated based on a general parametrization in combination with specific integer sequences following from a common construction scheme.

On the frequency module of the hull of a primitive substitution tiling

As part of the study of aperiodic tilings and tiling spaces, the frequency module of the hull of a primitive substitution tiling is computed.

The intrinsic group–subgroup structures of the Diamond and Gyroid minimal surfaces in their conventional unit cells

The group–subgroup structure of the symmetry groups describing the Diamond and Gyroid minimal surfaces in their conventional unit cells is presented.

Numerical Problems in Crystallography

Uwe Grimm (1963–2021)

Obituary for Uwe Grimm.

Report of the Executive Committee for 2020