Hello,
The 5 Platonic solids are the only possible CONVEX regular solids. If
one allows regular solids to be NON-CONVEX there exist (only) 4 more
types of regular solids. They are known as the Kepler-Poinsot solids.
On my website http://cage.rug.ac.be/~hs a page is devoted to those
solids. All images, some of them animated, were produced using POVRAY.
Although on the web one can find the coordinates of the vertices in a
numerical form and also the important data concerning the faces ex.
http://mac.povray.org/download/binaries/uniformia/uniform.html
I derived this data starting from the underlying dodecahedron or
icosahedron. The data expressed in an exact form better show the
appearance of the golden section in all of those solids.
The paper models of the solids are very nice!
Friendly greetings,
Herman

Brendan Ryan wrote:
> 
> Herman Serras wrote:
> >
> > Hello,
> >
> > If you want to read something about how the coodinates of the vertices
> > of a dodecahedron and icosahedron can be obtained starting from a cube:
> > take a look at some of my pages.
> > http://cage.rug.ac.be/~hs/
> > In this way one can see how the golden number/golden section occur in
> > those two solids.
> > A number of pictures are produced using POVRAY.
> 
> Interesting read and links.  My math teacher should like this.
> 
> > But P. Bourke has done a very interesting work in publishing the data
> > for people who aren't very interested in the mathematics behind those
> > polyhdra, and like their beauty!
> > I agree that I don't have such nice textures! I'd liked to learn more
> > about the possibilies of POVRAY!
> >
> 
> The tetrahedron has a color map where I used "hot" colors including
> 2*<1,1,0> for bright yellow in a marble pattern.
> The octahedron has a color map with a wrinkle pattern and blue colors
> that I picked out with the pick o color program.
> I put the pigment into my sky include file.  The cube or hexahedron has
> a pigment map that uses stone and concrete pigments,
> which I made for my museum, in a gradient y pattern.  The icosahedron
> has a marble color map that uses deeper blues I chose
> from the color picking program.  The dodecahedron has a granite pattern
> with a little white and a lot of gray25 as rgb .25.  It
> also has a low filter value of .15.
> I intended the polyhedra to represent the ancient greek elements.
> 
> tetrahedron     fire
> octahedron      air
> cube            earth
> icosahedron     water
> dodecahedron    ether
> 
> The texture on the plane was first developed for my Venus celestial box
> (sun and moon ones posted on December 31).
> Brendan

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

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