The last post “A quasiperiodic tiling with pentagons” is close to the original reasoning of Penrose, see the article “Penrose tiling” in Wikipedia. He dissected the Pentagon into six smaller ones and filled the gaps with other tiles. He took care to leave no gaps and to have no overlapping tiles. His work is fantastic. Note that he has not used a computer !
Now, similarly as for the pentagrams, we find a simplified iteration for pentagons without gaps. We simply use the pentagons that surround the pentagrams. Then this scheme results in many overlapping pentagons.
First I have drawn first the larger pentagons in yellow and then the smaller ones in semitransparent blue on top. This leaves the black borders of the large pentagons still visible.