HexDome
Hexagonal Geodesic Domes - Dimpled Domes
Deviations from a Sphere
It appears that dual-layer 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 dual-layer 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 high-frequency
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 rain-water 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 |
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