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This shows the relationship of second-phase
pentanon hubs of PS909. (Six of 20 shown
here.) The "X" marks indicate that a second
phase variable pentagon goes there.

Note that the spaces in the surface are filled
with a combination of wing and interval
triangles--called "fillers"--to maintain continuity
in the surface pattern. (Fillers are striped to
distinguish them here.)

PS909 was the last model in this series
that I actually built in completion. By
then, it was apparent that this system of
building space enclosures from wing and
interval triangles continues indefinitely--
in theory at least.

Neither was this system restricted to the
basic patterns shown here. I have
constructed other semispherical, 3-D
models based on different patterns
(octohedral, for example)--not shown
here.

The repetition of fundamental (golden
section) components to produce larger
structures has something of an organic
sense about it ...reminiscent of cellular
growth. Though the system presented
here is too constrained to represent any
true nature of cellular replication. It turns
out, however, that certain viral capsids
are similar (but not exact), in their
geometry, to some pentanon spheres.

You may also see a striking resemblance
between pentanon spheres and Penrose
Tiling--(a study by UK physicist, Roger
Penrose of fundamental patterning; first
published in Scientific American in 1976.)
It seems Penrose tiles and pentanon
spheres were developed around the
same time--independently.

Visit the hyperlinks below to take a look
at these (and other) related topics.

If for some reason you would like a copy of my
unpublished notes on "pentanon spheres", you
can order them by e-mail. (click here for my e-
mail address.) I may need to bill you $5.00 (per
copy) for printing and mailing costs.

Thanks for visiting gravityandspace.com and for
checking out the GeoSite folder. Aloha...van