The Small Stellated Dodecahedron – a classic three-dimensional (pentagram-faced) “star” – makes a wonderful fractal seed. It is a stellation of a dodecahedron where each pentagonal face is capped with a pentagonal pyramid composed of 5 golden triangles, a you could call it a 3-dimensional 5-pointed star. Some years ago when I was dabbling with POV-Ray, I made this primitive, rough study (with low resolution and lighting that didn’t quite do it justice) of a Small Stellated Dodecahedron fractal which is made by replicating smaller versions of itself and overlaying them on each of the 12 “arms” of the original, then doing this recursively as many times as your patience, resolution, etc. allows!
Here is a link (Math Monday: Fractal polyhedra clusters) to a rotating animation of a Small Stellated Dodecahedron fractal, which is one of the four Kepler-Poinsot Solids (all of which are featured with fold-up patterns (and more examples) in Sacred Geometry Design Sourcebook (SGDS):
