In “A tiling of 12-fold rotational symmetry from two hexagon grids” and following posts I have already discussed the projection method for the Stampfli tiling. It is quite similar to the projection method for the Ammann-Beenker tiling. But there is a special catch: You have to take care not to draw lines across two rhombs having a common side.
In the next post you will find the code you can put in the main tab of the previous programs. It includes the idea of “How to calculate the corner points …” to increase the relative size of the hexagons. The variable “magnification” in the program corresponds to the parameter L of the post. Using magnification=1 gives the Stampfli tiling with rhombs and using magnification=sqrt(3) gives the Socolar tiling. Note that the Socolar tiling has no rhombs and the sides of the tiles have the same length as the shortest distance between tiling points. Try out magnification=2+sqrt(3). This seems to give the Stampfli tiling again. You might want to change the program for the Ammann-Beenker tiling similarly.
In the following I will present the dualization method, which uses the same grids as the projection method. The results can be quite different.