This is a modification of the well-known tessellation of the plane with squares and regular octagons.
Is there anything more relaxing than constructing a tessellation?
The first of these used the center of a square as the center of rotation. This one, by contrast, uses an intersection as the center of rotation. In each case, 45 degrees is the angle used.
It’s hard to get regular pentagons, regular star pentagons, regular decagons, and related polygons to tessellate the plane while maintaining radial symmetry. This is my latest attempt.