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.
If I've tried this once, I've tried it at least fifty-five times….
RobertLovesPi.net 
I was just playing around with something like this! I’m a little confused as to the difference between radial symmetry and rotational symmetry, but I was able to create a tesselation with five-fold rotational symmetry. The center tile is a decagon surrounded by ten pentagons. The next level outwards is five pentagrams alternating with five diamonds, with pentagons filling the space between. Then ten decagons. Seems like it could go on forever. Thanks for sharing your tesselations!
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Marvelous!
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I like the way it needs a thin rhombus to make it work, which you almost don’t notice.
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I suspect that you would need even more different polygons as you continuing moving out from the center.
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