After that messy, irregular tessellation in the last post, I had to make something which looked better.
This is an adjustment and extension of the radial tessellation shown in the most recent post here. I am now confident that this pattern could be extended outward, without limit.
I believe this can be continued, outward, indefinitely. I also believe it is aperiodic. However, I do not have a proof for either of these conjectures.
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.
The yellow rhombi have angles of 40 and 140 degrees, while the blue rhombi have angles of 80 and 100 degrees, just like in the last post here. However, that post did not include the red rhombi, which have angles of 60 and 120 degrees.