Frameworks with forced symmetry II: orientation-preserving crystallographic groups

Frameworks with crystallographic symmetry.

Periodic frameworks with crystallographic symmetry are investigated from the perspective of a general deformation theory of periodic bar-and-joint structures in Euclidean spaces of arbitrary dimension. It is shown that natural parametrizations provide affine section descriptions for families of frameworks with a specified graph and symmetry. A simple geometrical setting for displacive phase tra...

Forced Orientation of Graphs

Computing with Crystallographic Groups

Algorithms are presented for the computation with crystallographic groups of arbitrary dimension, in particular for the determination of the Wyckoff positions and maximal subgroups of a space group, and for the determination of all space group types for a given point group. These algorithms have been implemented in the computer algebra system GAP, and are made publically available. The capabili...

Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups.

The Bilbao Crystallographic Server is a web site with crystallographic programs and databases freely available on-line (http://www.cryst.ehu.es). The server gives access to general information related to crystallographic symmetry groups (generators, general and special positions, maximal subgroups, Brillouin zones etc.). Apart from the simple tools for retrieving the stored data, there are prog...

The crystallographic fast Fourier transform. II. One-step symmetry reduction.

An algorithm for evaluation of the crystallographic FFT for 67 crystallographic space groups is presented. The symmetry is reduced in such a way that it is enough to calculate P1 FFT in the asymmetric unit only and then, in a computationally simpler step, recover the final result. The algorithm yields the maximal symmetry reduction for every space group considered. For the central step in the c...