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.)

(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