InternationalReciprocal spaceTables for Crystallography Volume B Edited by U. Shmueli © International Union of Crystallography 2010 |
International Tables for Crystallography (2010). Vol. B, ch. 4.6, p. 613
## Section 4.6.3.3.2.5. Relationships between structure factors at symmetry-related points of the Fourier image |

#### 4.6.3.3.2.5. Relationships between structure factors at symmetry-related points of the Fourier image

Scaling the Penrose tiling by a factor by employing the matrix scales at the same time its reciprocal space by a factor : Since this operation increases the lengths of the diffraction vectors by the factor τ in parallel space and decreases them by the factor in perpendicular space, the following distribution of structure-factor magnitudes (for point atoms at rest) is obtained: The scaling operations , , the rotoscaling operations (Fig. 4.6.3.14) and the tenfold rotation , where connect all structure factors with diffraction vectors pointing to the nodes of an infinite series of pentagrams. The structure factors with positive signs are predominantly on the vertices of the pentagram while the ones with negative signs are arranged on circles around the vertices (Figs. 4.6.3.24 to 4.6.3.27).