Sentence examples for two crystallographic representations of from inspiring English sources

Let and be two crystallographic representations of in and such that.

Let be two crystallographic representations of, and,, where is a maximal subgroup of.

Then for every there exist exactly two crystallographic representations of,, such that.

The normaliser of H in G is given by Corollary 5.1   Let and be two crystallographic representations of in and such that.

As a consequence, we have the following: Proposition 5.4   Let be two crystallographic representations of, and,, where is a maximal subgroup of.

Let and be two orthogonal crystallographic representations of.

These two approaches are shown to be related (Indelicato et al., 2012 ▶), hence the idea is that it is possible to study the transitions between icosahedral quasicrystals by considering two distinct crystallographic representations of in which share a common subgroup.

Recalling that two representations and of a group G are said to be equivalent if there are related via a similarity transformation, i.e. there exists an invertible matrix S such that then an immediate consequence of Proposition 4.1 is the following: Corollary 4.1   Let and be two orthogonal crystallographic representations of.

If we denote by and the two disjoint classes of crystallographic representations of in [ cf. equation (13)], we can build, in the same way as described before, the -graphs for and, for and.

In particular, we have We can then apply the same procedure to find the crystallographic representations of, and see that they split into two classes, each one of size 96.

After recalling, in §2, the definitions of point group and lattice group, we define, in §3, the crystallographic representations of the icosahedral group and the icosahedral lattices in six dimensions.