Four Sierpinskis

George W. Hart

Four Sierpinski triangles interweave in three dimensions, each linked with, but not touching, the other three. The twelve outer vertices are positioned as the vertices of an Archimedean cuboctahedron and the black support frame is the projection of this cuboctahedron to the circumsphere. These are fifth-level Sierpinski triangles, i.e., there are five different sizes of triangular holes. The strut diameters were made to vary with the depth of recursion, giving a visual and tactile sense of this depth. This 3-inch diameter, hand-painted, 3D-printed maquette was intended as a model for a possible large outdoor sculpture.

It takes some time to understand its structure. This short video gives a good sense it, as seen from many directions.
(Ignore the little rendering artifacts if you see some small distortions.)

I 3D-printed it from nylon, so this is how it looked before I painted it with acrylic.
Here's the view looking at one of its six openings with 4-fold rotational symmetry.

Here's the view along a 2-fold axis.  Two of the triangles are seen edge-on.

Copyright 2016, George W. Hart