The assembly is an intricate group
puzzle that challenges everyone to intuit the
underlying structure of the form. For each
piece, there are two coplanar pieces in its plane and
three more pieces in a parallel opposite plane.
The parts are laser-cut from 6 mm thick plywood and
mitered to join very precisely. By looking
carefully, it is easy to distinguish between a part
that is positioned properly and one that is
incorrectly placed.
When completed, we cut the tails off the cable ties
and put the two orbs out on display. It takes
most people some time to see that they are not
identical, but are mirror images of each other.
Here is one orb, which we can arbitrarily call
"right-handed". Observe the direction of the
curves. (You can also observe how the mating
edges of the parts were beveled, so they fit together
precisely.)
The other orb, the "left-handed" one, has parts that
curve the other direction. The exact same part
shapes are used in each case, but they are flipped
over and beveled on the opposite side for one orb.
Here's a rendering of the design looking down from the
top to show its five-fold axis of rotational
symmetry. The sculpture derives from an
underlying design that is spherical, and so looks
round like this from many directions, but I compressed
it by a factor of 1/2 along one axis to flatten
it. There are sixty identical components in the
underlying spherical form, but they are compressed
various amounts in various directions, depending on
how they are angled relative to the axis of
compression.
It turns out that there are six shapes of pieces after
the compression, shown above. Ten of each are
required for one orb. They are all "affine
equivalent", which means they can be stretched in a
linear way to become congruent to the others.
There is also a complex combination of dihedral angles
between the planes after compression, so it took a lot
of care to bevel all the mating edges properly.
The sculpture is called
Sword Dancing because
the pieces are reminiscent of a kind of traditional
ceremonial sword shown on the Middlesex University
logo. Sword dancing is a fascinating activity in
which performers make geometric structures from
swords. If you are unfamiliar with sword
dancing, see
this
video I made, which explains some of the
underlying math. The sculpture was not designed
with the University's logo's swords in mind; we
realized the connection only after the sculpture was
assembled.