Reading Stereographs

On an old paper, I found an interesting representation of some symmetry operations: stereographs.


Online I found a set of symmetry operations and related stereographs (see: <http://newton.ex.ac.uk/research/qsystems/people/goss/symmetry/Stereographs.html>), yet it's not clear to me how the representation is related to the symmetry operations (or: how are the representations obtained?).


Some samples from the website linked above:


* **C4**


[![C4](https://i.stack.imgur.com/qoE11.gif)](https://i.stack.imgur.com/qoE11.gif)
* **C5h** 


[![C5h](https://i.stack.imgur.com/EanKn.gif)](https://i.stack.imgur.com/EanKn.gif)
* **D6**


[![D6](https://i.stack.imgur.com/fHYMM.gif)](https://i.stack.imgur.com/fHYMM.gif)


I would like to understand the geometrical (and symbolical) meaning of a stereograph, in order to relate non-mnemonically it to its symmetry operation




The solid elements are the symmetry operations. The plus and open circle symbols show the positions of atoms and their symmetry mates. The center of the circle is the z-axis. The edge of the circle are directions perpendicular to the z-axis. In the examples in the question, all axes are either along z or perpendicular to z. It gets more complex in cubic symmetry, which also has axes in other directions.


[![enter image description here](https://i.stack.imgur.com/glyQm.gif)](https://i.stack.imgur.com/glyQm.gif)


Here, the triangles are three-fold axis along the body diagonals. The symbols are further explained at <http://pd.chem.ucl.ac.uk/pdnn/symm2/pntgrp1.htm>.


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