I'm quite proud of this new design,
comprising a dozen laser-cut wood parts, 7.5 inches in diameter.
The shape of each part is reminiscent
of a dragonfly.
Here's a view down a three-fold
Here's a view along a four-fold axis.
This is a 3.5 inch nylon model, made on a selective laser sintering
It is assembled in 0.004-inch layers, which are clearly visible in the
(I made it the opposite chirality from the wooden version.)
The design for Dragonflies
from the third stellation of the rhombic dodecahedron (RD). The image
above shows the RD in the top left and its three (successively larger
and more complex) stellations. The RD consists of twelve rhombic
faces. The RD stellations are derived by extending the RD's face
planes symetrically until they meet and enclose a volume outside
the inner polyhedron. Much of each face plane is hidden inside the
outer shell; we only see certain facets of the faces in the stellations
above. These four forms have many interesting geometric properties,
e.g., the first two are space-fillers and they all have been used as
the basis of mechanical puzzle designs.
The wooden components of Dragonflies
are designed as a subset of the complete face of the third
stellation of the RD. The image above shows how that subset lies within
the complete face plane. The subset was designed so that it does not
intersect with the other eleven copies of itself. Interweaving and
assembling the rigid physical parts is an interesting challenge.
The convex hull of the third stellation of the RD is the truncated
octahedron, which is the Archimedean solid with two hexagons and one
square at each vertex, shown at left above. This is a
polyhedron, which means it packs together with copies of itself to fill
space, as indicated at right above. So copies of the Dragonflies
sculpture can be
assembled together to form three-dimensional networks.
I have a number of designs in mind for possible large-scale sculptures
based on these concepts.
The above consists of nine units, outlining a cube standing on a
corner, totalling of 108 dragonflies.
Here is a 3.5 inch nylon model of this design.
Here it is again, in blue.
And here is a similar assemblage of just six units, totalling 72
A very interesting fact is that these same twelve components can be
assembled in a second configuration.
The components here have been translated radially outward, but not
They each connect to others in the same places, but to different
This image shows both configurations together, arranged
concentrically. Observe that for each part
of the original inner configuration, there is another part exactly
parallel to it in the outer configuration.
This is very interesting geometrically and conceptually, but in one
color it can be hard to understand.
This is a rapid prototyping model of the
It is a bit obtuse from certain points of view, but from others it
quite interesting visually.
I especially like this 3-fold view.
Using two colors brings out its structure nicely so you can see the two
I dyed it all yellow then painted the outer parts orange. I call it Orange and Yellow
Copyright 2009, George W. Hart