Hello,


> It struck me as the easiest and most uniform way to do it.  It could
> have been easier if I had used box{} for the cube, but then it would not
> have been constructed similar to the other polyhedra.

I think it's a good idea to try to obtain a uniform way to describe the
platonic solids. So I don't mean you should use "box" for the cube. But
the nice thing I learned from your include file is to avoid "polygon" by
using your macros. As I wrote, there can be difficulties if the 3D
polygon is not a planar one, and this can be a matter of rounding off.
The only polygon we're sure that it is a planar one is the triangle!


> 
> I did, however, find a link to already-provided polyhedral include files
> (on mac.povray.org) from your site.  I KNEW I was reinventing the
> wheel.  :/
> 
> Interesting that Mr. Towle seems (I have not been able to examine the
> include files yet; I still need something to unpack .SIT and .HQX files)
> to have provided the "pipes-and-balls" structures, too.  There is
> nothing new under the sun.

The .hqx files can be expanded using "stuffit". You can find this
program on the web.
I also examined some of the files from Mr. Towle. But being a
mathematician I want to construct the polyhedra (or obtain their data)
myself. I think Mr. Towle obtained his data using an other programme:
all his data are written in decimal form (not using square roots
etc...).

> 
> It also occurs to me that I should have used a unit cube.  I would not
> have found the bug in the icosa- and dodecahedra.  Heh.

One of the advantages starting from the cube and deriving the other four
platonic polyhedra form it is that one doesn't need to use spherical
geometry (or spherical trigonometry). I think most young people don't
study those things at school and the whole thing can be done starting
from the cube and using some analytical geometry. And... you see very
well the nice relations using the golden section that exist ex. in the
dodecahedron!
> 
> > Friendly greetings.
> 
> Back at you.  :)
> 
> Deaken

Greetings from Ghent!

Herman Serras

-- 
Herman Serras
Gent (Belgium)
http://cage.rug.ac.be/~hs/

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