p4 (pinwheel)

This pattern contains 4-fold and 2-fold rotation centers.
p4 pattern
The following tiling with congruent pentagons is constructed in the same way. It can generate Cairo tiling.
pentagon tiling with p4 symmetry
A slight modification will give a tiling with non-congruent pentagons, though having the same symmetries.
– GeoGebra Institute of Hong Kong

Information: p4 (pinwheel)