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A tiling with perfect 7-fold symmetry, in which regular 14-gons arise, along
with rhombs of three types, and varieties of hexagons, octagons, decagons, and
dodecagons, all irregular. Here again the tiling was made using the Generalized
Dual Method, and by forcing line intersections, the "higher" zonogons
proliferated.
A double torus knot is somehow involved.
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Attachments:
Download 'seventwoknot.jpg' (210 KB)
Preview of image 'seventwoknot.jpg'
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Dumb question: does that pattern ever repeat itself or is it always curved
round the center like that? i.e. does it go on forever, and if so does it
keep changing or repeating?
Anyway eneough of these objects, do it using pigments and warp { repeat
flip }!!!
--
Tek
http://evilsuperbrain.com
"Russell Towle" <rto### [at] inreach com> wrote in message
news:web.47e5e6a6463e56b68b4044ac0@news.povray.org...
>A tiling with perfect 7-fold symmetry, in which regular 14-gons arise,
>along
> with rhombs of three types, and varieties of hexagons, octagons, decagons,
> and
> dodecagons, all irregular. Here again the tiling was made using the
> Generalized
> Dual Method, and by forcing line intersections, the "higher" zonogons
> proliferated.
>
> A double torus knot is somehow involved.
>
Post a reply to this message
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"Tek" <tek### [at] evilsuperbraincom> wrote:
> Dumb question: does that pattern ever repeat itself or is it always curved
> round the center like that? i.e. does it go on forever, and if so does it
> keep changing or repeating?
>
> Anyway eneough of these objects, do it using pigments and warp { repeat
> flip }!!!
This tiling is finite but it could be infinite. It's not a dumb question.
It has to do with the Generalized Dual Method. An arrangement of lines leads to
a tiling. Here there were seven sets of lines, each set parallel to one of the
seven sides of a regular 7-gon. Each set had something like thirty lines. If
each of the seven sets had had an infinite number of lines, the tiling too
would have been infinite, and yet still it would have had a center of 7-fold
symmetry.
I guess I must be much in the minority, but I find these tilings fascinating.
They bear upon a subject I have studied since the 1960s. This particular tiling
is related to a space-filling of 7-dimensional cubes in 7-space. I find great
beauty in geometry and wish to illuminate this beauty using POV-Ray.
Post a reply to this message
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"Russell Towle" <rto### [at] inreachcom> schreef in bericht
news:web.47e6662f906def86e4edf5b0@news.povray.org...
>
> I guess I must be much in the minority, but I find these tilings
> fascinating.
> They bear upon a subject I have studied since the 1960s. This particular
> tiling
> is related to a space-filling of 7-dimensional cubes in 7-space. I find
> great
> beauty in geometry and wish to illuminate this beauty using POV-Ray.
>
Fascinating. Excellent work, Russell. And you certainly achieved that last.
Thomas
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