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Doesn't it seem to you guys like this frame thing should have all equal
angles and widths and stuff? I couldn't get it to work using all equal
angles. The frame device turned out to be much trickier than I expected, and
I had to cheat to make it work. It looked so simple at first! Hmmmmm...
Regards,
-Dave Blandston
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Attachments:
Download 'BallFrame.jpg' (48 KB)
Preview of image 'BallFrame.jpg'
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Yes. In a perfect dodecahedron, all elements are exactly equal. For fun, I
did a trigonometric analysis of the dodecahedron when I was very interested in
domes. There are lots of nice, pretty relationships in there that you can find
with a little patience and a calculator.
For starters, imagine a regular pentagon using unit length edges. Now
calculate the length of the diagonal. From there, you should be able to get a
grasp on the corner of your dodecahedron, and you can do it with simple trig.
Here is a helpful clue. You may know that the icosahedron is the "inverse" of
the dodecahedron.
Play with the numbers and soon you will find the face angle, the distance to
center, and all the needed relationships to calculate anything about it. You
can work it all out with little more than Pythagoras' Theorem if you are
patient.
Cheers!
Chip Shults
My robotics, space and CGI web page - http://home.cfl.rr.com/aichip
Post a reply to this message
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You can get the exact angles from shapes2.inc, it has a dodecahedron defined in
it.
Though it doesn't really do it in the most graceful way. I spent a long time
looking at regular polyhedra during my degree, it's really interesting how they
relate to each other. But I won't bore you folks with the details :)
--
Tek
http://www.evilsuperbrain.com
"Dave Blandston" <gra### [at] earthlink net> wrote in message
news:3ea41c1c@news.povray.org...
> Doesn't it seem to you guys like this frame thing should have all equal
> angles and widths and stuff? I couldn't get it to work using all equal
> angles. The frame device turned out to be much trickier than I expected, and
> I had to cheat to make it work. It looked so simple at first! Hmmmmm...
>
> Regards,
> -Dave Blandston
>
>
>
Post a reply to this message
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Thanks for the replies - maybe I'll have another go at it soon.
--
-David
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