Equilateral Pentagon That Tiles The Plane
With Two Non-consecutive Complementary to 360° Angles
A+C = 360° & C+2E = 360° & 2A+B = 360°
I obtained this pentagon from the type 9 of the general list of pentagons that tile the plane. If we want an equilateral pentagon, the result can be only a concave pentagon. The tiling is enchanting: