Ideal Object support structure
The
support structure is designed to look unlike the octohedron inside,
while blocking views of the beams as little as possible. It must
rigidly hold the mirrors at 10 feet so that beams are accurately
reflected to make the laser figure. It is self supporting to avoid guy
wires that would restrict movement around the octohedron. The picure
below shows the overall form of the structure.

The current design is made from 8 inch diameter steel tubing, bent to a
20 foot radius, and with welded-on flanges on the ends. These flanges
are bolted to welded steel boxes to join the various pieces of tubing.
The construction is much like traffic light and street light poles,
which are about the same diameter at the base and are attached to the
sidewalk with welded flanges and bolts.

Figure 2. Plan and elevation of structure with dimensions in inches.
At the four feet on the playa, flanges are bolted to a steel plate
which is nailed into the playa with inch diameter stakes down to an
appropriate depth. These bases are illuminated with red LEDs to prevent
people crashing into them at night.
Rigidity is important. Even though the stability requirements have been
minimized through optical design, a twist of about 0.1 degrees in the
member that holds the mirror box will throw the beam off the
termination at the top.
In 50mph winds, I calculate about 500 pounds of pressure total on one
of the semicircular arcs, which is about half its total weight. Most of
the weight and wind cross section are below 10 feet. With 8 inch
diameter tubing, each 45 degree section is about 160 pounds.
This all makes it sound like I know what I'm talking about, which is
not the case. I am not familiar with the engineering and fabrication
techniques involved, nor am I confident that this is the optimal way to
build the structure. An experienced person is needed, who can optimize
something that looks like what I show in the picture, or that has its
most important characteristics.
A possible construction scenario is as follows: 45 degree and smaller
pieces are transported to the site, having been fabricated in a shop,
and test assembled some place beforehand. A scaffold is built in the
center, which holds the central steel box the four arms are bolted to.
Portions of the scaffold hold the first 45 degree sections bolted to
this box to form a + sign. The sections are lifted by crane arms
attached to the scaffold. This central + can be jacked up at four
points to align it with the bottom 45 degree sections set into
position in lower scaffolds, and bolted to the +. The lower 45 degree
sections and their brace sections can be added afterwards, or built on
to the lower 45 degree sections on the ground and lifted up. Reverse to
take down.
If a crane was used, the semicircles might be attached to each other
differently. Two semicircles could be built on the ground. One is
tilted up with the crane and braced (possibly with temporary wires) so
that it is in its final position. The other is lifted into place, such
that at the crossing point it joins with the first. This seems simple,
but requres that the semicircles withstand tension from being lifted in
the center, whereas in operation they have more compression forces.
Alternatively, one semicircle could be built on the ground and lifted
into place with a crane, braced, and then two halves of the
opposite semicircle could be lifted into place after having been built
on the ground. It is important to minimize crane time, as these are
often shared between groups on the playa to minimize costs. Lifts are
convenient, but are also in short supply and expensive. A lift of some
kind would be useful for placement of the mirror boxes, while only a
ladder would be needed for manual adjustments.
I mention these scenarios to make it clear that the design and
construction scheme are one integrated concept that has to be worked
out in detail, and tested before hitting the playa. The more easily the
structure pops together on site, the more likely it can be successfully
completed at all.