
Pentagons
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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
Alternately, this can be seen as a tessellation of blue diconcave hexagons and yellow triconcave enneagons. Which do you see?
This polyhedron has 20 enneagons and 12+60=72 pentagons (of two types) as faces. I made it using Stella 4d, which is available at http://www.software3d.com/Stella.php.
Of the thirty faces of this polyhedron, only the yellow parallelograms are not pentagons. I used Stella 4d to make this; you may try it for free at http://www.software3d.com/Stella.php.