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Pentanon Spheres.
I have called this series of geometric constructs "Pentanon Spheres". This nick-
name is somewhat loosely applied and a little misleading, because these are not spheres at all, but are dodecahedral in shape. They are, however, all made of some combination of pentagons (hence the "pent"); and are viewed with a nine-sided symmetry at the vertexes (hence the "non").
Note: The black or shaded areas represent openings (windows?) in the surface of
the structure |
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Intervals and Wings.
Each pentagon component is viewed as
being comprised of isosceles triangular sub-components which I call (again loosely) "intervals" and "wings". These are considered as the basic components of pentanon spheres.
These triangles have proportions of
.6180339:1.0; and are sometimes called "golden triangles" because of their association with the Golden Section. |
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Variable Pentagons.
Wings and intervals combine to form (what I
call) "variable pentagons"; and variable pentagons combine to form pentanon spheres. |
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Variable
Pentagon |
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These pentagons are called "variable" because
the wing triangles rotate along the diagonal axis of the pentagon.
You can also see why I call wings "wings".
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Variable Pentagon
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