| Snarl A Sculpture/Puzzle by George W. Hart http://www.georgehart.com Dept. Computer Science Stony Brook University G4G6 exchange item Atlanta, Georgia March 2004 |
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This puzzle consists
of twenty identical flat pieces, each with the shape shown on the
reverse of
this page. Photocopy that template (enlarged) on to twenty sheets of
card
stock, cut on the edges, and assemble the pieces to form the structure
above.
When properly configured, the parts can be taped together just at their
tips,
without any interior contact. With paper, it is relatively easy to form
the
configuration if you bend the parts to get the arms past each other
when
necessary. For a tougher challenge, cut twenty copies of the shape out
of rigid
plastic, plywood, or metal. Then the arms are often blocked on the
wrong side
of each other compared to where you would like them to be. However it
can be
assembled; below left is a wooden model with twenty laser-cut parts
glued
together.
Snarl. Assembled
wooden model, 12 inch
Selective
laser sintering, nylon, 1 inch
The small attached version of Snarl,
shown above right, is a solid freeform fabrication model of
the assembled form. (I find it suggestive of the dried seedpod of a sweetgum tree.) It is made from fine nylon
powder by
computer-controlled laser-melting of cross sections, i.e., selective
laser
sintering (SLS). At this one-inch scale, there are slight
irregularities,
because its thin struts are at the technology’s limit. An
.stl file
for reproducing this on any SLS machine is available at http://www.georgehart.com
Snarl Template.
Make twenty copies on stiff card stock, rigid plastic, plywood,
or
metal.
Mathematically, the form derives from the
uniform
compound of five regular octahedra, a well known polyhedral compound
shown
below left, which has pairs of concentric coplanar equilateral
triangles in
twenty icosahedrally arranged planes. The figure above lies within two equilateral
triangles as shown below right. It is a subset of the plane, carefully
designed
to not intersect the nineteen copies of itself
in the
other icosahedral planes, yet to meet other copies of itself along the
short
outside edges.
