Welcome to TowerMania 2009!  All tower, all of the time.

Keeping in mind the shape has specific engineering purposes, here are
some salient points:

-  Triangular towers are quite stiff laterally, more so than quad
sided towers.  Triangles are the stiffest structures.

-  Triangular towers are generally less resistant to torsional (i.e.
twisting) than quad sided towers.

- Almost all unguyed towers have a diminishing cross section with
height.  That is, they are narrower near the top.  Their bases have to
be of greater cross section to resist the bending moment due to wind
loading and/or horizontal saucer impact.  In the case of guyed towers,
the cross section can remain the same as it gets taller, as the guy
wires control the horizontal load.  The Groom tower appears to have
constant cross section, but without guy wires.  This is very odd.  It
suggests the need for a constant internal volume.

-  Some towers of relatively large cross section contain internal RF
radiators for comm purposes.  These are usually referred to as self-
radiating masts.  This is a possibility, but why was the tower built
with a constant cross section?

-  The lighter than air tether concept is intriguing.  This has been
the traditional means of docking lighter than air craft.  The large
internal volume of the tower could contain equipment or personnel
lifts.  Perhaps a connection with the newly constructed very large
hangar?

-  All that aside, have a look at this paper called, "External
Calibration of Millimeter-Wave Atmospheric Radar Systems Using Corner
Reflectors and Spheres".  It may be found at:
http://www.arm.gov/publications/proceedings/conf11/extended_abs/bergada_m.pdf

The paper describes shooting metal spheres up out of a tower via air
cannon  to calibrate a weather radar system used for determining wind
shear.  Note that Figure 1 in the paper shows a schematic with a
calibration corner reflector pointed at the radar system.

Now we turn back to Groom and Google Earth.  Where is the tower
located?  Adjacent to the DYCOMMS RCS facility.  Note that the
easterly vertex of the tower appears to be pointed directly at the BDD
(Big Damn Dish).  There is some angular distortion due to the
satellite image angle, but it looks close.  Finally, look at the
shadow cast by the easterly vertex of the tower on the ground.  There
is something about a third or quarter way up attached to the tower
edge.  Compare this to the Figure 1 schematic in the paper and
calibration corner reflector.

It is known that in the past Groom has used aluminum spheres dropped
from aircraft to calibrate their RCS facility.  They live on today as
boundary markers.  Perhaps the tower is a "sphere cannon" to fire
calibration spheres up through the BDD's target area.  This would be
much more accurate than dropping from aircraft.