Dan Johnson wrote:
> 
> <nitpick>
> Plato associated the solids with the elements, and used the existence of
> the dodecahedron to postulate the existence of a fifth element witch he
> called cosmos, of either.  There is some disagreement about what color
> the fifth element should be, the most common are white, and black.
> There is common agreement about the other four.

Ah.  Well, come on, there's gotta be an ether element.  How do you
explain lightning?  ;)  (BTW, I'm sure you noticed the colors of my
polyhedra have nothing to do with their associations.)

 
> Tetrahedron Fire Red
> Octahedron Air, or Wind Yellow
> Cube Earth Green
> Icosahedron Water Blue
> 
> I would also like to note that your image nested_platonics.gif is
> remarkably similar to my third post to this server on 1/7/2001 to the
> p.b.i group titled "Nested polyhedron".  I think mine looks better,
> especially because you missed one symmetry between the icosahedron, and
> the dodecahedron.
> </nitpick>

Yes, I know... I swear, it's a coincidence!  Come on, everyone knows
Stella Octangula is a compound of two tetrahedra that fits perfectly in
a cube.  And the golden cube in the dodecahedron, that's pretty obvious
too.  <g>  Please fill me in on what I missed.


> Very good, haven't checked the math but I assume it is correct.  I have
> been planning a vastly improved version of my polyhedra.inc file now
> that I have been writing pov code for more than a few months.  I know
> there are more polyhedra geeks on this server than you and me, maybe
> with some teamwork we could include all of our best work in one
> collection.

Maybe some of them are real good at javascript and VRML.  We'll make an
even better page than Bulatov.  Or, maybe not. :)


BTW, it's interesting to note the colors in the compounds.  Five colors,
5!/5 or 24 permutations of color arrangement at each face, or 12 for
chiralty.  12 faces of the dodecahedron!  That led me to think each
permutation appears once, but that can't be, since opposite faces are
mirror images.  On the cube compound though, 5*4/2=10 permutations, 20
vertices, opposite ones are the same...  or for the octahedra,
5*4*3/2/3=10 permutations...  more relationships exist and any of them
relate to al three of course, but why is it that that first one appears
to be a coincidence?  Hmm...


-- 
David Fontaine  <dav### [at] faricynet>  ICQ 55354965
My raytracing gallery:  http://davidf.faricy.net/

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