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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. =)
>
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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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From: Herman Serras
Subject: Re: Platonic solids 140kbbu - the 4 regular non-convex solids
Date: 17 Mar 2002 03:15:25
Message: <3C945103.E0369F26@pandora.be>
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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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Herman Serras wrote:
>
> 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
>
When meshes have many triangles, they can appear curved.
The same effect appears to me in pictures of the great icosahedron.
Some
parts appear slightly curved, but I don't know if they would look that
way
with the actual object, so I'll need to print out cutouts from
http://www.geocities.com/SoHo/Exhibit/5901/ and build it.
I got interested in polyhedras when I borrowed the classic polyhedra
book from the
library (it's the one with the picture of yellow Platonic and
Kepler-Poinsot solids
on the cover jacket and dating back to anywhere from the 1950s to 1970).
That's when I got the idea of making a board game with polyhedra.
I hope to finally figure out a way to build solid polyhedra that would
be suitable
for such as game.
Brendan
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