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.
I made this duoprism, a four-dimensional polytope, using Stella 4d. You can try this program for yourself, free, at http://www.software3d.com/Stella.php.
I created this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php. Starting with the Platonic dodecahedron, I dropped the symmetry of the model down from icosahedral to tetrahedral, then stellated it six times. I also put the resulting polyhedron into “rainbow color mode” before making this .gif image.
I saw a tessellation similar to this on Facebook, and used Geometer’s Sketchpad and MS-Paint to re-create it with colors of my own choosing.