I got coordinates for the Platonic solids from the web site mentioned in
p.g.:
http://astronomy.swin.edu.au/~pbourke/polyhedra/

The tetrahedron, octahedron and icosahedron could be converted directly.
The cube was easy to figure out with two triangles per face.  I used
three triangles per face for the dodecahedron.
After converting the coordinates, I souped things up with the ancient
Greek elements.

Brendan

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Attachments:
Download 'brpolyhedra.png' (141 KB)

Preview of image 'brpolyhedra.png'

Brendan Ryan wrote:
> 
> I got coordinates for the Platonic solids from the web site mentioned in
> p.g.:
> http://astronomy.swin.edu.au/~pbourke/polyhedra/

Hey, that's exactly where I got mine from.  :)

> The tetrahedron, octahedron and icosahedron could be converted directly.
> The cube was easy to figure out with two triangles per face.  I used
> three triangles per face for the dodecahedron.

That sounds familiar, yes.

> After converting the coordinates, I souped things up with the ancient
> Greek elements.

I basically used P and I, as in Paul Bourke's pages.  Wanna compare code? 
Drop me an email.

>  [Image]

I really like the texture on the cube and on the dodecahedron.

Deaken

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You know what I like about that shape second from the right? When you first
look at it, it seems like it has a top and bottom, and is taller than it is
wide. But if you rotate it around, you can see that any of the vertices can
be the top or bottom, and it is in fact symmetrical in more ways than it
first appeared.

I found this out a long time ago when I made one out of cardboard for the
heck of it. =)

- Slime
[ http://www.slimeland.com/ ]
[ http://www.slimeland.com/images/ ]

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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.
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!

Herman Serras

Brendan Ryan wrote:
> 
> I got coordinates for the Platonic solids from the web site mentioned in
> p.g.:
> http://astronomy.swin.edu.au/~pbourke/polyhedra/
> 
> The tetrahedron, octahedron and icosahedron could be converted directly.
> The cube was easy to figure out with two triangles per face.  I used
> three triangles per face for the dodecahedron.
> After converting the coordinates, I souped things up with the ancient
> Greek elements.
> 
> Brendan
> 
>   ------------------------------------------------------------------------
>  [Image]

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

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I made the Platonic solids out of paper from a cutout and noticed that
effect with the octahedron.
I plan on making more sturdy models sometimes; large, sturdy and
colorful.
Brendan

Slime wrote:
> 
> You know what I like about that shape second from the right? When you first
> look at it, it seems like it has a top and bottom, and is taller than it is
> wide. But if you rotate it around, you can see that any of the vertices can
> be the top or bottom, and it is in fact symmetrical in more ways than it
> first appeared.
> 
> I found this out a long time ago when I made one out of cardboard for the
> heck of it. =)
>

Post a reply to this message

Deaken wrote:
> 
> Brendan Ryan wrote:
> >
> > I got coordinates for the Platonic solids from the web site mentioned in
> > p.g.:
> > http://astronomy.swin.edu.au/~pbourke/polyhedra/
> 
> Hey, that's exactly where I got mine from.  :)
> 

Herman's web site should help with getting coordinates for other
polyhedra.

> I basically used P and I, as in Paul Bourke's pages.  Wanna compare code?
> Drop me an email.

Sent.

> 
> >  [Image]
> 
> I really like the texture on the cube and on the dodecahedron.
>

Thanks, I thought that they were simplistic.

Brendan

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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

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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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Brendan Ryan wrote:
> 
> Deaken wrote:
> >
> > Brendan Ryan wrote:
> > >
> > > I got coordinates for the Platonic solids from the web site mentioned in
> > > p.g.:
> > > http://astronomy.swin.edu.au/~pbourke/polyhedra/
> >
> > Hey, that's exactly where I got mine from.  :)
> 
> Herman's web site should help with getting coordinates for other
> polyhedra.

I probably have that bookmarked somewhere.  I was all over the place looking
for coordinates I could actually use.

> > I basically used P and I, as in Paul Bourke's pages.  Wanna compare code?
> > Drop me an email.
> 
> Sent.

Thanks.  I'll dig up my code later and compare it (and, of course, shoot you
a copy).  From what I've seen, though, yours looks a lot simpler than mine. 
I DO tend to overwork things.

> > I really like the texture on the cube and on the dodecahedron.
> >
> 
> Thanks, I thought that they were simplistic.

Not mutually exclusive.  :)

Deaken

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Deaken wrote:
> 
> Brendan Ryan wrote:
> >
> > Herman's web site should help with getting coordinates for other
> > polyhedra.
> 
> I probably have that bookmarked somewhere.  I was all over the place looking
> for coordinates I could actually use.

I just went back and looked.  I have it bookmarked three times.

Yes, bookmarks sure keep ME organized and help me find things on the web.

Deaken

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