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.
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.
This particular tessellation is full of angles measuring 20 degrees, 40 degrees, and other angles which are not constructable using the traditional rules of Euclidean constructions. This is because this tessellation is based on a matrix which includes regular enneagons.
This collection of curves was built around a tessellation of the plane using regular hexagons. To make the second version, I inverted the colors, except for the black circles and arcs.