The tessellations of the faces of this rhombic triacontahedron first appeared in my last post here. For putting the whole thing together and creating this rotating .gif, I used a program called Stella 4d. If you want to, you can try Stella for free at this website.
The first of these used the center of a square as the center of rotation. This one, by contrast, uses an intersection as the center of rotation. In each case, 45 degrees is the angle used.
Stella 4d: Polyhedron Navigator is selling at 25% off to help cure the boredom of people in isolation because of COVID-19. This software is used to make almost all of the polyhedral images on this blog. Trying the program to see if you like it is free. The website to visit to try Stella is http://www.software3d.com/Stella.php.
Two of the heptagrams are centered in the middle, while the other fourteen are smaller, and form a ring around the two in the center.
The ten pentagrams meet at a common vertex in the center.
The patterns on the faces are from the last post here, immediately before this one. I used Stella 4d: Polyhedron Navigator to make this, and you can try this software for free at this website.
The fourteen heptagrams, also known as {7/3} star heptagons, meet at a common vertex in the center of the whole diagram. I did the math using Geometer’s Sketchpad, and then colored the result using MS-Paint.
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.
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