# Space Symmetry Groups: Wyckoff notation, diagram and positions

In the subject: "Introduction to Chemical Geology", I have given the spatial symmetry groups.

At present, I know the different symmetry operators: rotation axes, center of symmetry (or inversion), helical axes and sliding planes.

I also understand Bravais networks, point groups and planes.

For example, $$Pmm2$$. (Herman-Maugin Notation)

1) Primitive cell. It belongs to the orthorhombic system and derives from the point group $$2mm$$.

2) Ordinary plane of symmetry perpendicular to axis "a".

3) Another plane of ordinary symmetry perpendicular to axis "b".

4) Rotating axis of order parallel to axis "c".

This is the only thing I can deduce from the notation, but the problem is that they ask me for diagrams like this: I've been looking for resources on the Internet and I can't find any tutorial that explains how to give a spatial group ($$P4mm$$, $$I\overline{4}c2$$,...) to make diagrams like the previous one.

I hope you can give me advice and resources to face this kind of problems. Finally, I would also like to be told how to obtain Wyckoff's positions from a space group.