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This short article questions and investigates the possible range of values for the three angles of a unit cell in the triclinic system. Although no constraints are reported in manuals and tables for crystallography, the three angles are not really independent; the range of allowed values is...
Following a brief overview of current knowledge on lattices of subgroups of the space groups, it is shown that in the case of reducible space groups those lattices contain sublattices which are lattice isomorphic to the lattices of subgroups of layer and rod groups. Both sublattices involve the...
A new type of direct methods (DM) called Patterson-function DM are presented that directly explore the Patterson instead of the modulus function. Since they work with the experimental intensities, they are particularly well suited for handling powder diffraction data. These methods are based on...
The problem of coincidences of lattices in the space , with p + q = 2, is analyzed using Clifford algebra. We show that, as in , any coincidence isometry can be decomposed as a product of at most two reflections by vectors of the lattice. Bases and coincidence indices are constructed explicitly...
The charge-flipping algorithm in its band-flipping variant is capable of ab initio reconstructions of scattering densities with positive and negative values. It is shown that the method can be applied to reconstructions of difference electron densities of superstructures, i.e. densities obtained...
Medium- to high-resolution X-ray structures of DNA and RNA molecules were investigated to find geometric properties useful for automated model building in crystallographic electron-density maps. We describe a simple method, starting from a list of electron-density `blobs', for identifying...
Crystal-structure topologies, represented by periodic nets, are described by labelled quotient graphs (or voltage graphs). Because the edge space of a finite graph is the direct sum of its cycle and co-cycle spaces, a Euclidian representation of the derived periodic net is provided by mapping a...
A new real-space implementation of the molecular-replacement method is described. The method locates the search model in the target crystal by maximizing the matching between the search-model vectors and the Patterson self and cross vectors. In previous work, a new rotation function was...
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