Crystal structure lecture notes

[Shaverlag]

In the lecture notes is explained how you describe a translated latice point. In the figure used in the example the translation is (-0.5,0). However in the formula the latice is translated by (0.5,0). Is this just incorrect or am I missing something?

[Shaverlag]

Here is the figure used for this example

[anton-akhmerov]

Translation by (1/2, 0) and (-1/2, 0) are indistinguishable from the point of view of the crystal structure, so it isn’t quite right that the figure has a translation by (-1/2, 0).