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.
This is an expansion of the last post here. It may be possible to continue this tiling outward indefnitely, forming an aperioidic tiling — or it may not. I am simply uncertain about this