HexDome
Hexagonal Geodesic Domes  Dimpled Domes
Deviations from a Sphere
It appears that duallayer geodesic domes are not
"naturally" spherical.
In particular, if the truss material forms shapes which
are close to tetrahedra (which it seems that they should
for the sake of stability), then the thickeness of the
dome will inevitably come to vary over its surface.
Usually the regions where pentagons appear in the
surface of domes will have the shortest struts. In a
conventional (icosohedral) geodesic dome, this results in
these being the strongest (and heaviest) areas of the dome 
due to an increased density of structural material.
In a duallayer dome  by a miracle of geometry  the reduced
strut length is matched almost exactly by a reduced
thickness of the dome  resulting in strength and weight
being more evenly distributed over the dome's surface.
This variation in thickness means that it's not possible for
both the inner and outer layers of nodes in such domes to be
spherical  unless the trusses deviate significantly from
being tetrahedra.
Dimples
Because strut size decreases linearly (first degree
approximation) as the pentagons are approached  where as
the surface of the sphere at that point is flat (again, a
first degree approximation) that means that in high
frequency domes  if the inner surface forms a conventional
geodesic dome, the external surface must form a series of
"dimples".
Similarly, if the external surface of such a highfrequency
dome forms a sphere, the inner surface will form a series of
"pimples".
Consequences
These deviations from a convex shape may have some practical
consequences.
In particular if a dimple is present on the very top of a
dome, it may form a rainwater reservoir, or interfere with
the ventalation shaft that is naturally placed at the dome's
highest point.
Dimples or pimples?
Are dimples to be preferred over pimples  or the other
way around?
Or perhaps such domes should have both dimples and
pimples  with each surface being deformed inversely with
the density of material in each layer?
The point seems to be rather open to debate  and
could even be decided on aesthetic grounds.
Tim Tyler 
Contact 
http://hexdome.com/
