forthcoming articles

The 2D projection of all atomic positions in the β-Mn unit cells shows that they are situated on three circumferences containing 2D projections of 90 vertices of the {3, 3, 5} polytope on the same plane. The exhaustive description of the non-crystallographic symmetry of the β-Mn crystal has been achieved by using the 8D E₈ lattice in which both the 4D {3, 3, 5} polytope and cubic 6D B₆ lattice can be inserted.

A general approach to indexing of diffraction patterns originating from crystals of known structures is presented. Example algorithms are shown to be applicable to patterns of various types, e.g., Kikuchi patterns, Kossel patterns or Laue patterns.

Knotted and linked zeolite framework types, based on the sodalite cage (truncated octahedron), are described. Such structures exhibit non-crystallographic symmetry.

It is proved that any parallelo­hedron P as well as tiling by P, except the rhombic dodeca­hedron, can be embedded into the 3D pcu net. It is proved that for the rhombic dodeca­hedron, embedding into the 3D pcu net does not exist; however, embedding into the 4D pcu net does exist. For each parallelo­hedron the deterministic finite automaton is developed which models the growth of the crystalline structure with the same combinatorial type as the given parallelo­hedron.

High-resolution electron microscopy image contrast obtained from a rutile nanocrystal using direct electron detection is quantified and interpreted based on a model of mosaic crystals.